Hydroxide salts in the clouds of Venus: their effect on the sulfur cycle and cloud droplet pH

Paul B. Rimmer

0000-0002-7180-081X]Paul B. Rimmer
Department of Earth Sciences, University of Cambridge, Downing St, Cambridge CB2 3EQ, United Kingdom
Cavendish Laboratory, University of Cambridge, JJ Thomson Ave, Cambridge CB3 0HE, United Kingdom
MRC Laboratory of Molecular Biology, Francis Crick Ave, Cambridge CB2 0QH, United Kingdom

Sean Jordan
Institute of Astronoomy, University of Cambridge, Madingley Rd, Cambridge CB3 0HA, United Kingdom

Tereza Constantinou
Institute of Astronoomy, University of Cambridge, Madingley Rd, Cambridge CB3 0HA, United Kingdom

Peter Woitke
SUPA, School of Physics & Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK
Centre for Exoplanet Science, University of St Andrews, St Andrews, UK

0000-0002-8713-1446]Oliver Shorttle
Department of Earth Sciences, University of Cambridge, Downing St, Cambridge CB2 3EQ, United Kingdom
Institute of Astronomy, University of Cambridge, Madingley Rd, Cambridge CB3 0HA, United Kingdom

Alessia Paschodimas
Earth and Environmental Sciences, University of St Andrews, Irvine Building, North Street, St Andrews, KY16 9AL, United Kingdom
Centre for Exoplanet Science, University of St Andrews, St Andrews, UK

Richard Hobbs
Institute of Astronomy, University of Cambridge, Madingley Rd, Cambridge CB3 0HA, United Kingdom

The depletion of SO_2 and H_2O in and above the clouds of Venus (45 – 65 km) cannot be explained by known gas-phase chemistry and the observed composition of the atmosphere. We apply a full-atmosphere model of Venus to investigate three potential explanations for the SO_2 and H_2O depletion: (1) varying the below-cloud water vapor (H_2O), (2) varying the below-cloud sulfur dioxide (SO_2), and (3) the incorporation of chemical reactions inside the sulfuric acid cloud droplets. We find that increasing the below-cloud H_2O to explain the SO_2 depletion results in a cloud top that is 20 km too high, above-cloud O_2 three orders of magnitude greater than observational upper limits and no SO above 80 km. The SO_2 depletion can be explained by decreasing the below-cloud SO_2 to $20\,{\rm ppm}$. The depletion of SO_2 in the clouds can also be explained by the SO_2 dissolving into the clouds, if the droplets contain hydroxide salts. These salts buffer the cloud pH. The amount of salts sufficient to explain the SO_2 depletion entail a droplet pH of $\sim 1$ at 50 km. Since sulfuric acid is constantly condensing out into the cloud droplets, there must be a continuous and pervasive flux of salts of $\approx 10^{-13} \, {\rm mol \, cm^{-2} \, s^{-1}}$ driving the cloud droplet chemistry. An atmospheric probe can test both of these explanations by measuring the pH of the cloud droplets and the concentrations of gas-phase SO_2 below the clouds.

§ INTRODUCTION

Both sulfur dioxide (SO_2) and water vapor (H_2O) are known to be depleted in the cloud layer of Venus <cit.>, and to vary in abundance above the cloud top by an order of magnitude or more both spatially [Jessup et al., 2015, Encrenaz et al., 2019, Marcq et al., 2020], and temporally in years-long cycles [Marcq et al., 2013, Vandaele et al., 2017]. Both of these species participate in Venus's atmospheric sulfur cycle [Yung & Demore, 1982, Krasnopolsky, 1982, Krasnopolsky, 2007, Krasnopolsky, 2010, Krasnopolsky, 2012, Mills et al., 2007, Zhang et al., 2012, Bierson & Zhang, 2020]. Their photo-destruction in the upper cloud layer (60 – 70 km) leads to formation of sulfuric acid (H_2SO_4), that condenses out and forms the clouds in Venus's atmosphere [Yung & Demore, 1982]. The droplets rain out of the clouds at a height of $\lesssim 48$ km, where they evaporate [Yung & Demore, 1982, Krasnopolsky, 2007]. The H_2SO_4 then dissociates and replenishes SO_2 and H_2O in the lower atmosphere <cit.>. The behavior of all other known chemically reactive species in Venus's atmosphere is influenced by this cycle [Krasnopolsky, 2007, Krasnopolsky, 2010, Krasnopolsky, 2012], and many of these species participate in this cycle. The sulfur cycle in the atmosphere of Venus establishes a strong and persistent redox gradient through the atmosphere of Venus. Venus is more reduced above the clouds and more oxidized below the clouds.

Though this cycle is central to the atmospheric chemistry of Venus, it is not fully understood, and no self-consistent full atmospheric model of Venus yet accounts for this cycle.

There are several models of the lower atmosphere of Venus (0 – 40 km) that account for the efficient evaporation of H_2SO_4 and the effect of its dissociation products, SO_3 and H_2O, on the abundances of carbon monoxide (CO), carbonyl sulfide (OCS), and SO_2 [Krasnopolsky, 2007, Krasnopolsky, 2013]. Other models describe the middle atmosphere of Venus (60 – 120 km) <cit.>, investigating the chemistry above the clouds (60 – 80 km) where SO_2 is depleted and then re-appears between 85 and 105 km [Sandor et al., 2010, Belyaev et al., 2012]. Zhang et al., 2010 propose that night-side evaporation of H_2SO4 at 85 – 105 km, followed by rapid displacement to the day side by strong winds and subsequent photodissociation, can explain this behavior. The distribution of upper atmospheric aerosols at day and night side [Parkinson et al., 2015], could be applied as constraints for the proposed mechanism of Zhang et al., 2010. Pinto et al., 2021 suggest an alternative hypothesis, involving (SO)_2 chemistry. There has recently been a model of the upper clouds layer of Venus exploring the SO_2 depletion from $1\,\mathrm{ppm}$ to $\sim 10\,\mathrm{ppb}$, and the correlation with H_2O abundances in the clouds [Shao et al., 2020]. A diagram of the sulfur cycle and its connection to other trace atmospheric species in the atmosphere of Venus is shown in Figure <ref>.

At least three atmospheric models of Venus also exist, but they either do not predict the observed SO_2 depletion [Yung et al., 2009], do not couple the SO_2 depletion to the sulfur cycle [Greaves et al., 2020], or do not consider the H_2O and SO_2 depletion in concert. The best current full-atmospheric model that accounts for the SO_2 depletion, from Bierson & Zhang, 2020, reproduces the SO_2 reasonably well, though only by fixing the H_2O profile and by inhibiting the vertical transport within the clouds, as suggested by Marcq et al., 2018 and Bierson & Zhang, 2020.

To explain the depletion of sulfur dioxide and water in concert, either some unknown chemistry must take place within the cloud layer, or observations of lower atmospheric SO_2 and/or H_2O must be mistaken. We explore both of these possibilities in this paper.

In Section <ref> we show why the sulfur cycle cannot be explained without either decreasing the amount of sulfur in the lower atmosphere or increasing the amount of hydrogen in the clouds, either by increasing the water vapor in the clouds or by transporting the hydrogen into the clouds in a different form. We propose that hydrogen could be contained either in aerosols that are lifted by winds into the clouds from the surface, delivered exogenously, or contained within the clouds within some unknown chemical species. In Section <ref>, we discuss our full atmospheric model for Venus. We then show the results of our model if the observational constraints on SO_2 and H_2O in the lower atmosphere are wrong (Sections <ref> and <ref>) or if we introduce cloud chemistry (Section <ref>). In Section <ref> we also predict the effect of this source of hydrogen on the cloud chemistry, chiefly on how it would act as a pH buffer in the clouds. We discuss the implications of our results in Section <ref>, particularly about how rainout and replenishment of hydrogen is needed to sustain the SO_2 gradient. We also speculate about possible sources of hydrogen and their delivery into the clouds, and ways of reconciling the changing cloud chemistry with observations. Section <ref> contains our conclusions.

A scheme of the sulfur cycle on Venus. We include a hypothetical mechanism for cloud buffering by volcanic release of salts into the clouds, or levitation of dust particles with salts by winds into the cloud layer. For simplicity, this figure only shows the upward transport of species relevant for formation of the cloud and initiation of droplet chemistry, and not the settling, rainout and evaporation of cloud droplets, needed to complete the sulfur cycle.

§ THE PUZZLE OF SULFUR DEPLETION

There is good observational evidence that the concentration of SO_2, the dominant sulfur-bearing species in Venus's atmosphere, varies by several orders of magnitude between altitudes of 40 – 80 km (see Appendix <ref>. The concentration of SO_2 is above 100 ppm at 40 km and between 1 and 100 ppb at 80 km, and we call the decrease in SO_2 with height the “depletion” of SO_2. The standard explanation for this depletion predicts the major presumed constituent of the clouds of Venus: H2SO4. Near the top of the clouds:

\begin{align}
\ce{CO_2} + h\nu &\rightarrow \ce{CO} + \ce{O} \label{eqn:co2-pd}\\
\ce{SO_2} + h\nu &\rightarrow \ce{SO} + \ce{O} \label{eqn:so2-pd}\\
\ce{SO_2} + \ce{O} + \ce{M} &\rightarrow \ce{SO_3} + \ce{M} \label{eqn:so2-o}\\
\ce{SO_3} + 2\ce{H_2O} &\rightarrow \ce{H_2SO_4} + \ce{H_2O} \label{eqn:so3-h2o}
\end{align}

The H_2SO_4 condenses out to droplets that then drop down to $\sim 40$ km, where the droplets evaporate. These droplets are predicted to make up the cloud layer. This mechanism ends up reducing the upper atmosphere by replacing CO_2 with CO and SO_2 with SO. The excess oxygen is bound up in the sulfuric acid which has condensed out of the atmosphere.

An oxygen atom is needed to form SO_3, and this O must come from either CO_2 or SO_2 because they are by far the most abundant O-containing molecules. The formation of one molecule of H_2SO_4 is the destruction of one molecule of H_2O and at least one molecule of SO_2 (the sum of Reactions (<ref>) and (<ref>)), at most two molecules of SO_2 (the sum of Reactions (<ref>) and (<ref>)). Between one and two molecules of SO_2 is lost with every molecule of H_2O to make a molecule of H_2SO_4 this way, and so this mechanism predicts that the below-cloud H_2O and SO_2 concentrations be within a factor of two of each other. Therefore, the maximum depletion of SO_2 in the atmosphere by this mechanism is equal to $\big(\chi + 1\big)\ce{[H_2O]}$, where [H_2O] (cm$^{-3}$) is the atmospheric mixing ratio of H_2O and $\chi$ is the fraction of H2SO4-bound O that was produced by SO_2 dissociation.

The observational constraints, however, are $[\ce{SO_2}] \approx 150$ ppm and $[\ce{H_2O}] \approx 30$ ppm. Even if $\chi = 1$, and all water was converted to H_2SO_4, the SO_2 would only be depleted by $\sim 20\%$. This is insufficient to explain the several-orders-of-magnitude depletion of SO_2.

Therefore the SO_2 depletion is a puzzle for which there is no successful solution in the literature consistent with observations. This implies that either the observational constraints on H_2O and/or SO_2 in the lower atmosphere are wrong and their abundances below the clouds are within a factor of two of each other, or that some alternative chemistry explains the SO_2 depletion. We are not the first to notice the implications of this puzzle: a missing sulfur reservoir <cit.>.

One alternative mechanism to explain the SO_2 depletion is the formation of condensible sulfur allotropes out of SO_2 photodissociation or thermal dissociation products. The remaining sulfur cannot be in the form of SO, because the resulting concentrations of SO would be at least two orders of magnitude greater than indicated by above-cloud observations. This explanation requires photodissocation of both SO and SO_2 near the cloud top that is many orders of magnitude more efficient than predicted by any model, or similarly more efficient thermal dissociation of SO_2, and must explain 80% of the SO_2 depletion. 20% of the SO_2 will be converted into SO_3 and will react with H_2O to form H_2SO_4, condensing out. Another 20% will balance the reducing power of the SO_3 removal. The remaining 60% would have to go through the either or both of the total reactions:

\begin{align}
2\ce{SO_2} &\rightarrow \ce{S_2} + 2 \ce{O_2}, & {\rm Thermochemistry};\\
2\ce{SO_2} + 4h\nu &\rightarrow \ce{S_2} + 2 \ce{O_2} &  {\rm Photochemistry}.
\end{align}

This would either predict 150 ppm additional O_2 in the upper atmosphere of Venus, exacerbating the O_2 overabundance problem discussed in the Introduction, or would lead to oxidation of CO. However, oxidation of CO would cause it to become depleted, whereas we see that CO increases above the clouds. It is not possible that the excess oxygen would remain in the form of atomic oxygen, because atomic oxygen is not chemically stable at above-cloud altitudes. It is possible that the oxygen is stored in some other chemical species that has not yet been identified, but thus far there is no known candidate species at several ppm concentrations needed to contain the excess oxygen. For these reasons we do not consider this explanation further here.

§ THE MODEL

For this work we use a photochemistry-diffusion model based on the model of Rimmer & Helling, 2016. The model is composed of a solver and a network. The solver, Argo, solves the time-dependent set of coupled non-linear differential equations:

\begin{equation}
\dfrac{dn_{\ce{X}}}{dt} = P_X - L_Xn_{\ce{X}} - \dfrac{\partial \Phi_X}{\partial z},
\end{equation}

where $n_{\ce{X}}$ (cm$^{-3}$) is the number density of species $\ce{X}$ at height $z$ (cm) and time $t$ (s), $P_X$ (cm$^{-3}$ s$^{-1}$) is the rate of production of X at height $z$ and time $t$, $L_X$ (s$^{-1}$) is the rate constant for destruction of species X at height $z$ and time $t$. The term $\partial \Phi_X/\partial z$ (cm$^{-3}$ s$^{-1}$) describes the divergence of the vertical diffusion flux.

As described by Rimmer & Helling, 2016, the chemistry is solved by following the motion of a parcel up and down through a one-dimensional atmosphere described by a grid of set temperature, $T$ (K), pressure, $p$ (bar) and other properties. A parcel starts at the surface with a particular set of initial chemical conditions, and then moves through the atmosphere at a velocity determined by the Eddy diffusion coefficient:

\begin{equation}
t_{\rm chem} = \dfrac{\big(\Delta z\big)^2}{2 K_{zz}},
\end{equation}

where $\Delta z$ (km) is the change in height from one part of the grid to the next, and $K_{zz}$ (cm$^2$ s$^{-1}$) is the Eddy diffusion coefficient. The volume mixing ratios are recorded for each species at each grid height, constructing chemical profiles for the atmosphere. There is a method to account for molecular diffusion, described by Rimmer & Helling, 2016 and corrected by Rimmer & Helling, 2019. We do not solve above Venus's homopause, so molecular diffusion, though included, is not significant and we do not describe it in detail here. After the parcel makes a single complete trip, a UV radiative transfer model is run on the recorded profiles, completing a single global iteration and recording the actinic flux[The actinic flux is the total (direct and diffusive) spectral irradiance integrated over a unit sphere.] $F_{\lambda}$ (photons cm$^{-2}$ s$^{-1}$; photons will be excluded from the units hereafter).

This method reproduces results for modern Earth and Jupiter [Rimmer & Helling, 2016] and agrees with Eulerian solvers for chemical quenching heights in Hot Jupiter atmospheres [Tsai et al., 2017, Hobbs et al., 2019, Hobbs et al., 2020].

Some of the values of $L_X$ (and corresponding production coefficients) are the result of direct photodissociation and photoionization. These are all set to zero for the first global iteration, and then are calculated for global iteration $I$ using the chemical profiles of global iteration $I-1$. The photodissociation and photoionization rate constant for species X are:

\begin{equation}
k_{\lambda}(\ce{X}) = \dfrac{1}{2}\int F_{\lambda} \, \sigma_{\lambda}(\ce{X}) \; d\lambda
\end{equation}

where $\lambda$ (Å) is the wavelength, $z$ (km) is the atmospheric height, $\sigma_{\lambda}(\ce{X})$ (cm$^2$) are the photochemical cross-sections (see Appendix <ref>). The factor of 1/2 is typically included to account for rotation of the planet. Venus rotates too slowly to include this factor for the same reason, and would typically be treated as having a dayside and nightside chemistry. However, the zonal winds of Venus are very strong, horizontal mixing is fast, and for simplicity we consider the atmosphere to be a well-mixed average of day-side and night-side chemistries, which will be true for the long-lifetime and medium-lifetime species. The flux at height $z$ is given by:

\begin{equation}
F_{\lambda}(z) = F_{\lambda}(z_0) e^{-(\tau + \tau_a)/\mu_0} + F_{\rm diff}.
\label{eqn:actinic-flux}
\end{equation}

Here $F_{\lambda}(z_0)$ (cm$^{-2}$ s$^{-1}$ Å$^{-1}$) is the top-of-atmosphere (TOA) flux as described in Section <ref>, $F_{\rm diff}$ (cm$^{-2}$ s$^{-1}$ Å$^{-1}$) is the diffuse flux from scattering <cit.>, the cosine of the average zenith angle $\mu_0 = 0.54$ <cit.>, $\tau$ is the optical depth from molecular absorption calculated from the chemical profiles using the prior global solution as well as the photochemical cross-sections (see Appendix <ref> for details). In addition, $\tau_a$ is the additional optical depth due to Venus's mysterious UV absorber, described in Section <ref>.

Beyond these photodissociation and photoionization rate constants, the coefficients used to construct $P_X$ and $L_X$ are provided by the chemical network, Stand2020, which we introduce here. We start with the sulfur network of Hobbs et al., 2020 and add all relevant reactions involving species without thermochemical data from Greaves et al., 2020. The network includes 2901 reversible reactions and 537 irreversible reactions involving 480 species comprised of H/C/N/O/S/Cl and a handful of other elements, including condensation of H_2O, and a host of other species, most of which condense at temperatures far lower than achieved in Venus's atmosphere, see Appendix <ref>. The network, including added condensation chemistry for sulfuric acid and sulfur allotropes, is described in detail in Appendix <ref>.

In addition, we track the dissolution of SO_2 into the cloud droplets and subsequent liquid-phase chemistry for the cloud chemistry model described in Section <ref>.

The chemical profiles from the most recent global iteration, $I$ are compared to the profiles from the next most recent global iteration, $I-1$ in order to determine convergence. Convergence criteria are the same as for Greaves et al., 2020.

We give the parameters and initial conditions for our model in Section <ref>, including the temperature profile, Eddy diffusion, stellar irradiation, and surface boundary conditions for the chemistry. In Section <ref>, we discuss the consistency of these initial conditions compared to chemical equilibrium at the surface.

§.§ Parameters and Initial Conditions

The initial conditions and parameters we use are are similar to those used for Greaves et al., 2020. We use the same fixed temperature profile as Greaves et al., 2020, which was initially taken from Krasnopolsky, 2007 and Krasnopolsky, 2012. We use Eddy diffusion profiles from the same sources, though we also explore the effect of using the in-cloud Eddy diffusion coefficients of Bierson & Zhang, 2020 in Section <ref>. The profiles we use are shown in Figure <ref>.

We use a scaled top-of-atmosphere (TOA) solar spectrum from 1 – 10000 Å, compiled by Granville-Willett, 2017, for our TOA boundary condition. This data was compiled using Matthes et al., 2017 for the 401 – 1149 Å spectral region and Coddington et al., 2015 for the other wavelengths. The actinic flux is then multiplied by 1.913 to account for the difference in average distances of Earth and Venus from the Sun. The TOA spectrum is included in the Supplementary Materials.

We also include, in addition to molecular absorption and scattering as described above in Section <ref>, a parameterization of the mysterious UV absorber present within Venus's cloud layer. The parameterization originates with Krasnopolsky, 2012 and is the same as that used by Greaves et al., 2020, it takes the form:

\begin{align}
\dfrac{d\tau_a}{dz} &= 0.056 \; \mathrm{km}^{-1} \exp\Big\{-\dfrac{z-67 \, \mathrm{km}}{3 \, \mathrm{km}} - \dfrac{\lambda - 3600 \mathrm{\AA}}{1000 \mathrm{\AA}}\Big\}, & z > 67 \; \mathrm{km}; \notag\\
\dfrac{d\tau_a}{dz} &= 0.056 \; \mathrm{km}^{-1} \exp\Big\{- \dfrac{\lambda - 3600 \mathrm{\AA}}{1000 \mathrm{\AA}}\Big\}, & 58 \; \mathrm{km} < z \leq 67 \; \mathrm{km}; \label{eqn:mysterious-flux}\\
\dfrac{d\tau_a}{dz} &= 0.0 \; \mathrm{km}^{-1}, & z \leq 58 \; \mathrm{km}. \notag
\end{align}

Where $\tau_a$ is added to the optical depth in Eq. (<ref>).

The initial surface mixing ratios we set for Venus's atmosphere are given in Table <ref>, defining the bulk atmosphere. For all of the models presented outside of Section <ref>, we do not include PH_3. Now that we've defined our model and parameters, we will lay out the different scenarios that we consider for explaining the observed SO_2 depletion.

Initial Surface Abundances used for Model Atmospheres of Venus

CO_2     N_2
SO_2     H_2O
OCS     CO     HCl     H_2     H_2S     NO

0.96     0.03     150 ppm$^*$     30 ppm$^*$     5 ppm     20 ppm     500 ppb     3 ppb     10 ppb     5.5 ppb

$^*$The mixing ratios of SO_2 and H_2O are varied for some of the models.

Atmospheric temperature, $T$ (K, left), and $K_{zz}$ (cm$^{2}$ s$^{-1}$, right), as a function of height $h$ (km) <cit.>. The two values of $K_{zz}$ are for the cloud chemistry and the low-sulfur models (Sections <ref>, <ref>, <ref> and <ref>, solid)  and high-water models (Sections <ref> and <ref>, dashed and dotted), from Krasnopolsky, 2007, Krasnopolsky, 2012 and Bierson & Zhang, 2020 respectively.

§.§ Equilibrium Surface Composition

Here we discuss the consistency of the chemical boundary conditions (Table <ref>) compared to chemical equilibrium, and the implications these conditions may have on surface mineralogy. We find there are solutions where the gas-phase chemistry is consistent with our chosen boundary conditions and the condensed-phase chemistry is broadly consistent with observed surface mineral compositions. We will explore these conditions and their implications for hypothetical cloud chemistry in Section <ref>.

In June 1985, the Vega 2 lander determined the composition of the Venusian surface rock in the northern region of Aphrodite Terra <cit.>.  The rock was analysed by X-ray fluorescence employing instrumentation that had been improved based on the experience with the previous Venera 13 and 14 missions [Surkov et al., 1982, Surkov et al., 1984]. The measured oxide ratios are listed in Table <ref>. We have used these data, in combination with the observed gas composition at the surface in Table <ref>, to investigate the question in how far the gas at the bottom of the Venusian atmosphere is in chemical equilibrium and in phase equilibrium with the surface rock.

Oxide mass fractions [%] of the surface rock measured by the
Vega 2 lander [Surkov et al., 1986].

SiO2     TiO2     Al2O3     FeO     MnO     MgO
CaO     Na2O     K2O     SO3

$45.6 \pm 3.2$     $0.2 \pm 0.1$     $16 \pm 1.8$     $7.7 \pm 1.1$
$0.14 \pm 0.12$     $11.5 \pm 3.7$     $7.5 \pm 0.7$     $2.0$
$0.1\pm 0.08$     $4.7 \pm 1.5$

The following elements were not detected:
Cl, Cu and Pb $<$0.3% , Zn$<$0.2%, Pb, As, Se, Br, Sr, Y, Zr, Nb, Mo $<$0.1%.

These investigations were carried out by means of the chemical and phase equilibrium code GGchem [Woitke et al., 2018] taking into account the following 16 elements: H, C, N, O, F, S, Cl, Fe, Mn, Si, Mg, Ca, Al, Na, K, and Ti.  No information is available about phosphorous at the Venusian surface, so we have excluded that element from this investigation.  GGchem finds 442 gas phase species (atoms, ions, molecules and molecular ions) and 190 condensed species in its databases for this selection of elements. The thermochemical data for the molecules are based on the NIST-Janaf tables [Chase et al., 1982, Chase, 1986, Chase, 1998], as fitted by Stock, 2008, with some additions for diatomic molecules from Barklem & Collet, 2016.  Condensed phase data are taken from the SUPCRTBL database [Zimmer et al., 2016] and from the NIST-Janaf database. Some additional vapour pressure data are taken from Yaws, 1999, Weast, 1971, Ackerman & Marley, 2001, and Zahnle et al., 2016.

We consider a mixture of gas and condensed species at $T\!=\!735\,$K and $p\!=\!90\,$bars with total (gas $+$ condensed) element abundances $\epsilon^0$, see <cit.>. In order to find these element abundances we first convert the solid oxide mass ratios given in Table <ref> into element particle ratios. Second, we multiply by an arbitrary factor of 1000 and then add the observed gas phase element abundances from Table <ref>.  Third, we carefully adjust the total oxygen abundance $\epsilon^0_{\rm O}$ until the gas over the condensates has a SO2 concentration of 150 ppm in the model. The arbitrary factor in preparation step two causes the model to produce mostly condensed phases with only small amounts of gas above it. That factor has little influence on the results as long as it is large. The reason for this behaviour is that once GGchem has determined the solid composition in form of active condensates, which have supersaturation ratio $S\!=\!1$ (all other condensates have $S\!<\!1$), one can add arbitrary amounts of those condensates to $\epsilon^0_{\rm O}$, they will just fall out again without changing the resulting gas composition.

The results of this model are shown in Table <ref>. The resultant solid composition of the Venusian surface rock is a felsic mixture of enstatite (MgSiO3[s]) and quartz (SiO2[s]).  The condensates anorthite (CaAl2Si2O8[s]), albite (NaAlSi3O3[s]), and microcline (KAlSi3O8[s]) are the three main minerals forming feldspar which is found e.g. in basaltic rock on Earth. Iron is found to be entirely bound in magnetite (Fe2O3[s]). No carbonates and no phyllosilicates are found to be stable under the assumed conditions, nor any minerals containing chlorine. The only halide found to be stable is magnesium fluoride (MgF2[s]). Therefore, all carbon, nitrogen, hydrogen and chlorine assumed in the model is present in the gas, which allows us to directly fit the observed gas phase concentrations of CO2, N2, H2O and HCl.

Fitting the SO2 concentration is more difficult, because sulphur is mostly contained in anhydrite (CaSO4).  In the close vicinity of the equilibrium solution outlined in Table <ref>, we see that additional oxygen is used to form more anhydrite in the model on the expense of gaseous SO2 and anorthite (CaAl2Si2O8[s]) via

\begin{equation}
\ce{O} \,+\, \ce{SO2} \,+\, \ce{CaAl2Si2O8[s]} ~\longleftrightarrow~
\ce{CaSO4[s]} \,+\, \ce{Al2O3[s]} \,+\, 2 \ce{SiO2[s]} \ ,
\label{eq:regulation}
\end{equation}

which is a potentially important buffer mechanism to understand the SO2 concentration in the lower Venus atmosphere.  It allows us in the model to adjust the total oxygen abundance $\epsilon^0_{\rm O}$ to find the desired SO2 concentration (more oxygen means less SO2).

Table <ref> shows that it is possible to explain both the observed composition of the near-crust Venusian atmosphere and the solid composition of the surface rock by a simple consistent phase equilibrium model. All molecules that are predicted to be abundant in our model (those with percent or ppm concentrations) have observed counterparts.  The abundance hierarchy matches between model and observations.  Other common molecules like CH4 and NH3, which have extremely small abundances ($<\!10^{-15}$) in our model, are not observed. The Venus atmosphere can hence be classified as type B atmosphere according to Woitke et al., 2020, along with the atmospheres of Earth and Mars.  All predicted molecular concentrations are in reasonable agreement with the observed values, in particular when taking into account the large measurement uncertainties (see Table <ref>).  We note, however that this does not prove that the Venusian atmosphere is in chemical and phase equilibrium with the surface rock, it only shows that the data can be interpreted that way.

For the water-rich scenario, see Sect. <ref>, we can increase the hydrogen abundance to find a model with 200 ppm H2O, which has little effect on CO and OCS, but results in  slightly increased abundances of the ppb molecules,
149 ppm SO2,
12 ppm CO,
9 ppm OCS,
505 ppb HCl,
505 ppb HF,
110 ppb S2,
370 ppb H2S,
110 ppb S2O,
and 18 ppb H2, which is arguably still consistent with the observations.
For the sulphur-poor scenario, we can increase the oxygen abundance to find a model with 20 ppm SO2. In that case, the atmosphere is found to have a purer, more oxidising character with
30 ppm H2O,
2 ppm CO,
4 ppb OCS,
505 ppb HCl,
355 ppb HF,
and S2, H2S, S2O, H2 all $<$ 1ppb,
which seems inconsistent with the observations.

Results of the GGchem model for the bottom of the
Venusian atmosphere assuming the gas to be in chemical equilibrium
and in phase equilibrium with the surface rock at $T\!=\!735\,$K and

Gas phase composition

CO2     N2      SO2     H2O     CO      OCS
HCL     HF      S2      H2S     S2O     H2

96 %     3 %     150 ppm     30 ppm     20 ppm     5 ppm
500 ppb     500 ppb     -     10 ppb     -     3 ppb

97 %     3 %     150 ppm     30 ppm     12 ppm     9 ppm
505 ppb     355 ppb     114 ppb     57 ppb     17 ppb     3 ppb

All other molecules have concentrations $<$ 1 ppm in
the model.

Solid composition (results in mass fractions)

MgSiO3     SiO2     CaAl2Si2O8     NaAlSi3O8
CaSO4     Fe2O3
Al2O3     TiO2     KAlSi3O8     Mn3Al2Si3O12     MgF2

29.7 %     7.6 %      21.7 %      17.6 %     8.3 %     8.9 %
5.1 %     0.2 %     0.6 %     0.3 %     (trace)

MgSiO3 $=$ enstatite,
SiO2  $=$ quartz,
CaAl2Si2O8  $=$ anorthite,
NaAlSi3O8   $=$ albite,
CaSO4  $=$ anhydrite,

Fe2O3   $=$ magnetite,
Al2O3  $=$ corundum,
TiO2  $=$ rutile,
KAlSi3O8  $=$ microcline,
Mn3Al2Si3O12  $=$ spessartine,

MgF2  $=$ magnesium fluoride.
All other condensates are under-saturated in the model and have zero mass fractions.

§ HYPOTHESIS: THE OBSERVATIONAL CONSTRAINTS ARE WRONG

One possibility to consider is that the below-cloud observational constraints are incorrect. Possibly the below-cloud water vapor is much higher than observations suggest, a possibility considered by Yung & Demore, 1982. Or the below-cloud sulfur dioxide is much lower than most observations suggest.

In order to explore the sulfur-poor hypothesis we vary the below-cloud SO_2 abundance from 80 ppm down to 6 ppm with below-cloud H_2O kept at the nominal value (30 ppm). To explore the water-rich hypothesis we vary the below-cloud H_2O abundance from 30 ppm up to 200 ppm with SO2 kept at the nominal value (150 ppm). In this case we find that the observed above-cloud SO2 depletion is not achieved for any value of below-cloud H_2O due to H_2O self-shielding effects. Some support for the water-rich hypothesis is the $>100 \, {\rm ppm}$ abundances of water vapor observed in and directly below the clouds of Venus [Mukhin et al., 1982, Surkov et al., 1982, Bell et al., 1991], though these are inconsistent with $<100 \, {\rm ppm}$ abundances close to the surface [Bertaux et al., 1996].

To explore the possibility of the water-rich hypothesis further we test the effect of introducing a trap in the eddy diffusion profile within the cloud layer alongside varying the H_2O abundance below the clouds. Observational constraints on the eddy diffusivity as a function of altitude in the atmosphere are sparse. Marcq et al., 2018 have suggested that the existence of statically stable layers in the cloud region may inhibit dynamical exchange between the upper and lower regions of the atmosphere, a possibility explored by Bierson & Zhang, 2020. In the present work we test this possibility by modifying the nominal eddy diffusion profile taken from Krasnopolsky, 2007 and Krasnopolsky, 2012 to include a trap of constant lower $K_{zz}$ across the extent of the cloud layer. The range of values that we explore for $K_{zz}$ in the trap are 5000, 1000, 500 and $100 {\rm \, cm^2 \, s^{-1}}$, shown in figure <ref>. Such a $K_{zz}$ trap, if it exists in the Venus cloud layer, is particularly relevant to the water-rich hypothesis as enhanced water abundance below the clouds would result in lesser thermal heating flux at the cloud base due to H_2O IR absorption, which in turn increases the convective stability and decreases the eddy diffusivity, shown by Yamamoto, 2014. We investigate the results from combining a $K_{zz}$ trap and enhanced below-cloud water abundance.

§ HYPOTHESIS: ANOTHER SOURCE OF HYDROGEN IN THE CLOUDS

The SO_2 depletion can be explained if there is another source of hydrogen in the clouds. Here we will use NaOH as that source of hydrogen for the sake of convenience when calculating the cloud droplet chemistry. We are not claiming that this is the source of hydrogen. We will discuss possible sources of this excess hydrogen in Section <ref>.

Some SO_2 will dissolve into the cloud droplets directly, with a concentration in the droplet, $c {\rm \,(mol/L)}$, linearly proportional to the partial pressure of SO_2, with the Henry's Law constant, $H_{\ce{SO_2}} {\rm \big(mol/(L bar)\big)}$, as the constant of proportionality:

\begin{equation}
c(\ce{SO_2}) = H_{\ce{SO_2}} \; p f_{\ce{SO_2}}.
\label{eqn:henrys-law}
\end{equation}

Here $p f_{\ce{SO_2}}$ is the partial pressure of SO_2, with the total gas pressure $p$ (bar) and $f_{\ce{SO_2}}$ as the volume mixing ratio of SO_2, equal to $n_{\ce{SO_2}}/\big(\Sigma_{\ce{X}} n_{\ce{X}}\big)$.

For SO_2 dissolved in water, the Henry's Law constant is $\approx 10^{-2}$ mol/(L bar) [Burkholder et al., 2020]. For SO_2 dissolved in sulfuric acid, the constant increases with the sulfuric acid concentration between 0.1 and 1 mol/(L bar) [Zhang et al., 1998]. The SO_2 then participates in the following reactions (here g is gas-phase, $\ell$ is in the droplet). We first consider the dissolution of SO_2 and H_2O into the droplets by Henry's law.

\begin{align}
\ce{SO_2(g)} &\rightleftharpoons \ce{SO_2($\ell$)}, \label{eqn:liquid-first}\\
\ce{H_2O(g)} &\rightleftharpoons \ce{H_2O($\ell$)}. \label{eqn:liquid-second}
\end{align}

The rate constants for this reaction are balanced such that the concentration of SO_2 at any point agrees with Eq. (<ref>) when accounting for the droplet volume (see below). Also, in reality, the Henry's law constant for both water vapor and sulfur dioxide will vary with the composition of the droplet, and the composition of the droplet will vary as more water vapor and sulfur dioxide dissolves in the droplet. Our model does not account for these variations, and thus Henry's law as treated here is only an approximation. The rest of the reactions are dissociation reactions for which bimolecular rate constants are set to $k_f = 5 \times 10^{10}\,{\rm mol^{-1} \, L \, s^{-1}}$ in order to rapidly achieve equilibrium and avoid any dynamic effects, and the unimolecular rate constant is assigned a value that preserves equilibrium set by the $pK_a$ or $pK_b$. The rate constant for the reverse reaction is (with units s$^{-1}$):

\begin{align}
k_r &= \dfrac{\rho k_f}{\mu} \, 10^{-pK_a}, \\
k_r &= \dfrac{\rho k_f}{\mu} \, 10^{-pK_b},
\end{align}

where $\rho\,{\rm (g\,cm^{-3})}$ is the density of the liquid and $\mu\,({\rm g\, mol^{-1}})$ is the molar weight of the species. The reactions for the sulfates are:

\begin{align}
\ce{H_2SO_4($\ell$)} &\rightleftharpoons \ce{HSO_4^-($\ell$)} + \ce{H^+($\ell$)}, & pK_{a,1} = -2.8;\\
\ce{HSO_4^-($\ell$)} &\rightleftharpoons \ce{SO_4^{2-}($\ell$)} + \ce{H^+($\ell$)}, & pK_{a,2} = 1.99;
\end{align}

and the reactions involving sulfurous acid and sulfites:

\begin{align}
\ce{SO_2($\ell$)} + \ce{H_2O($\ell$)} &\rightleftharpoons \ce{HSO_3^-($\ell$)} + \ce{H^+($\ell$)}, & {\rm see \; below};\\
\ce{H_2SO_3($\ell$)} &\rightleftharpoons \ce{SO_2($\ell$)} + \ce{H_2O($\ell$)}, & {\rm see \; below};\\
\ce{H_2SO_3($\ell$)} &\rightleftharpoons \ce{HSO_3^-($\ell$)} + \ce{H^+($\ell$)}, & pK_{a,1} = 1.857;\\
\ce{HSO_3^-($\ell$)} &\rightleftharpoons \ce{SO_3^{2-}($\ell$)} + \ce{H^+($\ell$)}  & pK_{a,2} = 7.172.
\end{align}

The rate constant for SO_2 to react with H_2O is $2 \times 10^8 \, {\rm mol^{-1} \, L \, s^{-1}}$ [Eigen et al., 1961, Brandt & Van Eldik, 1995] and the rate constant for H_2SO_3 dissociation is $10^8$ s$^{-1}$ [Eigen et al., 1961, Brandt & Van Eldik, 1995]. These reactions are sufficiently fast to draw the gas-droplet chemistry into equilibrium at all atmospheric heights. It was for this reason that we chose NaOH as our candidate salt. Finally, we consider the self-dissociation of water and the dissociation of sodium hydroxide:

\begin{align}
\ce{H^+($\ell$)} + \ce{OH^-($\ell$)} &\rightleftharpoons \ce{H_2O($\ell$)}, & pK_a = 14\\
\ce{NaOH($\ell$)} &\rightleftharpoons \ce{Na^+($\ell$)} + \ce{OH^-($\ell$)}, & pK_b = 0.2 \label{eqn:liquid-last}
\end{align}

Sodium hydroxide is the example species we will use to buffer the clouds of Venus, freeing up more water in the droplet to react with SO_3, forming sulfuric acid, or with SO_2 to form sulfurous acid.

If the excess source of hydrogen is a salt, as is the case with NaOH, H^+ is replaced by Na^+. We calculate the pH where $\ce{pH} = - \log_{10}\big(a_{\mathrm{H^+}}\big)$, where $a_\mathrm{H^+}$ is the H^+ activity. The concentration of NaOH needed in the droplets to sequester SO_2 is determined by considering the cloud droplet volume as a function of height:

\begin{equation}
V_d(h) = \int \dfrac{4}{3}\pi r_d^3 \dfrac{\partial N_d}{\partial r_d} \, dr_d,
\label{eqn:droplet-volume}
\end{equation}

where $r_d$ ($\mu$m) is the droplet radius, and the function $r_d \big(\partial N_d/\partial r_d\big)$ is the droplet size distribution, which we take from Gao et al., 2014:

\begin{equation}
\dfrac{\partial N_d}{\partial r_d} = \dfrac{\partial n_d}{\partial r_d} V_{\rm atm}
\end{equation}

where $n_d$ (cm$^{-3}$) is the droplet number density (across all sizes) and $V_{\rm atm} = 4\pi R_p^2 \Delta z$, with $R_p = 6052$ km as the radius of Venus and $\Delta z$ (km) is the model height step.  We can calculate the amount of NaOH needed to deplete the SO2 to the observed levels. We do this by dividing the total number of SO_2 molecules by the total droplet volume at height $z$:

\begin{equation}
c(z) = \dfrac{p f_{\ce{SO_2}}(z)}{N_AkT(z)} \, \Bigg[\int \dfrac{4}{3}\pi r_d^2 \Bigg(r_d \dfrac{\partial n_d(z)}{\partial r_d}\Bigg)\, dr_d\Bigg]^{-1},
\end{equation}

where $N_A = 6.022 \times 10^{23}$ is Avogadro's Number and $k = 1.38065 \times 10^{-16}$ erg/K is Boltzmann's constant. The above equation is used to prescribe the initial concentration of NaOH (in units of mol/cm$^3$) for our solver. The NaOH will rapidly dissociate and the OH^- will then recombine with H^+ to form H_2O, and this, along with dissolved H_2O from the gas phase will react with SO_2 to form H_2SO_3. This will rapidly dissociate to form HSO_3^- and H^+, and will buffer the solution, meaning that if the H^+ activity is perturbed, the reactions between the anions and H^+ will bring the activity of H^+ back to a given value determined by the $pK_a$. It should be emphasized that Eq's (<ref>) and (<ref>) do not describe condensation of either of these species, who generally have partial pressures throughout Venus's atmosphere that are well below the vapor pressure. Rather, these are the equilibrium concentrations in the droplets due to dissolution, balanced with the partial pressures in the gas.

Prescribing the NaOH this way introduces extra hydrogen into the model in a way not accounted by mass balance or atmospheric redox balance. A full solution of the atmospheric chemistry coupled with surface chemistry would preserve this balance, but that would require us to identify the source of hydrogen. Though we speculate on possible sources of hydrogen, from the surface (delivered via volcanism or winds) or exogenous, in Section <ref>, we do not know enough about Venus's atmosphere, surface or clouds to confidently identify a source, and therefore do not self-consistently include this source in our model.

§ RESULTS

The depletion of SO_2 can be explained by the SO_2 dissolving into the clouds, if the cloud pH is higher than previously believed. It can also be explained by varying the below-cloud SO_2 and H_2O. We discuss the consequences of varying the SO_2 in Section <ref> and H_2O in Section <ref>. The results of incorporating cloud chemistry are presented in Section <ref>.

§.§ Sulfur-Poor Venus

SO_2 begins to significantly decrease through and above the clouds when surface $f_{\ce{SO_2}} \sim 50 {\rm \, ppm}$, and achieves best results for below-cloud concentrations of 15 ppm. See Figure <ref>. The depletion occurs at 70-80 km unless the surface SO_2 is lower, around 15 ppm. Besides being inconsistent with most below-cloud observational constraints on $f_{\ce{SO_2}}$ by almost an order of magnitude, the sulfur-poor model predictions agree with observations for all the species we consider reasonably well. The results agree with observations as closely as when we consider cloud droplet chemistry below with one possible exception of SO, which is below 1 ppb at between 80 and 100 km. This may be brought into better agreement by including a mesospheric source of sulfur acid vapor, or by adjusting the below-cloud concentrations of SO_2, since we have found that the above-cloud SO_2 is very sensitive to the below-cloud SO_2 and the Eddy diffusion profile when $f_{\ce{SO_2}} \approx $ 15 ppm. The 15 ppm below-cloud SO_2 model also predicts H_2 concentrations of $\sim 10 \, {\rm ppm}$ above 70 km.

Mixing ratios as a function of height for SO_2 (a), H_2O (b), O_2 (c) and CO (d) by varying the below-cloud abundance of SO_2 from 6 ppm to 80 ppm. No droplet chemistry is included.

§.§ Water-Rich Venus

For the water-rich case, SO_2 does not deplete for any value of below-cloud H_2O unless a $K_{zz}$ trap extending to 85 km in altitude is introduced in the eddy diffusion profile. Upon introduction of this trap the SO_2 begins to significantly deplete at the top of the atmosphere, and this depletion height then lowers with increasing below-cloud water abundance, achieving best results around surface $f_{\ce{H_2O}} = {\rm 200 \, ppm}$. See Figure <ref>. For in-cloud $K_{zz} = {\rm 5000 \, cm^2 \, s^{-1}}$ the depletion height is higher than observations suggest [Encrenaz et al., 2019], dropping off at $\gtrsim 75{\rm \, km}$, and the O_2 concentration in the upper atmosphere exceeds 100 ppm. The depletion height can be lowered further to $\sim {\rm \, 70 \, km}$ by decreasing the $K_{zz}$ value in the trap, however this exacerbates the overabundance of O_2 and causes CO to deviate from smooth monotonic growth with altitude. The CO profile has a downward spike at $\sim 70 {\rm \, km}$, consistent the profile of Pollack et al., 1993, as scaled by Marcq et al., 2005. This is likely due to the change of $K_{zz}$, see Section <ref>. Neither the SO_2 depletion or O_2 abundances agree with observations as well as in the sulfur-poor and cloud-chemistry cases. The reason for this is the self-shielding of the excess water, which is not as effectively removed as SO_2 within the clouds. The 200 ppm below-cloud H_2O model also predicts H_2 concentrations of $\sim 100 \, {\rm ppm}$ above 70 km, inconsistent with observations (see Appendix <ref>).

Mixing ratios as a function of height for SO_2 (a), H_2O (b), O_2 (c) and CO (d) by varying $K_{zz}$ (see Figure <ref>) with the abundance of below-cloud H_2O of 200 ppm. The divot in the water abundance for nominal K_zz is due to condensation. The CO profile when $K_{zz} = 1000 {\rm \, cm^{2} s^{-1}}$ bears a remarkable similarity to the CO profile from Marcq et al., 2005. No droplet chemistry is included.

§.§ Cloud Chemistry

In this scenario, described in Section <ref>, SO_2 depletion through the clouds is accomplished by removing the SO_2 into H_2SO_3 and H_2SO_4 via droplet chemistry. In our model, the droplet chemistry is driven specifically by sodium hydroxide (NaOH), and the NaOH itself buffers the cloud pH. The NaOH is a proxy used for convenience in modelling, and represents other plausible sources of delivered hydrogen, discussed in Section <ref>. We adjust the amount of NaOH as a function of height to reproduce the observationally constrained SO_2 profile (see Figure <ref>). This initial NaOH is prescribed for each height and is not solved for within the model. The function that reproduces the SO_2 depletion, given the estimated droplet volume, was determined by solving the aqueous chemistry and cloud chemistry for different amounts of NaOH, and the concentration of NaOH and the speciation of sulfuric and sulfurous acid as a function of height that results in the observed SO_2 profile is shown in Figure <ref>. The prediction that the bulk of the clouds is HSO_3^- only holds if there is no mechanism for oxidizing the sulfur in the clouds. Sulfite aerosols are rapidly oxidized in Earth's atmosphere [Townsend et al., 2012], and this may be the case for the atmosphere of Venus as well. We show the predicted mass loading in Figure <ref>. The mass of the lower cloud is largely in the form of sulfite, and this region overlaps with the larger mode 3 aerosols [Knollenberg & Hunten, 1980]. Profiles are similar for Ca(OH)_2, assuming the kinetics are identical between Ca(OH)_2 and NaOH. The similarity is due to the large $pK_a$ which results in all the Ca(OH)_2 becoming fully dissociated, along with the similar mass to basicity potential: the mass of a calcium atom is almost double that of a sodium atom, and each calcium carries two hydrides, which replace two protons.

We can then consider our solution of the droplet chemistry, set out in Equations (<ref>) – (<ref>), which predicts the H^+ activity, from which we can calculate the cloud droplet pH. As described in Section <ref>, the SO_2 depletion is set by the capacity of the liquid to hold SO_2, which is controlled by the amount of NaOH, and by the total volume of the liquid, which is determined by the cloud droplet size distribution. The predicted droplet pH is plotted as a function of height in Figure <ref>.

In this model, throughout the clouds the gas-phase SO_2 is in equilibrium with the concentration of sulfur in the droplet that is specifically in the form of SO_2; i.e., $\mathrm{SO_2(g)}\propto\mathrm{SO_2}(\ell)$ and adding or removing gas-phase SO_2 results in proportionally changing the droplet SO_2, and the balance of the other sulfur species. This equilibrium allows us to write out effective rate constants for SO_2 and H_2O dissolution into the droplets with rate constants tuned to reproduce the results from solving Eq's (<ref>) – (<ref>). For SO_2 the effective reaction is:

\begin{equation}
\ce{SO_2(g)} + \ce{H_2SO_4($\ell$)} \rightleftharpoons \ce{SO_2($\ell$)} + \ce{H_2SO_4($\ell$)}.
\end{equation}

The rate constants for the forward reaction, $k_f$ (cm$^3$ s$^{-1}$), and reverse reaction $k_r$ (cm$^3$ s$^{-1}$) are:

\begin{align}
k_f &= 10^{-32} \; \mathrm{cm^3 \, s^{-1}} \; e^{9000 \, {\rm K}/T}, \\
k_r &= 6.67 \times 10^{-36} \; \mathrm{cm^3 \, s^{-1}} \; e^{9000 \, {\rm K}/T}.
\end{align}

For H_2O the effective reaction is:

\begin{equation}
\ce{H_2O(g)} + 2\ce{SO_2($\ell$)} \rightleftharpoons \ce{H_2SO_3($\ell$)} + \ce{SO_2($\ell$)}.
\end{equation}

Neither of these reactions account for condensation. We determine the effective rate constants for the forward reaction, $k_f$ (cm$^3$ s$^{-1}$), and reverse reaction $k_r$ (cm$^3$ s$^{-1}$) to be:

\begin{align}
k_f &= 2.53 \times 10^{-36} \; \mathrm{cm^3 \, s^{-1}} \; e^{9000 \, {\rm K}/T}, \\
k_r &= 8.43 \times 10^{-38} \; \mathrm{cm^3 \, s^{-1}} \; e^{9000 \, {\rm K}/T}.
\end{align}

Finally, an effective reaction needs to be included to encapsulate the release of SO_2 when the droplet rains out and evaporates:

\begin{equation}
\ce{SO_2($\ell$)} + \ce{H_2SO_4(g)} \rightarrow \ce{SO_2(g)} + \ce{H_2SO_4(g)},
\end{equation}

with rate constant of $2.2 \times 10^{-4}$ cm$^3$ s$^{-1}$ $e^{-10000 \, {\rm K}/T}$.

The results of our model agree within an order of magnitude for all species considered, and within a factor of 3 for all species except for OCS and the sulfur allotropes. Our model underestimates S_4 and does not predict the steep below-cloud gradient of OCS. In addition, it over-predicts O_2 in the upper atmosphere by a factor of 2-3. Comparison of this model and the best sulfur-poor model, with $f(\ce{SO_2}) = 20$ ppm and Krasnopolsky's Eddy diffusion profile (from Section <ref>) is shown in Figure <ref>.

Predicted cloud droplet pH (bottom axis, solid black line) initial NaOH concentrations (mol/L, top axis, dashed green line), and the speciation of the sulfuric and sulfurous acid (red and blue lines), as a function of height (km) based on SO_2 depletion. The initial NaOH is an input that we use to reproduce the SO_2 depletion. This solution for SO_2 is not unique. Changing the pH by changing the initial NaOH will affect the SO_2 depletion. Alternatively, the pH could be higher than plotted, and the depletion could be limited by kinetics. The profiles with Ca(OH)_2 are similar.

Mass composition of the droplets (mass loading, mg m$^{-3}$) as a function of altitude (km). The total mass loading is based on Pioneer Venus observations summed over the three aerosol modes [Knollenberg & Hunten, 1980, Krasnopolsky, 2016]. The species mass loading is equal to the mass fraction multiplied by the total mass loading. The profiles with Ca(OH)_2 are similar.

Predicted volume mixing ratios of SO_2, H_2O, CO, OCS, O_2, HCl, H_2SO_4, H_2, SO, S_3, S_4 and H_2S as a function of height (km), and compared to data (see Appendix <ref>), for four models: the cloud-chemistry model (yellow dashed, Sections <ref> and <ref>), the sulfur-poor model with $f(\ce{SO_2}) = 20\,{\rm ppm}$ (red dash-dot, Section <ref>), the water-rich model with $f(\ce{H_2O}) = 200\,{\rm ppm}$ and in-cloud $K_{zz} = 5000\,{\rm cm^{2}\,s^{-1}}$ (blue dotted, Section <ref>), and the fiducial model with $f(\ce{SO_2}) = 150\,{\rm ppm}$, $f(\ce{H_2O}) = 30\,{\rm ppm}$ and no cloud chemistry (black solid). Observations and upper limits of these species (from Table <ref>) are also plotted in gray to compare. H_2SO_4 includes both condensed and gas-phase H_2SO_4.

§ DISCUSSION

Below-cloud SO_2 $<50\,\mathrm{ppm}$ is inconsistent with most observations but not all. Vega 1 and 2 observed $\ge100\,\mathrm{ppm}$ concentrations of SO_2 directly below the clouds, though the error bars are large and $50\,\mathrm{ppm}$ abundances would be within $2\sigma$ of the measurements [Bertaux et al., 1996]. Even lower SO_2 was measured within 20 km of the surface [Bertaux et al., 1996], which could indicate rapid surface depletion of SO_2 [Yung & Demore, 1982].

The reported observations of below-cloud SO2 at 100–$200\,\mathrm{ppm}$ also have large uncertainties, typically on the order of 50 ppm <cit.>, so true values below 50 ppm would amount to discrepancies of 2 – 3 $\sigma$. Exploring the hypothesis of low below-cloud SO_2 as an explanation for the above-cloud SO_2 depletion will require both more precise and more frequent observations of the below-cloud SO_2, to see whether it varies and by how much.  Such data may only be obtainable with in situ measurements.

Below-cloud H_2O is better constrained, so it is less likely that there is an undetected large source of water vapor beneath the clouds. There are some variations in the measurements, from less than 10 ppm to 60 ppm, but with relatively small error bars. There is some observational support for a large reservoir of water within the clouds, with 700 – 2000 ppm concentrations observed in the cloud layers by Vega 1,2 [Surkov et al., 1987] and Venera 13,14 [Mukhin et al., 1982, Surkov et al., 1982], and 100 – 200 ppm concentrations observed from the ground [Bell et al., 1991]. These high quantities may have been due to incidental sampling of cloud droplets which are expected to be composed of $\sim 15-25 \%$ water, even without considering the cloud pH buffer hypothesis proposed here. Even if these constraints were not so tight, the model where we increase the below-cloud water vapor predicts that the clouds to extend up to $\sim 80$ km, and the depletion would be more gradual and higher in the atmosphere. Further to this, the water-rich model overproduces O_2 above $\sim 70$ km pushing it beyond the observed upper limit by two orders of magnitude, overproduces H_2, and does not allow for SO_2 to return at the $\sim 1 {\rm \, ppb}$ level at 90 km, problems which are not shared by the other best fitting models.

In addition to enhancing the cloud layers, we had to vary the above-cloud $K_{zz}$ in order to induce sulfur and water vapor depletion. Decreasing the $K_{zz}$ to $\sim 1000 \, {\rm cm^{2} s^{-1}}$ creates a negative spike in the CO at $\sim 70 \, {\rm km}$, reproducing a feature seen in suggested mesospheric profiles [Marcq et al., 2005]. This is a consequence of varying the $K_{zz}$ and not increasing the below-cloud water vapor. Our model suggests that this CO negative spike may trace changes in the eddy diffusion, a hypothesis that is worth further investigation but is outside the scope of this paper.

Both the sulfur-poor and water-rich models predict $> 10 \, {\rm ppm}$ H_2 concentrations in the mesosphere, above 70 km, where the cloud chemistry model predicts $\sim 0.1 \, {\rm ppm}$ H_2 concentrations. Better observational constraints of H_2 may be useful for distinguishing these models.

As we have shown, cloud chemistry is a possible explanation for the depletion of SO_2. Aerosols could provide the excess hydrogen capable of depleting gas-phase SO_2. This hydrogen could be bound in salts, or could be in some other form, such as hydrocarbons. It is important that whatever the source of hydrogen, it is replenished to sustain the SO_2 gradient. Otherwise the hydrogen will be consumed, the clouds will be saturated with sulfur, and the gradient of SO_2 will disappear. It is also worth mentioning that three phases can participate in this chemistry: the gas phase, the liquid of the droplet (at atmospheric heights where the droplet has not frozen), and the solid aerosol material, either at the core, surrounding the droplet, or suspended within the droplet. This provides a rich and complex multi-phase chemistry worth exploring in the lab.

What follows in this section is a discussion of the requirements for and implications of cloud chemistry. In Section <ref>, we discuss possible sources of hydrogen within the clouds. The measured optical constants and spectral features of the clouds of Venus are consistent with cloud droplets composed of a large percentage of sulfuric acid. Any proposed cloud chemistry must either preserve sulfuric acid as the dominant species in the clouds, or must propose a species with similar optical properties and spectral features. We discuss the observable implications of our cloud chemistry in Section <ref>. The dissolution of hydrogen halides into the clouds is discussed in Section <ref>. The cloud chemistry also has implications for above-cloud radical concentrations, which affects the lifetime of hypothetical PH_3 within the clouds. We discuss the status of PH_3 and its lifetime within the clouds in Section <ref>. Finally, in Section <ref>, we briefly discuss the implications of different cloud chemistry for hypothetical life within the cloud droplets of Venus.

§.§ Possible Sources of Hydrogen in the Clouds

If a buffer explains the sulfur depletion, it is possibly a salt. Salts will dissociate quickly, and some will provide efficient buffers. The salts must get into the clouds in order to buffer them. This can be accomplished either by transport from the surface or exogenous delivery.

Exogenous Delivery: Exogenous delivery, meaning delivery of material from the interplanetary medium, is unlikely to provide significant material to buffer the clouds of Venus based on the estimated incoming flux of interplanetary dust. The clouds must be able to retain virtually all of the SO_2 over the timescale of transport through the clouds, requiring a flux of salts, $\Phi_s$ (mol cm$^{-2}$ s$^{-1}$), of:

\begin{equation}
\Phi_s = \dfrac{n_{\ce{SO_2}} \, H_0}{\tau_{\rm dyn}} = \dfrac{f_{\ce{SO_2}} \, nkT \, K_{zz}}{\mu_{\rm av} m_p \, N_A \, g \, (\Delta h)^2},
\end{equation}

where $n_{\ce{SO_2}} \, ({\rm cm^{-3}})$ is the number density of SO_2 at the height where SO_2 begins to deplete (50 km), $H_0 \, {\rm (km)}$ is the scale height, $R = 6052 \, {\rm km}$ is the radius of Venus, $\tau_{\rm dyn} \, {\rm (s)}$ is the dynamic timescale of the atmosphere at 40 km, $f_{\ce{SO_2}} = 150$ ppm is the volume mixing ratio of SO_2, $n = \Sigma_{\ce{X}} n_{\ce{X}} = 2.189 \times 10^{19}$ cm$^{-3}$ is the gas density at 50 km, the height where the depletion begins, $k = 1.38065 \times 10^{-16}$ erg/K is Boltzmann's constant, $T = 349.7$ K is the temperature at 40 km, $K_{zz} \approx 100$ cm$^2$ s$^{-1}$ is the Eddy diffusion of the droplets within the cloud, a low estimate more favorable for exogenous delivery. $\mu_{\rm av} = 44$ is the mean molecular weight of the atmosphere, $m_p = 1.6726 \times 10^{-24}$ g is the mass of a proton, $N_A = 6.022 \times 10^{23}$ is Avogadro's Number, $g = 8.87$ m s$^{-2}$ is the surface gravity of Venus and $\Delta h = 20$ km is the thickness of the cloud layer. Applying all these estimates yields:

\begin{equation}
\Phi_s \approx 10^{-13} \; \mathrm{mol \, cm^{-2} \, s^{-1}}.
\end{equation}

Continuous exogenous delivery of material is insufficient to match this flux even assuming that 100% of the material is in the form of hydrated minerals that will deplete SO_2. If we assume that delivery of exogenous material to Venus is comparable to delivery to Earth, 20 – 70 ktonnes/year [Peucker-Ehrenbrink, 1996, Greaves et al., 2020], which translates to $\sim 10^{-17}$ mol cm$^{-2}$ s$^{-1}$, or four orders of magnitude too little to account for the missing hydrogen.

One other possibility is stochastic delivery. If a recent airburst, a large impact that breaks up in the atmosphere, occurred in Venus's atmosphere, the metals released could permeate the clouds, providing a transient in-cloud source of hydrogen. If this is the case, then the depletion of SO_2 will be temporary, lasting as long as the below-cloud store of these elements persists, on the order of the diffusion timescale or $\sim 1000$ years.

Dust from the Surface: Transport from the surface also struggles to meet the required flux of hydrated material. Although calculations of dust transport favor a more dusty atmosphere for Venus than Earth [Sagan, 1975], Venera measurements suggest that the lower atmosphere is clear, placing upper limits on dust transport to the clouds. It is possible that there is heterogeneous low atmospheric weather, with dust rapidly transported to tens of km above the surface, and that Venera happened to land in a region where the vertical diffusion and winds were insufficient to change the atmospheric opacity. A low level haze inferred from Venera probe data [Grieger et al., 2004], and consistent with heavy metal frost at higher elevations on Venus's surface [Schaefer & Fegley, 2004], may itself be the suspended dust [Titov et al., 2018], and winds may cause that dust to periodically move into the clouds. The reaction products of the salt with SO_2 in and below the clouds could result in transient high abundances of water, which may then be removed by the left-over oxides. This could reconcile the transient observations of $>100\,{\rm ppm}$ of water vapor in and below the clouds [Mukhin et al., 1982, Surkov et al., 1982, Bell et al., 1991], with the $\sim 25\,{\rm ppm}$ abundances near the surface [Bertaux et al., 1996].

To explain the sulfur depletion, with dust containing 5 wt.% salt, requires a dust flux to the clouds of $\approx 16$ Gt/year, well within the estimates of surface dust fluxes estimated from analogue experiments [Greeley et al., 1984]. The composition of the dust and the form of the salts is unknown. Here we will speculate on some possible candidates. Our speculation is based on chemical and physical stability of the salts:

* NaOH: Sodium hydroxide is the example salt we use for our calculations, but is an unrealistic candidate salt. It is sufficiently stable to heat, persisting as a liquid up to 1661 K [Haynes, 2014]. However, it is known to react rapidly with SO_2 to form sodium sulfite and water vapor. Given the concentrations of below-cloud SO_2, NaOH cannot plausibly survive to reach the clouds unless it is injected rapidly, e.g. via a volcanic plume.

* Ca(OH)_2: Calcium hydroxide is stable as a solid at the surface of Venus. Strictly speaking, calcium hydroxide has no melting point. Instead, at 93 bar and $\sim 1000$ K it is expected to decompose into CaO and H_2O, based on extrapolations of the vapor pressure curve of Halstead & Moore, 1957. Ca(OH)_2 will undergo carbonation, and there is ample CO_2, but this reaction is very slow, and Ca(OH)_2 is kinetically stable at temperatures above 723 K [Materic & Smedley, 2011]. Ca(OH)_2 will also react rapidly with SO_2, but only in the presence of water vapor at concentrations of $>3000$ ppm [Liu et al., 2010]. The kinetic stability vs. the dynamic timescale for Ca(OH)_2 aerosols is unknown, but presently Ca(OH)_2 cannot be ruled out as a candidate.

* Mg(OH)_2 and Fe(OH)_2: Neither magnesium hydroxide nor iron hydroxide (either the Fe(II) hydroxide or Fe(III) hydroxides) are stable at Venus's surface temperature and pressure [Wang et al., 1998, Haynes, 2014].

* Other Hydroxides: It may be that more exotic hydroxides, such as Al(OH)_3, could deliver hydrogen to Venus's cloud layer. The requirements are sufficient concentrations to satisfy the required fluxes, and the thermochemical and kinetic stability of the salt in the presence of major atmospheric constituents.

* Oxides: Oxides, either resident surface oxides or oxides produced by the dehydration of hydroxides, may participate in cloud chemistry in unknown ways, sequestering SO_3 directly, for example, {Mg,Fe}O + SO_3 may be converted into {Mg,Fe}SO_4 directly. The subsequent dissociation in sulfuric acid will buffer the cloud droplet pH. There is some indirect evidence of the presence of oxides from the near-surface haze, since these oxides can react with hydrochloric acid vapor to form FeCl_3, which has been observed in the clouds and is a candidate for the mysterious UV absorber [Krasnopolsky, 2017].

* Sulfates: It is possible hydrogen-bearing sulfates could find their way into the clouds, but no known hydrogen-bearing sulfate is thermally stable at Venus's surface pressure and temperature. It is possible that they are produced from gas-phase reactions, e.g., the possible production of ammonium sulfate from reaction with NH_3 and SO_2 [Titov, 1983]. Sulfates that do not contain hydrogen are plausible aerosols. Indeed, we predict they are produced via cloud chemistry. But these aerosols will not deliver hydrogen and cannot directly participate in the depletion of gas-phase SO_2.

The above list is not intended to be exhaustive, and does not consider whether these salts are expected at the temperatures and pressures at the surface of Venus, where we would generally expect chemistry to tend toward thermodynamic equilibrium. The results of comparing our surface boundary conditions (Section <ref>) to chemical equilibrium (Section <ref>) predicts that no phyllosilicates or hydrated minerals are present at the surface of Venus if the surface and gas are in equilibrium.

GGchem model for the bottom of the Venus atmosphere, assuming chemical and phase equilibrium, as a function of surface temperature. The temperature of the current Venus surface (735 K) is marked as dotted vertical lines. A constant gas pressure of $90$ bar and constant total element abundances $\epsilon^0$ are assumed. $n_{\rm mol}/n_{\rm tot}$ are the molecular concentrations in the gas, and $n_{\rm solid}/n_{\langle\rm H\rangle}$ are the densities of solid species per hydrogen nuclei density. Only solid species which change substantially with temperature are shown. Other stable solids are MgSiO3[s], SiO2[s], CaAl2Si2O8[s], NaAlSi3O8[s], KAlSi3O8[s], CaSO4[s], Fe2O3[s], TiO2[s] and Mn3Al2Si3O12[s], which have about constant concentrations as listed in Table <ref>.

The model presented in Sect. <ref> can be used to explore the sensitivity of the mineral composition to surface temperature. Figure <ref> shows the results of our GGchem model  at the same constant pressure and total element abundances when varying the surface temperature between 450 K and 850 K.  Venus is just about 15 K too warm to have pyrite (FeS2[s]) as a stable condensate on the surface according to this model. For surface temperatures lower than about 720 K, the formation of FeS2[s] would start to remove the SO2 from the atmosphere according to the following complex net reaction

\begin{equation}
\frac{15}{11}\,\ce{SO2}
\,+\, \frac{1}{11}\,\ce{Fe2O3[s]}
\,+\, \ce{CaAl2Si2O8[s]}
\frac{2}{11}\,\ce{FeS2[s]}
\,+\, \ce{CaSO4[s]}
\,+\, \ce{Al2O3[s]}
\,+\, 2\,\ce{SiO2[s]} \ ,
\end{equation}

which is a variant of Eq. (<ref>) where the oxygen
on the left side is provided by Fe2O3[s]. At temperatures below about 580 K in this model, the first carbonate magnesite (MgCO3[s]) becomes stable, which could initiate a dramatic change of the atmosphere as the main atmospheric molecule CO2 could deposit at the surface to form MgCO3[s]:

\begin{equation}
\ce{CO2} \,+\, \ce{MgSiO3[s]} ~\longrightarrow~
\ce{MgCO3[s]} \,+\, \ce{SiO2[s]} \ ,
\end{equation}

leaving an atmosphere that is dominated by N2 with more H2O. Finally, below a temperature of about 520 K, the first phyllosilicate, talc (Mg3Si4O12H2[s]) becomes stable, which could partly remove the water from the atmosphere. Only for temperatures below 520 K our model predicts the presence of hydrogen-containing minerals.

Whether or not this means that the gas at the bottom of the Venusian atmosphere is in fact in chemical equilibrium, and whether the element abundances in the gas are regulated by outgassing/deposition via the contact with the hot rock at the surface are yet unsolved questions. Disequilibrium processes might supply phyllosilicates or hydrated salts. For example, geological processes such as volcanism may resurface Venus's crust with hydrated components (see also discussion below). Our phase-equilibrium model suggests that hydrogenated rock and salts are not stable on the surface of  Venus and will sublimate or react with the atmospheric gases to form other chemicals.  However, the salts may be stable enough to be swept up to greater altitudes and cooler temperatures, before they react away and equilibrium is restored.

More research in the lab and in situ observations of the clouds of Venus will be needed to determine if salts are present and, if so, what their chemistry is.

Volcanic Delivery: A variant of the dust delivery mechanism to achieve a hydrogen flux to the clouds is volcanism.  The presence of active volcanism on Venus has long been speculated upon, motivated both by the transient SO2 detected at 40 mbar by Pioneer Venus <cit.> and the recognition that SO2 may react with surface minerals and require continual replenishment [Fegley & Prinn, 1989].

Volcanism could deliver material to Venus's clouds in three ways: 1) as solid material deposited at the surface, which is subsequently lofted by winds; 2) as an explosive eruption introducing material into the below-cloud atmosphere, where vertical mixing slowly raises it into the cloud layer; and 3) as a large explosive eruption injecting material directly into the cloud layer.

Scenario (1) is effectively the `dust from the surface' mechanism described above.  Albeit, by explicitly considering volcanism a source of juvenile OH-bearing material is introduced, which could help overcome the short surface lifetime of some OH-bearing phases. The second and third possibilities take advantage of the dynamics of volcanism to shorten the distance, and thereby potentially increase the flux, of mineral sources of OH to the clouds by reducing the time the material spends at high temperature near Venus's surface.  Volcanism may also help loft material above the sluggish surface winds to an altitude where winds more readily carry dust higher <cit.>.

Modelling work by Glaze, 1999 and Airey et al., 2015 suggests that it is possible for volcanic eruption columns on Venus to reach the cloud base, however it requires particular circumstances that may or may not be frequently met: in particular, a high elevation vent and a magma containing several wt% water.  Whether such water-rich magmas exist on Venus is unknown; taking Earth as an analogue, magmas with $> 3\,\mathrm{wt}\%$ water occur only where subduction is introducing surface water back into the mantle, a tectonic mode that cannot have prevailed on Venus for hundreds of millions of years, if ever.  Voluminous water-rich explosive volcanism is also problematic given the tight constraints on the below-cloud the H2O mixing ratio of $<60\,\mathrm{ppm}$.  At best therefore, these constraints would imply a highly stochastic delivery of volcanic material directly into the clouds.

The best case for a volcanic contribution to mineral buffering of Venus's cloud chemistry is therefore by enhancing background dust levels in the below-cloud atmosphere.  Fegley & Prinn, 1989 estimate that a volcanic flux of $\sim1\,\mathrm{km^3\,yr^{-1}}$ is required to sustain atmospheric SO_2 at the levels observed.  This translates to a mass flux of $\sim{3\times10^{12}\,\mathrm{kg\,yr^{-1}}}$ of magma, or $\sim6\times10^{11}\,\mathrm{mol\,yr^{-1}}$ of hydrated phases assuming terrestrial-levels of water in Venus's magmas.  As an upper bound, this volcanic flux could provide a potential $4\times10^{-15}\,\mathrm{mol\,cm^{-2}\,s^{-1}}$ of hydrated phases to Venus's clouds if the entire mass was mobilised as dust in the atmosphere.  Being below the $\sim{10^{-13}\,\mathrm{mol\,cm^{-2}\,s^{-1}}}$ of salt delivery estimated above, rates of volcanism either need to be (at least) an order of magnitude larger than assumed here, or the magmas correspondingly more volatile rich, for volcanism to be contributing to chemical buffering of Venus's clouds by water delivery.  We note that although seeming unlikely, given all the current uncertainties on the composition and dynamics of Venus's interior, this possibility cannot be entirely ruled out.

§.§ Reconciling the Cloud Chemistry with Cloud Observations

There is considerable evidence that the clouds of Venus are mostly sulfuric acid or something very like sulfuric acid. The classic paper by Young, 1973 identifies most of the lines of evidence. The refractive index of the clouds obtained from infrared polarimetry, constrained to within 1.425 and 1.455 at the time, is best explained by droplets of $\sim 75\%$ sulfuric acid. In addition, the bottom of the cloud layer matches the condensation temperature of sulfuric acid, and specific spectral features between 8 – 13 $\mu$m are very similar to spectra of condensed sulfuric acid. Sulfuric acid is also expected at concentrations of $\sim 75\%$ based on models of H_2SO_4 and H_2O condensation [Krasnopolsky, 2015]. Subsequent studies have further refined the estimated concentrations of sulfuric acid in the clouds. Barstow et al., 2012 perform a retrieval on VIRTIS data of the atmosphere from Venus Express, and find that the 2.2:1.74 $\mu$m radiance ratio is sensitive only to the imaginary index of refraction, and therefore the sulfuric acid concentrations, and that most of the retrieved sulfuric acid concentrations in the lower clouds are between 85 – 96 wt%, or between  16 – 18 mol/L. Arney et al., 2014 used the same 2.2:1.74 $\mu$m radiance ratio and found that the sulfuric acid concentrations vary by time and latitude between 73 – 87 wt% in the upper clouds, or between 14 – 16 mol/L sulfuric acid concentration, lower than Barstow et al., 2012, suggesting that the concentration of sulfuric acid changes as a function of height. Titov et al., 2018 provide a comprehensive review of the research into Venus's clouds. None of the UV absorption due to our predicted profiles of gas-phase species, for the cloud model or any other model, explains the mysterious UV absorber, at $\lambda > 200$ nm. However, we do not consider the absorption properties of the aerosol particles themselves. It would be useful to determine the UV optical constants of these aerosols, or of sulfuric acid droplets themselves, to see whether a feasible candidate for the mysterious UV absorber is already in our midst.

Recent retrievals rely on infrared bands that constrain the index of refraction. If our proposed cloud chemistry is accurate and if all droplets have the same chemistry, hydrated sulfites and sulfates compose a large fraction of Venus's clouds. Sulfate achieves an index of refraction of $>1.44$ at $<20$ wt% H_2O [Cotterell et al., 2017], sufficient to explain the observed index of refraction. In addition, the S-H and S-O bonds are all similar, and so similar spectral features are expected. We predict a significant fraction of the clouds is made up of sulfites, in line with terrestrial SO_2 + H_2O chemistry [Terraglio & Manganelli, 1967]. The refractive index of sulfites is not as well known, though it has been measured for cyclic sulfites to be $\sim 1.5$ [Pritchard & Lauterbur, 1961], which is consistent with Venus cloud observations, particularly those that favor values higher than can be achieved by pure sulfuric acid [Markiewicz et al., 2018, Petrova, 2018], but may be achievable by sulfites and sulfates.

One other possibility is that the droplets of Venus do not all have the same chemistry. The salt content of the aerosols could be heterogeneous, either because they derive from different surface, volcanic or delivered materials, or because some cloud nuclei are produced photochemically, as sulfur allotropes and sulfuric acid. The observed bimodal distribution of cloud droplet sizes [Wilquet et al., 2009, Wilquet et al., 2012], is consistent with this hypothesis. It may be that the smaller more numerous cloud droplets lack salts, while less numerous droplets have salts. The salts will afford those droplets a far greater capacity for SO_2, and this may explain their larger size. If this is the case, we would predict the small mode droplets have a pH $< 0$ and the large mode droplets a pH $> 1$.

§.§ The Effect of Cloud Chemistry on Gas-Phase Halogens

Hydrogen halides have been observed on Venus, namely HCl and HF (see Appendix <ref>). Attempts have been made to observe HBr, but thus far only upper limits have been established [Krasnopolsky & Belyaev , 2016]. These hydrogen halides are likely to dissolve into the droplets, especially if the pH is higher than previously thought, and this may affect both the droplet chemistry and the atmospheric profiles of these halides. We investigate this possibility, considering only HCl, the sole hydrogen halide included in our model.

First, we have to determine the Henry's law constant for HCl dissolved into water/sulfuric acid mixtures. Williams & Golden, 1993 find that the effective Henry's Law of HCl in a solution of 50 wt% H2SO4 is:

\begin{equation}
H^* \approx 10^5 \, {\rm M/bar},
\end{equation}

at room temperature (which we will use as a proxy for the cloud layer). We use the relation (where $H^*$ (mol/(L bar)) is the effective Henry's law constant and $K_a$ is the acid dissociation constant):

\begin{equation}
H^* = H \Big(1 + \dfrac{K_a}{a_{H^+}}\Big),
\end{equation}

to solve for the hydrogen activity, $a_{H^+}$. The concentration of 50 wt% H2SO4 is approximately 2 mol/L, which will completely dissociate, and result in a pH of roughly -0.5, or an $a_{H^+} \approx 2$. For HCl, the $K_a \approx 2 \times 10^6$. This means that $H \approx 0.1$ for HCl in sulfuric acid.

We can now predict the depletion of HCl for the sulfuric acid case, where pH $\sim -3$. The equation for the capacity, $\kappa$, of the cloud droplets for a particular species, assuming that the dissociation products are not removed and so a simple equilibrium is achieved, is:

\begin{align}
\kappa &= \dfrac{H^* p(\ce{HCl}) N_A}{n(\ce{HCl})} \, \int 4 \pi r_d^2 \, \Bigg(r_d \dfrac{dn_d}{dr_d}\Bigg) \, dr_d\\
&= H \Bigg(1 + \dfrac{K_a}{a_{H^+}}\Bigg) \, kTN_A \, \int \dfrac{4}{3} \pi r_d^2 \, \Bigg(r_d \dfrac{dn_d}{dr_d}\Bigg) \, dr_d. \label{eqn:capacity}
\end{align}

Though it is true that, if there is any Na^+ or other cation, it will form a salt with Cl^-, this will act in solution as though entirely dissociated, and so effectively the amount of Cl- and H^+ due to HCl remains unchanged. If $\kappa < 1$, then the capacity of the droplets is not great enough to appreciably affect the composition of the gas-phase species. In the pure sulfuric acid case, $c \approx 1.6 \times 10^{-5}$, and so very little HCl will be in the droplets, compared to the amount in the gas-phase.

At higher pH, the situation changes, but still, at pH $\sim 1$, $\kappa \approx 0.16$, and so there should not be significant depletion. The value of $\kappa$ in Equation (<ref>) can be set to one, and $a_{H^+}$ solved for to predict the pH at which HCl should be significantly depleted, pH $\approx 1.8$. Though the profiles of gas-phase hydrogen halides should not not be affected at lower pH's, the concentrations of halogens in the droplets could be significant, and it would be informative to measure these concentrations in situ.

§.§ The Presence and Lifetime of Phosphine

A broad time-variable feature has been observed at 267 GHz by both ALMA and JCMT [Greaves et al., 2020, Greaves et al., 2020]. The existence and source of the feature has been disputed [Snellen et al., 2020, Thompson, 2020], though see the reply by Greaves et al., 2020. This feature has been attributed to phosphine [Greaves et al., 2020, Greaves et al., 2020], consistent with possible in situ detection of phosphine discovered during re-analysis of Venus Pioneer data [Mogul et al., 2021]. The updated ALMA data indicates that the 267 GHz feature is now consistent either with 1.5-7 ppb phosphine (PH_3) or $\sim 50$ ppb mesospheric SO_2 [Greaves et al., 2020, Lincowski et al., 2021], through this amount of SO_2 is not consistent with the non-detection of the 267.5 GHz SO_2 feature, from the same ALMA data, providing a 10 ppb upper limit [Greaves et al., 2020]. Careful modelling of different PH_3 profiles by Lincowski et al., 2021 demonstrate that the proposed in-cloud profile for PH_3 from Greaves et al., 2020 is insufficient to explain the observed feature. This leaves open the possibility that the signal is due to $\sim 50$ ppb mesospheric SO_2, with an anomalous velocity shift, or mesospheric PH_3 in quantities difficult to reconcile with the PH_3 lifetime, unless there is an unknown mesospheric source of PH_3. Further observations will be needed to determine which if either PH_3 or SO_2, or if some other unidentified molecule is the source of the 267 GHz feature.

Greaves et al., 2020 and Bains et al., 2020 estimated the lifetime and required flux of 20 ppb PH_3. The amount inferred from the ALMA observations has decreased to 1 ppb [Greaves et al., 2020], and we can apply our new model results to estimate that a flux of $10^7$ cm$^{-2}$ s$^{-1}$ PH_3 is required to explain PH_3 at these abundances, assuming the 267 GHz feature probed the clouds (this also includes effective dry deposition of PH_2 set to fix the abundance of PH_2 at the surface equal to zero, and dry deposition of PH_3 fixed to $10^{-4} {\rm \, cm \, s^{-1}}$). We also find that PH_3 is efficiently destroyed above 60 km, and the steep gradient in its profile is consistent with the non-detection above 61 km [Encrenaz et al., 2020]. The in-cloud PH_3 profile cannot explain the observed feature [Lincowski et al., 2021], but this profile is expected if there were a source of PH_3 in the clouds.

§.§ Implications for Hypothetical Life in the Clouds of Venus

The implications of this cloud chemistry on hypothetical Venusian life depends on how and in what form the sulfur is depleted. If surface, volcanic or exogenous delivery is responsible, this would explain the provision of various alkaline salts and/or other metals, essential for life as we know it. The higher pH is within the range where known acidophiles can thrive [Messerli et al., 2005]. However, although acidophilic and halophilic extremophiles exist on Earth, there are, as far as we know, no known extremophiles that are both acidophilic and halophilic enough to thrive in these conditions [Belilla et al., 2019].

If on the other hand the pH is being buffered within the clouds by the organisms themselves, either by use of phosphine or by burning hydrocarbons, sacrificing themselves so that others may live, then the available water will be produced and scavenged by means of the reaction. The remaining question is whether the biomass is sufficient to explain the sulfur depletion, and there is no reliable estimate of the biomass in the clouds of Venus. Early estimates based on tentative detections of phosphine have been made [Lingam & Loeb, 2020], but there is significant work left to better constrain the possibility that life is making use of the in-cloud SO_2.

§ CONCLUSION

In this paper, we discussed the puzzle of SO_2 depletion in the cloud layer. If the below-cloud observations of SO_2 and H_2O are correct, then there is too little H_2O to explain this depletion. We found that increasing the amount of below-cloud H_2O predicts chemistry above the clouds that does not agree with observations, but decreasing the below-cloud SO_2 results in above-cloud chemistry that generally agrees with observations. We also explored the possibility that hydrogen is delivered into the clouds in the form of aerosols, salts or metals, either from an exogenous source, from dust rising up from the surface, from volcanism, and from processes occurring within the clouds themselves. These processes buffer the pH of the clouds to values of 1-2. We discuss the implication of these predictions for observations of other trace gas-phase species and the optical properties of the clouds themselves.

Probes into the clouds of Venus will be necessary to determine what is happening within the clouds: the depletion of SO_2, the droplet chemistry (whether or not this chemistry has anything to do with the SO_2 depletion), the mysterious UV absorber, the known presence of heavy metals such as iron, the plausible presence of several reduced species in surprisingly large quantities [Greaves et al., 2020, Mogul et al., 2021]. In particular, the DAVINCI+ mission concept is planned to travel into and below the clouds to measure atmospheric redox and better constrain the chemical cycles that are thought to sustain the clouds [Garvin et al., 2020]. The cloud chemistry itself can be examined by including a design like the “JPL Venus Aerosol Mass Spectrometer Concept”, where a nebulizer is incorporated onto a mass spectrometer to separate gas and cloud particles and analyze the aerosol chemistry directly [Baines et al., 2018]. This would be the most straight-forward way to test this hypothesis, and other hypotheses, e.g. Krasnopolsky, 2017, that involve cloud chemistry.

Probes to the surface will be relevant for constraining the surface mineralogy and determining whether Venus's surface composition is in chemical equilibrium. These observations can be combined with a climate history of Venus, based on observations and models, to discover more about Venus's atmospheric evolution. Specifically, Figure <ref> can also be used to speculate about the possible cause for the origin of the thick Venusian atmosphere that we observe today. If Venus once was a cooler planet with a thinner N2 dominated atmosphere, just like Earth, but for some reason it warmed up to temperatures above 580 K, possibly due to large amounts of CO_2 released during global resurfacing [Strom et al., 1994], all carbonates in the surface rock would decompose and liberate even more CO2 into the atmosphere.  Not only would this increase the greenhouse effect, but it would also make the Venusian atmosphere thicker. Both effects would have increased the surface temperature, leading to a run-away build-up of the thick CO2 Venusian atmosphere that we find today. Observations of surface minerals, possible with VERITAS [Smrekar et al., 2020], and EnVision [de Oliveira et al., 2018], would allow us to test the predictions of this and other hypotheses for the present state of Venus's atmosphere and climate, in particular, whether the surface and atmosphere of Venus are at thermochemical equilibrium.

To prepare for these missions, experiments are needed in Venus analogue environments to predict the chemistry that takes place, especially the largely unexplored chemistry that may take place within high concentrations of sulfuric acid, and the surface chemistry that may take place on efflorescent sulfates. In the meantime, a detailed cloud model of the form published by Gao et al., 2014, but that incorporates this chemistry, would be of value in order to see if any remote predictions would distinguish between sulfuric acid/water droplets and sulfate/sulfite/water droplets. It may be possible to falsify the cloud chemistry hypothesis based on a combination of cloud formation and radiative transfer models and observations. It is unlikely the puzzles addressed in our paper are likely to be resolved without returning to the clouds of Venus. If other missions to other planets are any indication, what we find will be entirely unexpected.

The authors thank Joanna Petkowska-Hankel for the preparation of Fig. <ref>. P. B. R. thanks the Simons Foundation for funding (SCOL awards 599634). P. W. acknowledges funding from the European Union H2020-MSCA-ITN-2019 under Grant Agreement no. 860470 (CHAMELEON). We thank David Grinspoon, Stephen Mojzsis and Kevin Zahnle for helpful discussions, Alex T. Archibald for his advice for improving the Earth-relevant reactions for our network, and the entire team involved with Greaves et al., 2020 for initiating this investigation into the atmospheric chemistry of Venus. We also thank the two anonymous referees for helpful and insightful comments that helped improve the quality of this manuscript. A. P. thanks Sami Mikhail for providing Venus and Venus II books and Christiane Helling for the support.

Argo [Rimmer & Helling, 2016], GGchem [Woitke et al., 2018]

§ OBSERVATIONAL CONSTRAINTS ON THE ATMOSPHERIC COMPOSITION OF VENUS

The species we included in our network robustly, and that are also observationally constrained in Venus's atmosphere are carbon dioxide (CO_2), molecular nitrogen (N_2), sulfur dioxide (SO_2), water vapor (H_2O), carbon monoxide (CO), molecular oxygen (O_2), carbonyl sulfide (OCS), sulfuric acid vapor (H_2SO_4), hydrogen chloride (HCl), sulfur monoxide (SO), trisulfur (S_3), tetrasulfur (S_4), hydrogen sulfide (H_2S) and molecular hydrogen (H_2). Phosphine (PH_3) is also included in our network but not in a robust way. PH_3 may have been observed in the atmosphere of Venus (see Section <ref> for details). There are also many remote observations that constrain cloud properties such as average particle size and indirectly infer that the clouds are made of droplets of high concentration sulfuric acid (See Section <ref>). To this date no definitive in situ measurements of the cloud droplet chemistry have been made, and so virtually nothing is directly known about the cloud droplet chemistry. Observations have been made by a variety of instruments on the ground, by orbital probes, and by in situ probes. We compiled this data ourselves from a variety of sources, and a more complete compilation has been made by Johnson & de Oliveira, 2019, which includes several reactive species not incorporated into our network, such as HF, as well as unreactive species. Our compilation is given in Table <ref>.

Observational Constraints of Chemical Species in the Atmosphere of Venus

Species     $h_{\rm min}$
$h_{\rm max}$     Mixing Ratio$^*$
Reference     Obs Type

(km)     (km)

SO_2             ppm

30.0              40.0              $130.   \pm     50.     $         Marcq et al., 2008                 Venus Express

0.                22.0              $130.   \pm     35.     $         Gelman et al., 1979                Venera 12

22                22                $185.   \pm     43.     $         Oyama et al., 1979                 Pioneer Venus

35                45                $130.   \pm     40.     $         Bézard & de Bergh, 2007                Ground

12                12                $22.5   \pm     2.5     $         Bertaux et al., 1996               Vega 1, Vega 2

22                22                $38.0   \pm     3.8     $         Bertaux et al., 1996               Vega 1, Vega 2

42                42                $132.5  \pm     14.     $         Bertaux et al., 1996               Vega 1, Vega 2

52                52                $107.5  \pm     42.5    $         Bertaux et al., 1996               Vega 1, Vega 2

35                45                $130.   \pm     40.     $         Bézard & de Bergh, 2007                Ground

42                42                $180.   \pm     70.     $         Pollack et al., 1993               Ground

62                62                $0.5    \pm     0.1     $         Zasova et al., 1993                  Ground

62                62                $1.5    \pm     0.5     $         Zasova et al., 1993                  Ground

22                22                $38.    \pm     10.     $         Bertaux et al., 1996               Vega 1

12                12                $25.    \pm     10.     $         Bertaux et al., 1996               Vega 1

52                52                $150.   \pm     70.     $         Bertaux et al., 1996               Vega 1

52                52                $65.    \pm     30.     $         Bertaux et al., 1996               Vega 2

42                42                $125.   \pm     50.     $         Bertaux et al., 1996               Vega 1

42                42                $200.   \pm     100.    $         Bertaux et al., 1996               Vega 2

42                42                $< 176. $                         Oyama et al., 1980                 Pioneer Venus

22                22                $185 \pm 43.1$
Oyama et al., 1980                 Pioneer Venus

42                42                 $324 \pm 148$                        Oyama et al., 1980                 Pioneer Venus

52                52                $< 600. $                         Oyama et al., 1980                 Pioneer Venus

22                22                $< 300. $                         Hoffman et al., 1980               Pioneer Venus

52                52                $< 10.  $                         Hoffman et al., 1980               Pioneer Venus

30                40                $130.   \pm     50.     $         Marcq et al., 2008                 Venus Express

88                88                $0.012  \pm     0.003   $         Encrenaz et al., 2012              Ground

70                70                $0.075  \pm     0.025   $         Encrenaz et al., 2012              Ground

70                70                $0.125  \pm     0.050   $         Na et al., 1990                    Ground

45                55                $140.   \pm     37.     $         Arney et al., 2014                 Ground

45                55                $126.   \pm     32.     $         Arney et al., 2014                 Ground

65                75                $0.38   \pm     0.07    $         Na et al., 1990                    IUE

65                75                $0.05   \pm     0.02    $         Na et al., 1990                    IUE

75                85                $50.0   \pm     10    $         Greaves et al., 2020                 Ground$^{**}$

SO_2             ppm
H_2O             ppm

30        40        $31   \pm 2           $     Marcq et al., 2008               Venus Express

30        40        $30   \pm 10          $     de Bergh et al., 1995             Venus Express

5         40        $30   \pm 10          $     Bézard & de Bergh, 2007              Venus Express

51.3      51.3      $6.3  \pm 4.          $     Donahue et al., 1997             Pioneer Venus

55.3      55.3      $4.2  \pm 3.          $     Donahue et al., 1997             Pioneer Venus

69.5      69.5      $3.   \pm 1.          $     Cottini et al., 2012             Venus Express

15        30        $10.  \pm 1.          $     Evans & Ingalls, 1969               Ground

49        58        $700. \pm 300.        $     Mukhin et al., 1982              Venera 13, 14

46        50        $2000.\pm 400.        $     Surkov et al., 1982              Venera 13, 14

26        45        $30.  \pm 10.         $     de Bergh et al., 1995             Ground

15        30        $30.  \pm 10.         $     de Bergh et al., 1995             Ground

0         15        $30.  \pm 10.         $     de Bergh et al., 1995             Ground

10        10        $45.  \pm 10.         $     Meadows & Crisp, 1996             Ground

0         10        $7.   \pm 3.          $     Donahue & Hodges, 1992             Pioneer Venus

10        26        $28.  \pm 18.         $     Donahue & Hodges, 1992             Pioneer Venus

58        60        $20.  \pm 10.         $     Moroz et al., 1990               Ground

52        60        $1000.\pm 500.        $     Surkov et al., 1987              Vega 1, Vega 2

42        42        $150. \pm 50.         $     Moroz et al., 1979               Venera 11, 12

22        22        $60.  \pm 30.         $     Moroz et al., 1979               Venera 11, 12

35        45        $40.  \pm 20.         $     Bézard et al., 1990              Ground

10        40        $30.  \pm 10.         $     Pollack et al., 1993             Ground

15        25        $30.  \pm 10.         $     de Bergh et al., 1995             Ground

0         15        $30.  \pm 15.         $     de Bergh et al., 1995             Ground

0         0         $20.  \pm 10.         $     Moroz et al., 1979               Venera 11, 12

30        40        $26.  \pm 4.          $     Marcq et al., 2006               Ground

30        40        $35.  \pm 4.          $     Tsang et al., 2008               Venus Express

30        40        $30.  \pm 4.          $     Tsang et al., 2008               Venus Express

30        40        $34.  \pm 2.          $     Arney et al., 2014               Ground

30        40        $33.  \pm 3.          $     Arney et al., 2014               Ground

15        30        $33.  \pm 2.          $     Arney et al., 2014               Ground

15        30        $32.  \pm 2.          $     Arney et al., 2014               Ground

0         15        $44.  \pm 9.          $     Bézard & de Bergh, 2007              Venus Express

0         15        $30.  \pm 10.         $     Bézard et al., 2011              Venus Express

0         15        $31.  \pm 9.          $     Chamberlain et al., 2013             AAT

0         15        $29.  \pm 2.          $     Arney et al., 2014               Ground

0         15        $27.  \pm 2.          $     Arney et al., 2014               Ground

0         15        $25.7 \pm 1.4         $     Fedorova et al., 2015            Venus Express

0         15        $29.4 \pm 1.6         $     Fedorova et al., 2015            Venus Express

65        74        $6.0  \pm 4.0         $     Fedorova et al., 2016            Pioneer Venus

70        110       $1.0  \pm 0.9         $     Fedorova et al., 2008            Venus Express

45        55        $20.0 \pm 10.         $     Meadows & Crisp, 1996             Ground

0         15        $45.  \pm 15.         $     Meadows & Crisp, 1996             Ground

65        100       $1.8  \pm 1.8         $     Sandor & Clancy, 2005              Ground

65        120       $2.5  \pm 0.6         $     Encrenaz et al., 2015            Ground

65        75        $3.0  \pm 1.0         $     Cottini et al., 2012             Venus Express

65        75        $5.0  \pm 2.0         $     Cottini et al., 2012             Venus Express

65        65        $0.8         $     Bell et al., 1991             Ground

55        55        $100.0       $     Bell et al., 1991             Ground

40        40        $200.0       $     Bell et al., 1991             Ground

H_2O             ppm
CO             ppm

36        36        $27.5         \pm 3.5         $     Marcq et al., 2008       Venus Express

35        35        $23.0         \pm 2.0         $     Tsang et al., 2008       Venus Express

35        35        $32.0         \pm 2.0         $     Tsang et al., 2008       Venus Express

22        22        $20.0         \pm 0.4         $     Oyama et al., 1979       Pioneer Venus

64        64        $45.0         \pm 10.0        $     Fegley, 2014      Venera 13, 14

0         0         $3.8          \pm 3.2         $     Fegley, 2014      Venera 13, 14

52        52        $32.0         \pm 22.0        $     Oyama et al., 1980       Pioneer Venus

42        42        $30.0         \pm 18.0        $     Oyama et al., 1980       Pioneer Venus

22        22        $20.0         \pm 3.0         $     Oyama et al., 1980       Pioneer Venus

0         42        $28.0         \pm 7.0         $     Gelman et al., 1979      Venera 12

64.       64.       $45.0         \pm 10.0        $     Connes et al., 1968      Ground

64.       64.       $51.0         \pm 1.0        $     Young, 1972       Ground

90        90        $180.         \pm 90.0        $     Wilson et al., 1981      Ground

36        36        $23.0         \pm 5.0         $     Pollack et al., 1993     Ground

40        40        $29.0         \pm 7.0         $     Pollack et al., 1993     Ground

35        45        $45.0         \pm 10.0        $     Bézard et al., 1990      Ground

36        36        $23.0         \pm 10.0        $     Pollack et al., 1993     Ground

28        28        $23.0         \pm 10.0        $     Bézard & de Bergh, 2007      Ground

42        42        $30.0         \pm 15.0        $     Bézard & de Bergh, 2007      Ground

36        36        $24.0         \pm 2.0         $     Marcq et al., 2006       Ground

36        36        $27.0         \pm 3.0         $     Cotton et al., 2012      Ground

68        71        $70.0         \pm 8.0        $     Krasnopolsky, 2008        Ground

68        68        $51.0         \pm 4.0         $     Krasnopolsky, 2010        Ground

68        68        $40.0         \pm 4.0         $     Krasnopolsky, 2010        Ground

104       104       $560.0        \pm 100.0       $     Krasnopolsky, 2014        Ground

70        70        $35.0         \pm 10.0        $     Marcq et al., 2015       Ground

30        30        $30.0         \pm 5.0         $     Collard et al., 1993     Galileo

30        30        $40.0         \pm 5.0         $     Collard et al., 1993     Galileo

35        35        $30.0         \pm 15.0        $     Marcq et al., 2005       Ground

104       104       $560.0        \pm 100.0       $     Krasnopolsky, 2014        Ground

65        75        $70.0         \pm 10.0        $     Grassi et al., 2014      Venus Express

65        75        $60.0         \pm 5.0         $     Grassi et al., 2014      Venus Express

CO             ppm
O_2             ppm

52        52        $43.  \pm 25. $     Oyama et al., 1979       Pioneer Venus

42        42        $16.  \pm 8.  $     Oyama et al., 1979       Pioneer Venus

52        52        $44.  \pm 25. $     Oyama et al., 1980       Pioneer Venus

42        42        $16.  \pm 7.  $     Oyama et al., 1980       Pioneer Venus

35        58        $18.  \pm 4.  $     Mukhin et al., 1982      Venera 13, 14

60        100        $<2.8$     Marcq et al., 2018      Ground

O_2             ppm
OCS             ppm

30        30        $14.0         \pm 6.0         $     Pollack et al., 1993     Ground

33        33        $3.25         \pm 0.75        $     Marcq et al., 2008       Venus Express

29        37        $40.0         \pm 20.0        $     Mukhin et al., 1982      Venera 13, 14

33        33        $4.4          \pm 1.0         $     Pollack et al., 1993     Ground

28        28        $30.0         \pm 10.0        $     Pollack et al., 1993     Ground

38        38        $0.35         \pm 0.1         $     Marcq et al., 2005       Ground

0         30        $15.0         \pm 5.0         $     Bézard & de Bergh, 2007      Ground

30        30        $14.0         \pm 6.0         $     Pollack et al., 1993     Ground

29        37        $40.0         \pm 20.0        $     Mukhin et al., 1983      Venera 13, 14

36        36        $0.52         \pm 0.05        $     Marcq et al., 2006       Ground

30        30        $16.0         \pm 8.0         $     Bézard & de Bergh, 2007      Ground

38        38        $0.35         \pm 0.1         $     Bézard & de Bergh, 2007      Ground

36        36        $0.44         \pm 0.1         $     Arney et al., 2014       Ground

36        36        $0.57         \pm 0.12        $     Arney et al., 2014       Ground

36        36        $0.5          \pm 0.02        $     Marcq et al., 2005       Ground

36        36        $0.46         \pm 0.01        $     Marcq et al., 2005       Ground

36        36        $0.54         \pm 0.13        $     Arney et al., 2014       Ground

36        36        $0.61         \pm 0.12        $     Arney et al., 2014       Ground

65        65        $<0.004                       $     Krasnopolsky, 2010        Ground

65        65        $0.005        \pm 0.003       $     Krasnopolsky, 2010        Ground

OCS             ppm
H_2SO_4             ppm

50          52          $3.0 \pm 2.0$        Oschlisniok et al., 2012            Venus Express

H_2SO_4             ppm
HCl             ppm

15        25        $0.41         \pm 0.04        $     Arney et al., 2014       Ground

15        25        $0.42         \pm 0.055       $     Arney et al., 2014       Ground

74        74        $0.4          \pm 0.03        $     Krasnopolsky, 2010       Ground

61        67        $0.76         \pm 0.1         $     Iwagami et al., 2008     Ground

74        74        $0.4          \pm 0.03        $     Krasnopolsky, 2010       Ground

70        70        $0.4          \pm 0.04        $     Sandor & Clancy, 2012       Ground

90        90        $0.2          \pm 0.02        $     Sandor & Clancy, 2012       Ground

35        70        $0.5          \pm 0.12        $     Connes et al., 1967       Ground

74        74        $0.4          \pm 0.04        $     Krasnopolsky, 2010       Ground

36        36        $0.42         \pm 0.07        $     Young, 1972       Ground

50        50        $0.61         \pm 0.06        $     Young, 1972       Ground

30        40        $0.005        \pm 0.002       $     Bézard et al., 1990      Ground

70        70        $0.4          \pm 0.04        $     Bézard et al., 1990      Ground

15        30        $0.5          \pm 0.05        $     Bézard et al., 1990      Ground

45        55        $0.5          \pm 0.05        $     Iwagami et al., 2008     Ground

65        75        $0.6          \pm 0.1         $     Connes et al., 1967      Ground

HCl             ppm
PH_3             ppb

55.0      60.0      $20.0 \pm 10.0$      Greaves et al., 2020     Ground$^{\dagger}$

55.0      60.0      $1.5 \pm 1.0$      Greaves et al., 2020     Ground$^{\dagger}$

60.0      65.0      $< 5.0$      Encrenaz et al., 2020

PH_3             ppb
SO             ppb

84.0      90.0      $ 8.0 \pm 2.0         $     Encrenaz et al., 2015            Ground

84.0      90.0      $ 8.0 \pm 2.0         $     Encrenaz et al., 2015            Ground

75.0      85.0      $ 5.0 \pm 4.0        $     Na et al., 1990                  Ground

SO             ppb
S_3             ppb

23.0      23.0      $0.04         \pm 0.01        $     Bézard & de Bergh, 2007      Venera 11-14

3.0       19.0      $0.065        \pm 0.035       $     Maiorov et al., 2005     Venera 11

3.0       19.0      $11.          \pm 3.0         $     Krasnopolsky, 2013        Venera 11

10.0      19.0      $18.          \pm 3.0         $     Krasnopolsky, 2013        Venera 11

S_3             ppb
S_4             ppb

3.0       10.0      $4.   \pm 3.9 $     Krasnopolsky, 2013        Venera 11

10.0      19.0      $6.   \pm 2.0 $     Krasnopolsky, 2013        Venera 11

S_4             ppb
H_2S             ppb

70.0      70.0      $<13.0$      Krasnopolsky, 2008     Ground

H_2S             ppb
H_2             ppm

0.0      25.0      $<10.$      Donahue et al., 1997     Pioneer Venus

22.0      64.0      $<10.$      Oyama et al., 1980     Pioneer Venus

49.0      58.0      $25. \pm 10$      Mukhin et al., 1982     Venera 13,14

H_2             ppm

$^*$ Values and errors as found in the cited literature.

$^{**}$ If interpreted as mesospheric SO_2, see Section <ref>

$^{\dagger}$ If interpreted as mesospheric PH_3, see Section <ref>

$^{\ddagger}$ Based on their wet profile, which fits their data best.

§ THE CHEMICAL NETWORK: STAND2020

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