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henry constant

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ehsan:
Hi dears
I am working on modeling the dissolution of hydrogen sulfide in water
What correlation and constancy does Phreeqc software use to obtain the henry constant of hydrogen sulfide in aqua phase(H2S(aq))?
I think this correlation is to get an henry constant.

--- Code: ---log(KH)=(a1 + a2*temp + a3/temp + a4*(log10(temp))+a5/(temp^2) + a6*(temp)^2)
--- End code ---
But I do not see a1,a2,a3,a4,a5,a6 in the database for hydrogen sulfide(H2S(aq)).

dlparkhurst:
The Henry's law constant for H2S(g) is defined in PHASES. For phreeqc.dat, here is the definition:

--- Code: ---H2S(g)
H2S  =  H+ + HS-
log_k    -7.93
-delta_h   9.1
-analytic -45.07  -0.02418  0  17.9205 # H2S solubilities, 0 - 300°C, 1 - 987 atm, Jiang et al., 2020, CG 555, 119816
-T_c  373.2; -P_c  88.20; -Omega 0.1

--- End code ---

The definition of the equilibrium constant for H2S(aq) for the reaction and equilibrium constant for H2S(aq) is in SOLUTION_SPECIES. In phreeqc.dat, the definition is as follows:

--- Code: ---HS- + H+ = H2S
-log_k 6.994
-delta_h -5.30 kcal
-analytical  -11.17  0.02386  3279.0
-dw 2.1e-9
-Vm  1.39  28.3  0  -7.22  -0.59 # ref. 1 + Hnedkovsky et al., 1996, JCT 28, 125

--- End code ---

Note that for high temperature and pressure, an additional aqueous species, (H2S)2(aq) was added to phreeqc.dat (and Amm.dat) purely to improve the fit to experimental data:

--- Code: ---2H2S = (H2S)2 # activity correction for H2S solubility at high P, T
-analytical_expression   10.227  -0.01384  -2200
-Vm   36.41  -71.95  0  0  2.58

--- End code ---

ehsan:
This is the equation that I used to calculate the dissolution of hydrogen sulfide in water.

--- Code: ---m_h2s = (P*y_h2s*phi(h2s(g)))/AC(h2s(aq))KH*PF
PF=exp(V_m*(P-P_ref)/RT)
--- End code ---
But when I calculate the henry constant, I get an unusual value of KH

--- Code: ---temp = 373K
KH_H2S =10^(a1 + a2*temp + a3/temp + a4*(log10(temp))+a5/(temp^2) + a6*(temp)^2)

a1 = -45.07;  a2 = -0.02418;  a3= 0;  a4 = 17.9205;a5 = 0;a6 = 0
ans = 9.9236e-09

a1 = 10.227;  a2 = -0.01384;  a3= -2200;  a4 =0;a5 = 0;a6 = 0;
ans=3.3167e+06

--- End code ---
I do not know how to use this Henry constant inside (m_h2s) equation.

dlparkhurst:
I do not know the meaning of all of your variables, but my guess is that you are not using the right reaction. The reaction in phreeqc.dat is H2S(g) -> H+ + HS-.

Here is a calculation of the solubility of H2S given a partial pressure of 1 atm. It uses the element Sg in phreeqc.dat, which represents the sulfide valence state without any reactions to any other valence state. You get essentially the same result if you use H2S instead of H2Sg.

--- Code: ---SOLUTION
EQUILIBRIUM_PHASES
H2Sg(g) 0 10
END

--- End code ---

In this pure system, the solubility of H2S(g) is 0.1016 mol/kgw.

The pH is 3.97. The  log10 activity of H2Sg- is -3.970.

The partial pressure of H2Sg(g) is 1 atm. The fugacity of H2Sg(g) is 0.992. The log10 fugacity is -0.0035.

The log10 of the Henry's log K at 25 C is

-45.07 + (-0.02418*298.15) + 17.9205*log10(298.15) = -7.94

The Henry's law relation is

log K = log[act(H2Sg-)] + log[act(H+)] - log[fug(H2Sg(g))]

-7.94 = -3.97 + -3.970 - -0.0035