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A Discussion of the Effect of pH on
the Solubility of Hydrogen Sulfide
John J. Carroll
©1998 - Publication Rights Reserved
This paper examines the effect of pH on the solubility
of hydrogen sulfide in water. It is shown that in acidic solutions
(low pH), the solubility is only slightly different from pure water.
In alkaline solutions (high pH), the solubility is dramatically
increased.
Introduction
The solubility of hydrogen sulfide in water is important in industrial
practice, especially in these environmentally aware times. The fate
of such an unfriendly component such as hydrogen sulfide is
important to track. Hydrogen sulfide is highly toxic, has a noxious odor, and can form
harmful reaction products (such as SOx).
Since aqueous hydrogen sulfide is acidic, the effect of pH is also very
important. The purpose of this paper is to discuss this effect.
Several simplifying assumptions are made in the development
presented in this paper. Therefore, the numerical results should be considered
approximate.
Solubility in Water
The solubility of hydrogen sulfide in "pure" water at low
pressure has been studied thoroughly and was recently reviewed
by Carroll and Mather (1989) (also see Carroll, 1990).
At low pressure (less than 200 kPa or so), the solubility
of the molecular H2S in water is given by the strict Henry's law
(Carroll, 1991). Molality (moles of solute per kg of solvent)
is a convenient unit
for this analysis, and thus Henry's Law is given by:
mH2S H = yH2S P
where yH2S is the mole fraction of hydrogen sulfide
in the vapor, P is the total pressure, mH2S is the molality
of the molecular form of the hydrogen sulfide in the water (moles per
kilogram of water), and H is the Henry's constant.
The product of the vapor phase mole fraction and the total pressure gives
the partial pressure of the given species.
Once dissolved in water, H2S is involved in a series of chemical reactions.
The chemical reactions are: (1) the dissociation of the
molecular H2S to form the bisulfide ion, (2) the dissociation of
the bisulfide ion to the sulfide ion, and (3) the self ionization
of water. The reactions are given below:
Each of these reactions has an associated equilibrium relation,
the so-called "mass action" relations.
These are given below:
In the final form of these equations (the expressions on the right),
it has been assumed that the activity coefficients are unity.
This may be a good assumption for dilute solutions,
but it is not the case in general. One must resort
to one of the ionic activity coefficient models to
account for this effect. The assumption of unit
activity coefficients will be used throughout this
paper, even though it is known to be in error.
It does not, however, detract from the general
conclusions of this paper. For a detailed discussion
of ionic activity coefficients, the reader is referred
to the monograph by Zematis et al. (1986).
In addition the equilibrium constants for these
three reactions have been studied over a wide
range of temperature. The K's, as a function of the temperature,
are available in the literature (see Roberts and Tremaine,
1985, for example).
We are usually interested in the total hydrogen
sulfide in the aqueous solution. To obtain this value,
we merely sum the concentrations of the various sulfide
species:
tH2S = mH2S + mHS-
+ mS=
Another relation required is that of electroneutrality.
The solution cannot have a net charge. Mathematically,
this is given by:
mH+ = mHS- + 2 mS=
+ mOH-
When dealing with an acid or a base, the additional ions must
also be accounted for in this relation. For example, in a sodium
hydroxide solution, the sodium ion must be included in the
left hand side of this equation. And in hydrochloric acid, the
chloride ion must be included in the right hand side.
Finally, we require the definition of the pH:
pH = -log(aH+) ~ -log(mH+)
These are the common logarithms (base 10). Again, the
activity coefficient is usually neglected.
The Solubility in Strong Acids
At first, it seems to be a logical assumption that the
presence of an acid would drive the hydrogen sulfide out
of solution. However, experimental evidence (and a thorough
analysis) demonstrates that this is not the case.
Measurements by Kendall and Andrews (1921) and others
(and analyzed by Carroll, 1991) show that the presence of hydrochloric
acid can be modeled in a fashion similar to the effect of a neutral
ionic solute (such as sodium chloride). It is an interesting
observation that the measured solubility, as a function of HCl
concentration, exhibits a maximum. At low acid concentrations, the
HCl salts-out the hydrogen sulfide (i.e., reduces the solubility).
As the acid concentration increases, the solubility increases
and if the HCl concentration is large enough the solubility is
actually greater than in pure water. However, for the purposes
of this discussion, we can neglect any "salt" effects.
Furthermore, Douabul and Riley (1979) found that the
solubility of H2S in 5 molar sulfuric acid was essentially the same
as in "pure" water.
What dictates the amount of the molecular form of hydrogen
sulfide in the aqueous solution is its partial pressure. The ionization
reactions are shifted to the left, but this has little effect on the
amount of molecular hydrogen sulfide. Since these reactions do not
proceed very far to begin with, then this should have a small effect on
the total solubility. Thus to a reasonable approximation, the
solubility of H2S in an acidic solution is equal to that in pure water.
It is also worth noting that different acids will have
different salting-in effects. Thus it is a bit of a misnomer to talk
about the solubility of H2S at low pH without discussing which
acid is present.
The Solubility in Strong Bases
The treatment for the solubility in strong bases is the same as
that in acids, but the effect is dramatically different.
As with the case of strong acids, the amount of the molecular
species is dictated by the partial pressure. However, in this case
the reactions are shifted to the right producing more of the
ionic sulfide species and thus dramatically increasing the total
hydrogen sulfide concentration, tH2S (per the equation given earlier).
Just as with the acid, there is a salting-out effect due to
the presence of the ionic species. Different bases will have different
salting-out effects. Thus it is insufficient just to discuss the
solubility as a function of pH without further including the effect
of the particular base under investigation.
Numerical Results
We will only consider the case of 25ĒC and a total pressure
of 101.325 kPa (1 atm). At these conditions the partial
pressure of H2S is 98.15 kPa and we have the following:
H = 991 kPa/molal
K1 = 1.039 E-07
K2 = 6.43 E-16
Kw = 1.019 E-14
The equilibrium constants were taken from Roberts
and Tremaine (1985) and the Henry's constant is from
Carroll (1990).
Pure Water
First, solving Henry's Law for the concentration of the
molecular species gives:
mH2S = 0.099 molal
And from the expressions for the chemical equilibrium,
we obtain the following:
mHS-= 1.01 E-04 molal
mS= = 6.4 E-16 molal
mH+ = 1.01 E-04 molal
mOH- = 1.01 E-10 molal
Therefore, in pure water, the hydrogen sulfide solution
has a pH of about 4. It is worth repeating that this pH
arises without the addition of any acid or base.
Effect of pH
Fig. 1 shows the effect of pH on the solubility of
hydrogen sulfide. Note, the concentration of the S=
ion is not plotted because in every case it would be
off scale (i.e., less than 1E-8 molal). In addition,
the plot only goes to a pH of 8 because beyond this point
the concentration of the ionic species become so large
that neglecting the activity coefficients results in
significant error. Even at a concentration of 1 molal,
the activity coefficients have a very large effect.
Fig. 1
The Approximate Solubility of Hydrogen Sulfide as a
Function of the pH
The model predicts that the molecular form of the
hydrogen sulfide has a concentration independent of the
pH. This was an assumption that was built into the model.
As discussed earlier, a salt effect would have to be
included to accurately predict the solubility
of the molecular H2S.
At low pH (acidic solutions), the predominant form
of the sulfide species is the molecular H2S. This
continues to be the case until a pH of about 6 when
significant amounts of the bisulfide ion are present.
Further increases in the pH results in the formation of
more bisulfide. By a pH of slightly less than 7, there
are equal amounts of the molecular and bisulfide forms.
At a pH of 8, the concentration of the bisulfide ion
is about ten times that of the molecular H2S.
The bisulfide ion is the dominant hydrogen sulfide
species for pH greater than this value.
A Comment on Carbon Dioxide
The behavior of the solubility of carbon dioxide is
very similar to that of hydrogen sulfide in many respects.
Carbon dioxide also forms a weak diprotic acid when
dissolved in water. And at low pressure the solubility can be
estimated using the strict Henry's law. Thus many
of the observations about H2S can be directly translated
to the behavior of CO2. Of course the numerical results
will be different for the two gases, but the qualitative
phenomena are the same.
A Comment on Alkanolamines
Aqueous solutions of alkanolamines are commonly used in industrial
practice to remove hydrgen sulfide and carbon dioxide from gas streams.
Commonly employed amines include monoethanolamine (MEA), diethanolaime (DEA),
and methyldiethanolamine (MDEA).
These compounds are effective as solvents because they form weak bases
when dissolved in water, similar to ammonia.
As was just demonstrated, the solubility of
hydrogen sulfide increases dramtically in a solution with a high pH.
However, the reaction with a weak base can be reversed with
a reduction in pressure
and by the application of heat. Thus the solvent can be regenerated.
With a strong base, such a sodium hydroxide, the reaction is irreversible.
Details of the alkanolamine process can be found in Kohl and
Nielsen (1997)
Conclusions
It was the purpose of this paper to briefly discuss
the effect of pH on the solubility of hydrogen sulfide
and to provide the tools for a more detailed analysis.
It was shown in this work that for low pH (acidic
solutions), the presence of the acid has only a small
effect on the solubility. This effect is
essentially a "salt" effect, similar to that observed
for a neutral salt such as sodium chloride.
On the other hand, as expected, the presence of a base
(an alkali) greatly increases the solubility because of the
formation of ionic species (notably the bisulfide ion).
References
- Carroll, J.J., Chem. Eng., 97 (10),
227-230, (1990).
- Carroll, J.J., Chem. Eng. Prog., 87 (9),
48-52, (1991).
- Carroll, J.J., Chem. Eng. Prog., 88 (8),
53-58, (1992).
- Carroll, J.J. and Mather, A.E., Geochim. Cosmochim. Acta,
53, 1163-1170, (1989).
- Douabul, A.A. and Riley, J.P., Deep-Sea Res.,
26A, 259-268, (1979).
- Kendall, J. and Andrews, J.C., J. Am. Chem. Soc.,
43, 1545-1548, (1921).
- Kohl, A.L. and Nielsen, R.B., Gas Purification,
5th ed., Gulf Publishing, Houston, TX, (1997). - Earlier
editions of this book were under the authorship of Kohl
and Risenfeld and are equally useful.
- Roberts, B.E. and Tremaine, P., Can. J. Chem. Eng.,
63, 294-300, (1985).
- Zematis, J.F., Clark, D.M., Rafal, M., and Scrivner, N.C.,
Handbook of Aqueous Electrolyte Thermodynamics,
American Institute of Chemical Engineers - DIPPR,
New York, NY, (1986).
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