9.18 Vapor Pressure
373
For substances with a low concentration (x k << 1) in a solution, the ability of
the molecules of that substance to escape from the solution as a gas depends on how
‘sticky’ the molecules are with the various materials at the solution-gas interface.
Still, one should expect that the vapor pressure of the dissolved substance in low
concentration in solution will be proportional to the substance’s concentration in
the solution:
p k ≈ x k K
H
k .
(9.131)
This is Henry’s law. The proportionality constant K H
k is Henry’s coefficient for the
substance labeled by k, also called its ‘volatility’. For dilute concentrations of the
substance in solution, the inverse of Henry’s coefficient is close to the ‘solubility’ of
the gas. (Formally, the solubility of a material is the ratio of the maximum amount of
material that can be dissolved in a given amount of solvent, both usually measured
in moles.) When a gas is in equilibrium with a liquid, the solution will have become
saturated with the gas. The solubility can range from almost zero (immiscible) to
infinite (perfect miscibility).
Henry’s coefficient is not easy to predict, since it depends on how the substance
forms bonds with the solvent, or becomes ionic. For example, carbon dioxide
will react with water to form hydronium and carbonate ions. These ions must
reform CO 2 at the liquid-gas interface before CO 2 is released into the vapor state
(Table 9.2).
Henry’s coefficient varies with temperature. From Eq. (9.131), we have
d ln K H
s
dT
=
d ln p s
dT
(9.132)
to which we can apply the Clausius–Clapeyron equation (9.127) to find
d ln K H
s
dT
=
ρ s λ s
RT 2 .
(9.133)
Table 9.2 Henry’s law
coefficient for various gases
in aqueous solution near
293.15 K
Gas
K H (in atm)
ρ s λ s /R (in K)
N 2
9.1 × 10 4
1300
O 2
4.3 × 10 4
1700
Ar
4.0 × 10 4
1300
CO 2
0.16 × 10 4
2400
CO
5.8 × 10 4
1300
The second column determines the heat of dissolution λ s . From R. Sander, Compilation of Henry’s law
constants (v.4.0) for water as solvent, Atmos Chem
Phys, 14 (8), 4399–4981 (2015).)
373
For substances with a low concentration (x k << 1) in a solution, the ability of
the molecules of that substance to escape from the solution as a gas depends on how
‘sticky’ the molecules are with the various materials at the solution-gas interface.
Still, one should expect that the vapor pressure of the dissolved substance in low
concentration in solution will be proportional to the substance’s concentration in
the solution:
p k ≈ x k K
H
k .
(9.131)
This is Henry’s law. The proportionality constant K H
k is Henry’s coefficient for the
substance labeled by k, also called its ‘volatility’. For dilute concentrations of the
substance in solution, the inverse of Henry’s coefficient is close to the ‘solubility’ of
the gas. (Formally, the solubility of a material is the ratio of the maximum amount of
material that can be dissolved in a given amount of solvent, both usually measured
in moles.) When a gas is in equilibrium with a liquid, the solution will have become
saturated with the gas. The solubility can range from almost zero (immiscible) to
infinite (perfect miscibility).
Henry’s coefficient is not easy to predict, since it depends on how the substance
forms bonds with the solvent, or becomes ionic. For example, carbon dioxide
will react with water to form hydronium and carbonate ions. These ions must
reform CO 2 at the liquid-gas interface before CO 2 is released into the vapor state
(Table 9.2).
Henry’s coefficient varies with temperature. From Eq. (9.131), we have
d ln K H
s
dT
=
d ln p s
dT
(9.132)
to which we can apply the Clausius–Clapeyron equation (9.127) to find
d ln K H
s
dT
=
ρ s λ s
RT 2 .
(9.133)
Table 9.2 Henry’s law
coefficient for various gases
in aqueous solution near
293.15 K
Gas
K H (in atm)
ρ s λ s /R (in K)
N 2
9.1 × 10 4
1300
O 2
4.3 × 10 4
1700
Ar
4.0 × 10 4
1300
CO 2
0.16 × 10 4
2400
CO
5.8 × 10 4
1300
The second column determines the heat of dissolution λ s . From R. Sander, Compilation of Henry’s law
constants (v.4.0) for water as solvent, Atmos Chem
Phys, 14 (8), 4399–4981 (2015).)