Physical Chemistry , 1st ed.

The way to make a proportionality an equality is to define a proportionality

constant Ki, so now we have

piKixi (7.31)

where the value of the constant Kidepends on the components and also the

temperature. Equation 7.31 is calledHenry’s law,after the British chemist

William Henry, who was a contemporary and friend of John Dalton (of mod-

ern atomic theory and Dalton’s law of partial pressures fame).Kiis called the

Henry’s law constant.

Notice the similarity and difference between Raoult’s law and Henry’s law.

Both apply to the vapor pressure of volatile components in a solution. Both say

that the vapor pressure of one component is proportional to the mole fraction

of that component. But whereas Raoult’s law defines the proportionality con-

stant as the vapor pressure of the pure component, Henry’s law defines the

proportionality constant as some experimentally determined value. Some

Henry’s law constants are listed in Table 7.1.

Many applications of Henry’s law define the system from a different per-

spective. Instead of specifying the solution composition, the liquid phase and

the equilibrium gas component pressure are specified. Then the question is

asked, what is the equilibrium mole fraction of the gas in the resulting equi-

librium solution? The following example illustrates.

Example 7.9

The Henry’s law constant Kifor CO 2 in water is 1.67 108 Pa (Pa pascal;

1 bar  105 Pa) at some particular temperature. If the pressure of CO 2 in

equilibrium with water were 1.00 106 Pa (which equals 10 bar, or about 10

atm) at that temperature, what is the mole fraction of CO 2 in the solution?

Can you estimate the molarity of the CO 2 solution?

Solution

In this example, we are specifying the equilibrium partial pressure of the gas

in the gas phase, and determining the mole fraction in the liquid solution

(rather than the other way around, which has been the habit so far). Using

equation 7.31, we have

1.00 106 Pa (1.67 108 Pa) xi

Solving, we find that

xi0.00599

Notice that the units have canceled. This is expected for a mole fraction, which

is unitless. Since the mole fraction of CO 2 is so small, we will assume that the

volume of 1 mole of solution is the molar volume of water, which is 18.01 mL

or 0.01801 L. We further approximate that the mole fraction of H 2 O mole-

cules is about 1.00, so that the number of moles of CO 2 dissolved in the wa-

ter is 0.00599 mole. Therefore, the approximate molarity of the solution is

0.

0

0

.

0

0

5

1

9

8

9

01

m

L

ol0.333 M

The higher number for the molar concentration of this solution belies the

tiny mole fraction in the liquid phase. Carbonated beverages are typically

made by using this pressure of gaseous carbon dioxide.

184 CHAPTER 7 Equilibria in Multiple-Component Systems

Table 7.1 Some Henry’s law constants for

aqueous solutionsa

Compound Ki(Pa)

Argon, Ar 4.03 109

1,3-Butadiene, C 4 H 6 1.43 1010

Carbon dioxide, CO 2 1.67 108

Formaldehyde, CH 2 O 1.83 103

Hydrogen, H 2 7.03 109

Methane, CH 4 4.13 107

Nitrogen, N 2 8.57 109

Oxygen, O 2 4.34 109

Vinyl chloride, CH 2 CHCl 6.11 107

aTemperature is 25°C.