Physical Chemistry Third Edition

250 6 The Thermodynamics of Solutions

the behavior in Figure 6.9 as follows:In sufficiently dilute solutions nonionic solutes

obey Henry’s law and the solvent obeys Raoult’s law.

The line in Figure 6.9 that represents Henry’s law for ethanol in diethyl ether approx-

imately represents the vapor pressure of ethanol for small values of its mole fraction

(near the left edge of the diagram). This extrapolated line has an intercept of approxi-

mately 160 torr at the right edge of the diagram, which is the value of the Henry’s law

constant for ethanol in diethyl ether at the temperature of the figure.

EXAMPLE 6.4

At 40◦C, a solution of ethanol (component 2) in benzene (component 1) having a mole fraction

of ethanol equal to 0.0200 has a partial vapor pressure of ethanol equal to 30.2 torr. Assuming

that Henry’s law holds at this composition, find the value of the Henry’s law constant for

ethanol in benzene.

Solution

k 2 

P 2

x 2



30 .2 torr

0. 0200

 1. 51 × 103 torr

Exercise 6.9

Find the value of the Henry’s law constant for benzene in ethanol at 40◦C. The partial vapor

pressure of benzene is equal to 12.8 torr if the mole fraction of benzene is equal to 0.0130.

The Chemical Potential in a Dilute Solution

Physical chemists always want to write a single equation that applies to as many

different cases as possible. We would like to write equations similar to Eq. (6.1-8) for

the chemical potential of every component of every solution. Consider a dilute solution

in which the solvent and the solute are volatile. We equilibrate the solution with a vapor

phase, which we assume to be an ideal gas mixture. Using Henry’s law, Eq. (6.2-1), for

the partial vapor pressure of substance numberi(a solute) and using the fundamental

fact of phase equilibrium:

μ

(soln)

i μ

(g)

i μ

◦(g)

i +RTln

(

kixi

P◦

)

(dilute solute)

In order to make this equation resemble Eq. (6.1-8), we write this equation as

μ(soln)i μ◦i(H)+RTln(xi) (dilute solute) (6.2-2)

where we let

μ◦i(H)μ◦i(g)+RTln

(

ki

P◦

)

(6.2-3)

The chemical potentialμ◦i(H)corresponds to a new standard state for a solute, which

we call theHenry’s law standard state. It is equal to the chemical potential that the

pure liquid would have if it had a vapor pressure equal tokiinstead ofPi∗. We specify a