Concise Physical Chemistry

c12 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

188 SOLUTION CHEMISTRY

Written in terms of Gibbs chemical potentials, this gives us

μ 2 (g)=μ◦ 2 (g)+RTln

p 2

p◦

=μ◦ 2 (g)+RTlnp 2

whereμ◦ 2 (g) is the standard state free energy for an ideal gas at a partial pressurep 2

in a mixture of gases. The analogous expression for an ideal solute at mole fraction

X 2 in a mixture of solutes is

μ 2 (sol)=μ◦ 2 (sol)+RTlnX 2

(We shall usually treat the special case of only one solute dissolved in one solvent.)

Equality of the two Gibbs potentials at equilibrium gives

μ 2 (sol)=μ 2 (g)

μ◦ 2 (g)+RTlnp 2 =μ◦ 2 (sol)+RTlnX 2

or

RTln

p 2

X 2

=μ◦ 2 (sol)−μ◦ 2 (g)

This leads to an expression with only constants on the right-hand side:

ln

p 2

X 2

=

μ◦ 2 (sol)−μ◦ 2 (g)

RT

or

p 2

X 2

=e

μ◦ 2 (sol)−μ◦ 2 (g)

RT =econst=k

which is Henry’s law,p 2 =kX 2. Notice that the difference between Raoult’s law

and Henry’s law is merely in the arbitrary selection of a standard state.

12.7 BOILING POINT ELEVATION

The utility of Henry’s law becomes apparent when we consider a very important

class of binary solutions, the class of nonvolatile solutes in a volatile solvent—for

example, sugar (sucrose) in water. The nonvolatile solute has no measurable vapor

pressure, hence Raoult’s law does not apply because there is nop◦Bin Figs. 12.3 and

12.4. The total vapor pressure is due to the solvent:

p=X 1 p 1 ◦