Concise Physical Chemistry

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

192 SOLUTION CHEMISTRY

π

solvent solution

membrane

FIGURE 12.6 Osmotic pressure,π.

ambient pressureμ◦ 1 (p)plus the change resulting from the increase in pressure to

p+π:

μ◦ 1 (p+π)=μ◦ 1 (p)+

∫ p+π

p

(

∂μ 1

∂p

)

T

dp

The variation of a perfect differential of a thermodynamic function is

dμ=

(

∂μ

∂p

)

T

dp+

(

∂μ

∂T

)

p

dT

but the second term on the right drops out becauseT=const.We shall refer to the

molar volume of solvent asVm, 1 and note that (Klotz and Rosenberg, 2008)

(

∂μ 1

∂p

)

T

=Vm, 1

The Gibbs chemical potential of the pure solvent subjected to a pressure change from

ptop+πat constantVm, 1 is

μ◦ 1 (p+π)=μ◦ 1 (p)+

∫ p+π

p

Vm, 1 dp=μ◦ 1 (p)+πVm, 1