Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS

Therefore The Gibbs potential of themixture

161

where are partial pressures correspondingto particles
A and B, respectively. So,

It can be seen that

namely

where (see alsoProblem4.54).

b) Toderive thepressuredifference, wenoticethat for thesystemwith

a semipermeable membrane, only the chemical potentials of the solvent

are equal, whereas the chemicalpotentials of the solute do nothave to be

(since theycannotpenetrate through themembrane). Wewill writefirst

the Gibbsfreeenergy on the left and right of the membrane, and

respectively. will bedefined by(S.4.56.6),with whereas

The chemicalpotentials of the solvent aregiven by

Equating weobtain