An Introduction to Thermal Physics · Problem 3.38

Interactions and Implications — Daniel Schroeder

Physics — Statistical Mechanics · chemical-potential-gas-mixture

Problem

Suppose you have a mixture of gases (such as air, a mixture of nitrogen and oxygen). The mole fraction

x_i

of any species

i

is defined as the fraction of all the molecules that belong to that species:

x_i = N_i/N_{\text{total}}

. The partial pressure

P_i

of species

i

is then defined as the corresponding fraction of the total pressure:

P_i = x_i P

. Assuming that the mixture of gases is ideal, argue that the chemical potential

\mu_i

of species

i

in this system is the same as if the other gases were not present, at a fixed partial pressure

P_i