Chapter 3.5, Problem 38P

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: $x_i=N_i\text{/}{N}_{total}$. 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 of 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 $P_i$.