Problem 3.38. Suppose you have a mixture of gases (such as air, a mixture of nitrogen and oxygen). The mole fraction x; of any species i is defined as the fraction of all the molecules that belong to that species: x; = Ni/Ntotal. The partial pressure P; of species i is then defined as the corresponding fraction of the total pressure: P; = x;P. Assuming that the mixture of gases is ideal, argue that the chemical potential l; of species i in this system is the same as if the other gases were not present, at a fixed partial pressure P;.
Problem 3.38. Suppose you have a mixture of gases (such as air, a mixture of nitrogen and oxygen). The mole fraction x; of any species i is defined as the fraction of all the molecules that belong to that species: x; = Ni/Ntotal. The partial pressure P; of species i is then defined as the corresponding fraction of the total pressure: P; = x;P. Assuming that the mixture of gases is ideal, argue that the chemical potential l; of species i in this system is the same as if the other gases were not present, at a fixed partial pressure P;.
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Transcribed Image Text:Problem 3.38. Suppose you have a mixture of gases (such as air, a mixture of
nitrogen and oxygen). The mole fraction x; of any species i is defined as the
fraction of all the molecules that belong to that species: x; = Ni/Ntotal. The
partial pressure P; of species i is then defined as the corresponding fraction of
the total pressure: P; = x;P. Assuming that the mixture of gases is ideal, argue
that the chemical potential l; of species i in this system is the same as if the other
gases were not present, at a fixed partial pressure P;.
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