Suppose you have a mixture of gases (such as air, a

Chapter 3, Problem 38P

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QUESTION:

Problem 38P

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

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QUESTION:

Problem 38P

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

ANSWER:

Step 1 of 4

The partial pressure of any component in the mixture of ideal gas is defined as the fraction of the total pressure.

Here,  is the mole fraction of all molecules of the gas in the mixture of ideal gas and  is the total pressure of the mixture of ideal gas.

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