What is the formula for the chemical potential of a perfect gas?

The formula for the chemical potential of a perfect gas is expressed as:

μ = μ* + RT ln(p/p*)

In this context, μ represents the chemical potential of the gas, μ* is the standard chemical potential, R is the ideal gas constant, T is the absolute temperature, and p is the pressure of the gas, while p* refers to the standard pressure.

This equation illustrates how the chemical potential of a gas is influenced by its pressure relative to some standard pressure. The term RT ln(p/p*) captures the contribution to the chemical potential due to deviations from the standard state. When the pressure of the gas increases above the standard pressure, the logarithmic term becomes positive, increasing the chemical potential. Conversely, if the pressure is below the standard, the logarithmic term is negative, decreasing the chemical potential.

Understanding this formula is crucial because it helps elucidate how the chemical potential varies in response to changes in pressure, which is a fundamental concept in thermodynamics and physical chemistry.

In comparison, the other choices refer to different variables such as composition (mole fraction), volume, and mass, which are not the correct parameters for describing the chemical potential in the context of a perfect gas. Hence, they do not represent the relationship accurately