Consider a monoatomic ideal gas, with Zint = 1. The partition function is then Zmonoatomic ideal gas = i 277m 3N/2VN N N! hm Use F = kT]n Z, the Stirling approximation ]11N! = N ]11N N and the appropriate partial derivative to derive the chemical potential of the monoatomic ideal gas as a function of T, N and V. You may want to compare your result with what you got in Weekly Practice 9. (a) Take the atomic mass of Xenon to be 131 (Xenon has 8 different stable isotopes and many more metastable ones). What is the chemical potential for pure Xe gas at 1 atm and T = 300 K? Use the ideal gas law and give the answer in eV. (b) Flepeat the computation from part (a) if Xe is only 1% (by number density or, equivalently, partial pressure) of a mixture of different gasses. Note: if pure Xenon is allowed to come in contact with the gas in part (b), the net flow of Xenon atoms should be into the mixture. This tells you that your answer to part (b) should be smaller than your answer to part (a)