Consider a closed containing a solid in equilibrium with its vapor. The volume of the solid is much less than that of the container. Let the partition function of the solid be given by Q-qss where Ns is the number of molecules in the solid phase. Minimize the total Helmholtz free energy at fixed N, V, and T, and show that the equilibrium condition is given by Ng=qo/q2 where Ng is the number of gas phase molecules and qg is the partition function of a gas phase molecule.

Lab reagent, hypothesis test.a reference solution used as a lab reagent is purported to have a concentration of 5 mg/dl. six samples are taken from this solution and the following concentrations are recorded: (5.32, 4.88, 5.10, 4.73, 5.15, 4.75) mg/dl.these six measurements are assumed to be an srs of all possible measurements from solution.they are also assumed to have a standard deviation of 0.2, a normal distributin, and a mean concentration equal to the true concentration of the solution.carry out a significance test to determine whether these six measurements provide reliable evidence that the true concentration of the solution is actually not 5 mg/dl.