$(16$ pts$)$ Start from $[A-A(0)]=-kTlnQ,$

a$)(8$ pts$)$ Derive an expression for $([A{m}_{m-Am}(0)])$ in terms of $N_2(g)$ molecule $($indistinguishable$).$

b$)(8$ pts$)$ Calculate the numerical value of $([A_m-A_m(0)])$ for $N_2(g)$ at $298K.$ Show your work.

Given that $B=1\mathrm{.}99c{m}^{-1},=2358c{m}^{-1},M=28\frac{g}{m}ol.$