P$.9$ Assume that a sealed vessel at constant pressure of $\frac{1}{b}ar$

initially contains $2\mathrm{.}00$mol of $N{O}_2(g).$ The system is allowed

to equilibrate with respect to the reaction

$2N{O}_2(g)N_2{O}_4(g).$ The number of moles of $N{O}_2(g)$

and $N_2{O}_4(g)$ at equilibrium is $2\mathrm{.}00-2$ and $,$ respectively,

where $$ is the extent of reaction.

a$.$ Derive an expression for the entropy of mixing as a func$-$

tion of $.$

b$.$ Graphically determine the value of $$ for which $S_{\text{m}\text{i}\text{x}\text{i}\text{n}\text{g}}$

has its maximum value.

c$.$ Write an expression for $G_{\text{p}\text{u}\text{r}\text{e}}$ as a function of $.$ Use

Equation $104$ to obtain values of $G_m$ for $N{O}_2$ and $N_2{O}_4.$

d$.$ Plot $G_{\text{m}\text{i}\text{x}\text{t}\text{u}\text{r}\text{e}}=G_{\text{p}\text{u}\text{r}\text{e}}+G_{\text{m}\text{i}\text{x}\text{i}\text{n}\text{g}}$ as a function of $$ for

$T=298K$ and graphically determine the value of $$ for

which $G_{\text{m}\text{i}\text{x}\text{t}\text{u}\text{r}\text{e}}$ has its minimum value. Is this value the

same as for part $($b$)?$