The molar volume $V(c\frac{m^3}{m}ol)$ of a binary mixture has been correlated from

experimental data: $V=62x_1+37x_2-84x_1{x}_2,$

where $x_1$ and $x_2$ are the mole fractions of components $1$ and $2$ respectively.

a$)$ What are the molar volumes $($in $c\frac{m^3}{m}ol)$ of the pure components $V_1$ and $V_2?$

b$)$ What are the partial molar volumes $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_1$ and $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_2$ for the mixture at $x_1=0\mathrm{.}6.$

c$)$ What are the partial molar volumes at infinite dilution $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_1^{}$ and $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_2^{}?$

d$)$ Sketch $V$ vs$.x_1,$ and show in the graph; i$)$ the values of $V_1$ and $V_2,$ and ii$)\frac{?}{\text{b}\text{a}\text{r}}(V{)}_1\frac{,}{b}ar(V{)}_2$

at $x_1=0\mathrm{.}6$; iii$)\frac{?}{\text{b}\text{a}\text{r}}(V{)}_1^{}$ and $\frac{?}{\text{b}\text{a}\text{r}}(V{)}_2^{}.$ Note: this is only a sketch, it does not need to be a

perfect scale.

e$)$ The following figure has mixing properties $M=M-x_1{M}_1-x_2{M}_2$ for six binary

mixtures.

Based on the figure, answer these questions:

what mixtures from $($a$)$ to $($f$)$ have an exothermic behavior, and what mixtures

have an endothermic behavior?

Is there any common behavior for $G$ in the six binary mixtures?