The total volume of a mixture at a given $T$ and $P$ is given by:

$V=V_1{x}_1+V_2{x}_2-75x_1{x}_2$

The molar volumes of the pure components are $V_1=120\frac{c{m}^3}{\text{m}\text{o}\text{l}}$ and $V_2=25\frac{c{m}^3}{\text{m}\text{o}\text{l}}.$

Please provide the following:

$($a$)$ What is the molar volume $(\frac{c{m}^3}{\text{m}\text{o}\text{l}})$ of a mixture containing $3$ moles of component $1$ and $4$ moles of component $2?$

$($b$)$ What is the total volume $(c{m}^3)$ of a mixture containing $3$ moles of component $1$ and $4$ moles of component $2?$

$($c$)$ What would be the volume $(c{m}^3)$ of a mixture containing $3$ moles of component $1$ and $4$ moles of component $2$ if the solution were an ideal solution?

$($d$)$ What is the excess volume $(c{m}^3)$ of a mixture containing $3$ moles of component $1$ and $4$ moles of component $2?$

$($e$)$ Please sketch the ideal and actual molar volumes $(\frac{c{m}^3}{\text{m}\text{o}\text{l}})$ of this mixture as a function of $x_1,$ with clearly labeled axes.