Q$1.$ a$)$ show that the van der Waals equation can be given by the equation $P=\frac{RT}{((\frac{?}{\text{b}\text{a}\text{r}}(V))-b)}-\frac{a}{\frac{?}{\text{b}\text{a}\text{r}}(V{)}^2},$ where $\frac{?}{\text{b}\text{a}\text{r}}(V)=$ molar volume?

b$)$ A gas that behaves ideally has a density of $1\mathrm{.}92gd{m}^{-3}$ at $150$kPa and $298K.$ What is the molar mass of the sample?

Q$2.$ a$)$ Prove that: $\frac{P{V}_c}{T_c}=\frac{3}{8}R?$ Find the critical temperature and critical pressure of the gas?

Q$3.($a$)$ Starting from the main KMT equation show that $\sqrt[\phantom{2}]{\frac{?}{\text{b}\text{a}\text{r}}(u{)}^2}=u_n=m=\sqrt[\phantom{2}]{\frac{3RT}{{}_m}}?$