The critical temperature and critical pressure of a gas are $31°\mathrm{C}$ and $728$ atmospheres respectively.
Calculate the constants $\text{'}\mathrm{a}\text{'}$ and  $\text{'}\mathrm{b}\text{'}.$

Calculate the volume occupied by $2.0$ mole of ${\mathrm{N}}_2$ at $200 \mathrm{K}$ and $8.21$ atm pressure,

if $\frac{{\mathrm{P}}_{\mathrm{C}}{\mathrm{V}}_{\mathrm{C}}}{{\mathrm{RT}}_{\mathrm{C}}}=\frac{3}{8}$ and $\frac{{\mathrm{P}}_{\mathrm{r}}{\mathrm{V}}_{\mathrm{r}}}{{\mathrm{T}}_{\mathrm{r}}}=2.4$.

Using the Van der Waals equation, calculate the pressure of $10.0 \mathrm{mol}$ ${\mathrm{NH}}_3$ gas in a $10.0 \mathrm{L}$ vessel at $27 °\mathrm{C}$.
 

$\left(\mathrm{P}+{\mathrm{n}}^2\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT} \mathrm{a}=4.2 {\mathrm{L}}^2 \mathrm{atm}/{\mathrm{mol}}^2 , \mathrm{b}=0.037 \mathrm{L}/\mathrm{mol}$

The pressure of real gases is less than the  pressure of an ideal gas because of: