Match the gases under specified conditions listed in Column I with...

(A) $-p, s(\mathrm{ B})-r$ (C) $-p, q$ (D) $-r$ Explanation van der Waals' equation \left( p+\frac{n^2 a}{V_m^2}\right)\left( V_m-b\right)=n R T For hydrogen gas $(p=200 \mathrm{ atm}, T=273 \mathrm{ K})$ As pressure is large $V_m$ can be assumed small, thus ' $b$ ' can not be ignored, while due to high pressure $a / V_m^2$ can be considered negligible in comparison to $p$. p\left( V_m-b\right)=R T \quad $\text{ and } \quad$ Z=1+$\frac{p b}{R T}$ For hydrogen gas $(p \sim 0, T=273 \mathrm{ K})$ when pressure occurs of low about $1 \mathrm{ atm}$ or less and temperature is not very close to the point of liquification \left[T_c \left(\mathrm{H}}_{2}\right)=33.3\mathrm{ K}\right]gas behaves ideally. For P V=n R T Temperature is close to the point of liquification \left[T_C \left(\mathrm{CO}_2\right)=304.2\right] thus, deviation from ideality appears very high (due to high attractive force of attraction). For real gas with very large molar volume. As molar volume is very large $a / V_m^2$ will be negligible and at the same time ' $b$ ' in comparison to $V_m$ is also considered negligible, thus, $p V_m=n R T$