States of Matter 1 Question 7
7. The volume of gas $A$ is twice than that of gas $B$. The compressibility factor of gas $A$ is thrice than that of gas $B$ at same temperature. The pressures of the gases for equal number of moles are
(2019 Main, 12 Jan I)
(a) $p_{A}=2 p_{B}$
(b) $2 p_{A}=3 p_{B}$
(c) $p_{A}=3 p_{B}$
(d) $3 p_{A}=2 p_{B}$
Show Answer
Solution:
- Given, $Z_{A}=3 Z_{B}$
Compressibility factor $(Z)=\frac{p V}{n R T}$ [for real gases]
On substituting in equation (i), we get
$$ \frac{p_{A} V_{A}}{n_{A} R T_{A}}=\frac{3 p_{B} V_{B}}{n_{B} R T_{B}} $$
Also, it is given that
$$ V_{A}=2 V_{B}, n_{A}=n_{\mathrm{B}} \text { and } T_{A}=T_{B} $$
$\therefore$ Eq. (ii) becomes
$$ \Rightarrow \quad \begin{aligned} \frac{p_{A} \times 2 V_{B}}{n_{B} R T_{B}} & =\frac{3 p_{B} V_{B}}{n_{B} R T_{B}} \ \Rightarrow \quad 2 p_{A} & =3 p_{B} \end{aligned} $$
