States of Matter - Result 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
$$ V _A=2 V _B, n _A=n _B \text { and } T _A=T _B $$
$\therefore$ Eq. (ii) becomes
$$ \Rightarrow \quad \begin{aligned} \frac{p _A \times 2 V _B}{n _B R T _B} & =\frac{3 p _B V _B}{n _B R T _B} \ \Rightarrow \quad 2 p _A & =3 p _B \end{aligned} $$
