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) $3 p _A=2 p _B$

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Solution:

  1. 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

$$ \Rightarrow \quad \begin{aligned} \frac{p _A \times 2 V _B}{n _B R T _B} & =\frac{3 p _B V _B}{n _B R T _B} \ \Rightarrow \quad 2 p _A & =3 p _B \end{aligned} $$



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