Q. If pressure of $CO_{2}$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4b^{2}},$ then mass of the gas in container is

A) $11\ g$
B) $22\ g$
C) $33\ g$
D) $44\ g$
Explanation

(b) Vander Waal’s gas equation for $\mu$ mole of real gas
$\left( P + \frac{\mu^{2}a}{V^{2}} \right)(V - \mu b) = \mu RT$
$P = \left( \frac{\mu RT}{V - \mu b} - \frac{\mu^{2}a}{V^{2}} \right)$
Given equation,
$P = \left( \frac{RT}{2V - b} = \frac{a}{4b^{2}} \right)$
On comparing the given equation with this standard equation, we get
$\mu = \frac{1}{2}$
Hence $,\ \mu = \frac{m}{M}$
$\Rightarrow mass\ of\ gas,\ m = \mu M = \frac{1}{2} \times 44 = 22g$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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