First slide

Temperature and heat-thermal properties of matter

Question

If pressure of CO₂ (real gas) in a container is given by $P = \frac{RT}{2 V - b} - \frac{a}{4 b^{2}}$ then mass of the gas in container is

Moderate

A

11 gm
B

22 gm
C

33 gm
D

44 gm

Solution

Vander wall's gas equation for $μ$ mole of real gas
$(P + \frac{μ^{2} a}{V^{2}}) (V - μb) = μRT \Rightarrow P = \frac{μRT}{V - μb} - \frac{μ^{2} a}{V^{2}}$ on comparing the given equation with this standard equation we get $μ = \frac{1}{2}$ . Hence $μ = \frac{m}{M}$ $\Rightarrow$ mass of gas $m = μm = \frac{1}{2} \times 44 = 22 gm .$

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