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JEE Advanced levelSingle correct optionDifficulty 3 of 3rg043

The critical density of a van der Waals gas of molar mass $M$ is

A $\frac{M}{3 b}$
B $\frac{M}{b}$
C $\frac{3 M}{b}$
D $\frac{M}{27 b}$

Answer: A

At the critical point the molar volume is

V_{c} = 3 b

. Density is molar mass divided by molar volume, so

ρ_{c} = M / V_{c} = M /3 b

. For example, argon with

b = 0.032 L mo l^{- 1}

gives

ρ_{c} \approx 40/0.096 \approx 0.42 g m L^{- 1}

.

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