The unit of the van der Waals gas equation parameter 'a' in $\left(P+\frac{an^{2}}{V^{2}}\right)(V-nb)=nRT$ is :

(B) $\mathrm{dm}^{3}\mathrm{~mol}^{-1}$

(C) $\mathrm{kg}\mathrm{~m}\mathrm{~s}^{-1}$

(D) $\mathrm{kg}\mathrm{~m}\mathrm{~s}^{-2}$

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · States of Matter

The unit of the van der Waals gas equation parameter 'a' in

(P + \frac{a n ^{2}}{V ^{2}}) (V - nb) = n R T

is :

(A)atm dm $^{6}$ mol $^{- 2}$ ✓ Correct
(B) $dm^{3} mol^{- 1}$
(C) $kg m s^{- 1}$
(D) $kg m s^{- 2}$

Answer: (A)

Solution

The term

\frac{a n ^{2}}{V ^{2}}

is added to pressure, so it must itself have the units of pressure. Hence

a = \frac{P V ^{2}}{n ^{2}}

, whose units are

\frac{atm ( d m ^{3} ) ^{2}}{mo l ^{2}} = atm d m^{6} mo l^{- 2}

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Single correct option

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