Q. The units of van der Waals’ constants $a,\ b$ respectively, are
A) $L\ {atm}^{2}\ {mol}^{- 1}\ and\ mol\ L^{- 1}$
B) $L\ atm\ {mol}^{2}\ and\ mol\ L^{- 1}$
C) $L^{2}atm\ {mol}^{- 2}\ and\ {mol}^{- 1}\ L$
D) $L^{- 2}\ {atm}^{- 1}\ {mol}^{- 1}\ and\ L\ {mol}^{- 2}$
Explanation
(c)
van der Waals’ equation is
$\left( p + \frac{n^{2}a}{V^{2}} \right)\ (V - nb) = nRT$
$\therefore\ \ Units\ of\ a = \frac{pV^{2}}{n^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{atm\ \times L^{2}}{{mol}^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = L^{2}\ atm\ {mol}^{- 2}$
$\therefore\ \ \ \ Units\ of\ b = \frac{V}{n}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{L}{mol} = {mol}^{- 1}L$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.