Question

The units of van der Waal's constants $a,\, b$ respectively, are

• A. $L\, atm ^{2} mol ^{-1}$ and $mol ^{-1}$
• B. $L$ atm $mol ^{2}$ and $mol\, L$
• C. $L ^{2}$ atm $mol ^{-2}$ and $mol ^{-1} L$
• D. $L ^{-2} atm ^{-1} mol ^{-1}$ and $L\, mol ^{-2}$

Answer 1

Answer: (C)

van der Waals' equation is $\left(p+\frac{n^{2} a}{V^{2}}\right)(V-n b)=n R T$
$\therefore $ Units of $a=\frac{p V^{2}}{n^{2}}$
$=\frac{\text{atm} \times L^{2}}{\text{mol}^{2}}$
$=L^{2}$ atm mol $^{-2}$
$\therefore $ Units of $b=\frac{V}{n}$
$=\frac{L}{m o l}=m o l^{-1} L$