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

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

Tardigrade Admin · Accepted Answer

van der Waals' equation is (p+(n2 a/V2))(V-n b)=n R T ∴ Units of a=(p V2/n2) =( textatm × L2/ textmol2) =L2 atm mol -2 ∴ Units of b=(V/n) =(L/m o l)=m o l-1 L

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

$L a t m^{2} m o l^{- 1}$ and $m o l^{- 1}$

$L$ atm $m o l^{2}$ and $m o l L$

$L^{2}$ atm $m o l^{- 2}$ and $m o l^{- 1} L$

$L^{- 2} a t m^{- 1} m o l^{- 1}$ and $L m o l^{- 2}$

van der Waals' equation is $(p + \frac{n ^{2} a}{V ^{2}}) (V - nb) = n RT$
$∴$ Units of $a = \frac{p V ^{2}}{n ^{2}}$
$= \frac{atm \times L ^{2}}{mol ^{2}}$
$= L^{2}$ atm mol $^{- 2}$
$∴$ Units of $b = \frac{V}{n}$
$= \frac{L}{m o l} = m o l^{- 1} L$

Q. The units of van der Waal's constants a,b respectively, are

Latm2mol−1 and mol−1

L atm mol2 and molL

L2 atm mol−2 and mol−1L

L−2atm−1mol−1 and Lmol−2