Question

For real gases the relation between, P, V and T is given by van der Waals' equation

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

where 'a' and 'b' are van der Waals' constants, 'nb' is approximately equal to the total volume of the molecules of a gas. 'a' is the measure of the magnitude of intermolecular attraction.

(i) Arrange the following gases in the increasing order of 'b' Give reason.

$O_2,C{O}_2,H_2,He$

(ii) Arrange the following gases in the descending order of magnitude of 'a'. Give reason.

$C{H}_4,O_2,H_2$

Answer 1

(i) The molar volume occupied by the gas molecules $\propto$ size of the molecules and van der Waals' constant 'b' represents the molar volume of the gas molecules. Hence, the value of 'b' increases in the following order

$H_2<He<O_2<C{O}_2$

(ii) van der Waals' constant 'a' is the measure of the magnitude of intermolecular attraction. The magnitude of intermolecular increases with increase in the size of the electron cloud in a molecule. Hence, for the given gases magnitude of 'a' decreases in the following order

$C{H}_4>O_2>H_2$

Greater the size of the electron cloud, greater is the polarisability of the molecule and greater is the dispersion forces or London forces.