Question

For real gas, van der Waals equation is written as:

 $ \left( p+\dfrac{a{{n}^{2}}}{{{V}^{2}}} \right)\left( V-nb \right)=nRT $

Where a and b are van der Waals Constants.

Two sets of gases are:

(I) $ {{O}_{2}} $ , $ C{{O}_{2}} $ , $ {{H}_{2}} $ , and $ He $

(II) $ C{{H}_{4}} $ , $ {{O}_{2}} $ , and $ {{H}_{2}} $

The gases in set I are in increasing order of ‘b’ and gases in set II are in decreasing order of ‘a’ are arranged below. Select the correct order from the following:

(A) (I) $ {{O}_{2}} $ < $ He $ < $ {{H}_{2}} $ < $ C{{O}_{2}} $ ; (II) $ {{H}_{2}} $ > $ {{O}_{2}} $ > $ C{{H}_{4}} $

(B) (I) $ He $ < $ {{H}_{2}} $ < $ {{O}_{2}} $ < $ C{{O}_{2}} $ ; (II) $ C{{H}_{4}} $ > $ {{O}_{2}} $ > $ {{H}_{2}} $

(C) (I) $ {{H}_{2}} $ < $ {{O}_{2}} $ < $ He $ < $ C{{O}_{2}} $ ; (II) $ {{O}_{2}} $ > $ C{{H}_{4}} $ > $ {{H}_{2}} $

(D) (I) $ He $ < $ {{H}_{2}} $ < $ C{{O}_{2}} $ < $ {{O}_{2}} $ ; (II) $ C{{H}_{4}} $ > $ {{H}_{2}} $ > $ {{O}_{2}} $

Answer 1

Hint: In the van der Waals equation, the two factors ‘a’ and ‘b’ designate the magnitude of intermolecular attraction and excluded volume respectively. The intermolecular attraction factor ‘a’ between the gases depends upon the strength of attraction between the component molecules. For multicomponent molecules, the more the number of atoms, the higher is the volume.

Complete step by step answer:

The intermolecular attraction factor ‘a’ between the gases depends upon the strength of attraction between the component molecules. Those molecules that experience the weakest attraction will have the smallest value of the constant while those having the strongest attraction have the largest ‘a’ values. Among the given gases, all the molecules are nonpolar we the attraction between the molecules will be decided on the basis of the size and the number of electrons in the valence shell.

The decreasing order of the size of the molecules is: $ C{{H}_{4}} $ >$ {{O}_{2}} $ > $ {{H}_{2}} $ .

So this will also be the order for the decreasing ‘a’ factor.

Coming to the factor of excluded volume ‘b’ is merely the actual volume of 1 mole of the molecules and this can be deduced by comparing the volumes of the molecules. For multicomponent molecules, the more the number of atoms, the higher is the volume. Otherwise, the volume will depend upon the molecular size of gases.

As the order of the size is:  $ He $ <$ {{H}_{2}} $ < $ {{O}_{2}} $ <$ C{{O}_{2}} $ , so the correct answer is option (B).

Note:

The van der Waals equation was introduced for the real gases when it was seen that the ideal gas equation could not explicitly describe the behaviour of the real gases. This equation accounts for the intermolecular forces of attraction between the molecules which were earlier considered to be absent and also the volume of the molecules I took into consideration.