Q. 34

# For real gases the relation between p, V and T is given by van der Waals equation:P + an2(V - nb) / V2= nRTWhere‘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 magnitude of intermolecular attraction.(i) Arrange the following gases in the increasing order of ‘b’. Give reason. O2, CO2, H2, He(ii) Arrange the following gases in the decreasing order of magnitude of ‘a’. Give reason. CH4, O2, H2

(i) As the Vander Waals constants,‘b’ is approximately equal to the total volume of the molecules of a gas. Hence, the increasing order of ‘b’ is as follows:

He < H2< O2< CO2

This is because the parameter ‘b′ is proportional to the proper volume of a single particle, and the volume of CO2 is maximum followed by O2 which is followed by H2 and He. Or in other words the value of ‘b’ is directly proportional to the size of gas molecules. Hence we get the order shown above.

The volume of CO2 is maximum; this is because CO2 contains 3 atoms, whereas O2 has greater volume than H2 because Oxygen atom has 2 shells whereas H has only one shell. Hence, H is smaller in size than O. And He is having the lowest volume because it is single atom and has only one shell like H, but unlike He, H-H is having greater volume than He.

(ii) The value of‘a’ for any gas depends on the strength of inter molecular attraction. Molecules having the weakest forces of attraction has the smallest value of ‘a’ whereas the molecules having the strongest force of attraction has the largest a values.

Hence, as the surface area of CH4 is highest so, it has highest Vander Waal’s force of attraction so, has highest value of ‘a’, followed by O2 and H2.

So the decreasing order is found to be:

CH4> O2> H2

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