Question

In van der Waals, an equation of state of the gas law, the constant b is a measure of:
(A) intermolecular repulsions
(B) intermolecular attraction
(C) volume occupied by the molecules
(D) intermolecular collisions per unit volume

Answer 1

We will attempt this question with the help of Van der Waals gaseous equation. As we know that Van der Waals equation is an equation that gives the relationship between the pressure, volume, temperature, and amount of real gases taking into consideration the molecular size and the molecular interaction forces.

Complete answer:
Let us begin this solution with the concept of Van der Waals gaseous equation:-
- As we know that Van der Waals equation is an equation that gives the relationship between the pressure (P), volume (V), temperature (T), and amount of real gases (n) taking into consideration the molecular size and the molecular interaction forces (attractive and repulsive forces). Mathematically for a real gas containing ‘n’ moles, the equation is written as:-
$(P+\dfrac{a{{n}^{2}}}{{{V}^{2}}})(V-nb)=nRT$
where, ‘a’ and ‘b’ are constants specific for each gas.
There were 2 corrections made for real gases which lead to the formation of Van der Waals equation:-
(A)Volume Correction: Since the particles have a definite volume, the volume available for their movement is less than the entire container which means volume in the ideal gas is hence an overestimation and has to be reduced for real gases which is shown below:-
${{V}_{correction}}=nb$
(B)Pressure Correction: As we know that real gas particles do interact. The interactions for inside particles cancel each other but the particles on the surface and near the walls of the container do not have particles above the surface and on the walls due to which there will be net interactions or pulling of the bulk molecules towards the bulk that is away from the walls and surface. Hence the particles exhibit lower pressure in case of real gas than shown by ideal gas which is shown as:-
${{P}_{correction}}=a\dfrac{{{n}^{2}}}{{{V}^{2}}}$
-From the above data, we conclude that constant ‘b’ is a measure of: (C) volume occupied by the molecules.
So, the correct answer is “Option C”.

Note:
-Merits of Van der Waals Equation of State are that it is able to predict the behavior of gases better than the ideal gas equation and is applicable not only to gases but also tol fluids as well.
-Demerits of Van der Waals Equation is that this equation gives more accurate results of all real gases only above critical temperature but the results are only acceptable below the critical temperature.