Question

A real gas obeying van der Waals equation will resemble ideal gas if:
(A) Constants a and b are small
(B) a is large and b is small
(C) a is small and b is large
(D) Constants a and b are large

Answer 1

Hint: Van der Waals equation was derived by Johannes Diderik van der Waals. It is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases.

Complete step by step answer:
Van der Waals equation is a modified version of the Ideal gas law which states that the gases consist of point masses that undergo perfectly elastic collisions. However, it fails to explain the behaviour of real gases. So the Van der Waals equation was devised and it helps us define the physical state of a real gas.
We know that the ideal gas equation is:
PV = nRT
For a real gas, the Van der Waals equation is written as;
$(P + \dfrac{a}{{{V^2}}})(V - b) = RT$

‘a’ and ‘b’ constants are specific to each gas. These are called van der Waals constants. They have positive values. The constant 'a' represents the magnitude of intermolecular forces of attraction.
While the Van der Waals constant 'b' represents the effective size of the molecules.
If constants ‘a’ and ‘b’ are small, the term $\frac{a}{{{V^2}}}$ and b can be neglected compared to P and V. The equation reduces to PV=RT.
Hence, a real gas will resemble an ideal gas when constants ‘a’ and ‘b’ are small.
So, the correct answer is “Option A”.

Note: The units of constants ‘a’ and ‘b’ are not the same. Unit of “a” is atm $li{t^2}mo{l^{ - 2}}$. Unit of “b” is litre $mo{l^{ - 1}}$.