Question

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

Answer 1

Ideal gas law states that gases are made up of point sized particles that are constantly under motion and undergo elastic collisions throughout. However the law fails to explain the contradicting behaviour of real gases from that suggested by the law. So the Van der Waals equation was derived to define the physical properties of a real gas.

Formula used:
The Van der Waals equation for one mole of a real gas can be written as,
$\left( {P + \dfrac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT$
Where, a and b are positive constants known as Van der Waals constants whose values are specific to each gas.

Complete step by step solution:
We know that the Van der Waals equation is a modified form of the ideal gas equation and helps in defining the physical state and properties of a real gas. The ideal gas law neglects the intermolecular forces between gaseous particles and the volume of gas particles. These are taken into consideration in the real gas equation using the Van der Waals constants.
The constant ‘a’ denotes the magnitude of the inter particle forces of attraction and the constant ‘b’ denotes the volume occupied by the particles of gas. Both these values are considered negligible in the ideal gas equation. So, if the constants a and b are small then their respective terms in the real gas equation, i.e., $\dfrac{a}{{{V^2}}}$and $b$, can be neglected as compared to $P$and $V$.
As a result, the equation would reduce to $PV = RT$and thus, resembling the ideal gas equation.

Thus, the correct answer is A.

Note:
The unit of constant ‘a’ is ${\text{atm }}{{\text{L}}^2}{\text{ mo}}{{\text{l}}^{ - 1}}$ and that of constant ‘b’ is ${\text{L mo}}{{\text{l}}^{ - 1}}$. The constant ‘a’ denotes the magnitude of the inter particle forces of attraction and the constant ‘b’ denotes the volume occupied by the particles of gas. Both these values are considered negligible in the ideal gas equation.