Question
A real gas obeying van der Waals equation will resemble ideal gas, if the
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 :
constants $$a$$ and $$b$$ both are small
Solution :
According to van der Waals' equation for $$1\,mole$$ of a real gas, $$\left( {P + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT$$
If $$a$$ and $$b$$ are small, $$\frac{a}{{{V^2}}}$$ and $$b$$ can be neglected as compared to $$P$$ and $$V$$ and the equation reduces to $$PV = RT.$$ Hence, a real gas will resemble an ideal gas when constants $$a$$ and $$b$$ are small.