Question

Assertion: The compressibility factor for $H_2$​ and $He$ is $(1+\frac{Pb}{RT})$
Reason: The compressibility factor for $H_2$​ and $He$ can be derived from Van der Waal's equation.

• A. Both assertion and reason are correct and reason is the correct explanation for assertion.
• B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
• C. Assertion is correct but reason is incorrect.
• D. Assertion is incorrect but reason is correct.

Answer 1

The correct option is B Both assertion and reason are correct but reason is not the correct explanation for assertion.

The compressibility factor for $H_2$ and $He$ can be derived from Van der Waal's equation which is $(P+\frac{a^2}{V})(V-b)=RT$
The value of $a$ is very small for hydrogen and helium because they have low molar mass.
Thus we can neglect the term $\frac{a^2}{V}$
Hence, the Van der Waal's equation becomes $PV-Pb=RT$
So, the expression for the compressibility factor becomes $Z=\frac{PV}{RT}=(1+\frac{Pb}{RT})$
Althouh the compressiblity factor has been derived using vanderwaal's equation but it does't explain why is it so i.e. due to low molar mass.
Thus, both assertion and reason are correct but reason is not the correct explanation for assertion.