Question

Assertion :Compressibility factor Z according to van der Waal's equation may be written as $Z=\frac{1}{1-\left(\frac{nb}{V}\right)}-\frac{an}{RTV}$. Reason: For real gases $Z><1$.

• 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

According to van der Waal's equation,

$(P+\frac{n^{2}a}{V^2})(V-nb)=nRT$

$Z=PV/RT=1+\frac{bP}{RT}-\frac{a}{RTV}+\frac{ab}{RT{V}^2}$

and for real gases

Case 1: Very low pressure: P↓↓⟹V↑↑

(P−a/V2)≈P and (V−b)≈V⟹Z≈1

Case 2: Low-pressure P↓⟹V↑

(V+b)≈V. On solving, we get Z=1+a/(RTV)⟹Z>1.

Case 3: Very high-pressure P↑↑⟹V2↓↓

(P−a/V2)≈P. On solving, we get Z=1−Pb/(RT)⟹Z<1.

Z><1 according to nature of gas as

Thus, Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

Hence, the correct option is $\text{B}$