Question

Match the van der Waal's equation for one mole of gas given in column B to the conditions given in column A.

Column A	Column B
(A) High pressure	(i) $PV=RT+Pb$
(B) Low pressure	(ii) $PV=RT-\frac{a}{V}$
(C) $P\to 0$	(iii) $PV=RT$
(D) Neither $a$ nor $b$ is negligible	(iv) $(P+\frac{a}{V^2})(V-b)=RT$

• A. (A)-(i), (B)-(iv), (C)-(i), (D)-(ii)
• B. (A)-(i), (B)-(ii), (C)-(iii), (D)-(iv)
• C. (A)-(iv), (B)-(iii), (C)-(ii), (D)-(i)
• D. (A)-(iv), (B)-(ii), (C)-(iii), (D)-(i)

Answer 1

The correct option is B (A)-(i), (B)-(ii), (C)-(iii), (D)-(iv)

According to vander waal's equation,
$[P+\frac{n^{2}a}{V^2}][V-nb]=nRT$

At high pressure, $a/V^2$ can be neglected in comparson to P so equation becomes,
$P[V-nb]=nRT$
$PV=nRT+nPb$

At lower pressure: V is large and b is negligible in comparison with V. Then Vander Waalsequation reduces to
$[P+\frac{n^{2}a}{V^2}]\left[V\right]=nRT$

$PV=RT-a/V$

As $P\to 0$
gas behaves like an ideal gas and equation become,
$PV=RT$

And
Neither a nor b is negligible, it is vander waal's equation
$[P+\frac{a}{V^2}][V-b]=RT$