Question

The van der Waals' equation for $\left(\frac{1}{2}\right)$ mole of a gas is:

• A. $(P+\frac{a}{V^2})(V-b)=RT$
• B. $(P+\frac{a}{4V^2})(V-\frac{b}{2})=\frac{RT}{2}$
• C. $(P+\frac{a}{4V^2})\left(\frac{V-b}{2}\right)=RT$
• D. $(P+\frac{a}{4V^2})\left(\frac{V-b}{2}\right)=2RT$

Answer 1

The correct option is B $(P+\frac{a}{4V^2})(V-\frac{b}{2})=\frac{RT}{2}$

Vander Waal's $e{q}^n$ is:
$\left(P+\frac{a{n}^2}{V^2}\right)(V-nb)=nRT$
For $n=1$
$\left(P+\frac{a}{V^2}\right)(V-b)=RT$
When $n=\frac{1}{2}$
$\left(P+\frac{a}{4V^2}\right)(V-\frac{b}{2})=\frac{RT}{2}$
$\left(P+\frac{a}{4V^2}\right)(2V-b)=RT$