Question

The van der Waals' equation for $0.5mol$ gas is:

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

Answer 1

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

Using Vanderwaal's equation of real gases and substitute $n=0.5$ we get,

$(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$
For $n=\frac{1}{2},(P+\frac{a}{4V^2})(V-\frac{b}{2})=\frac{1}{2}RT$
$(P+\frac{a}{4V^2})(2V-b)=RT$