Question

The Van der Wall equation for $1$ mole of a real gas is $(P+\frac{a}{V^2})(V-b)=RT$ where $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature, $R$ is the molar gas constant and $a,b$ are Van der Wall constants. The dimensions of $a$ are the same as those of :

• A. $PV$
• B. $PV$${}^2$
• C. $P$${}^2$$V$
• D. $P/V$

Answer 1

The correct option is B $PV$${}^2$

As we know that the Vander Wall equation for 1 mole of a real gas is

$(P+\frac{a}{V^2})(V-b)=RT$

We cannot add or subtract quantities of different dimensions. Therefore

$\left[P\right]=\left[a/V^2\right]$

$⟹\left[a\right]=\left[P{V}^2\right]$