Question

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$
Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.

The dimensions of $a$ are

• A. $M{L}^5{T}^{-2}$
• B. $M{L}^{-1}{T}^{-2}$
• C. $L^3$
• D. $L^6$

Answer 1

The correct option is A $M{L}^5{T}^{-2}$

From the given equation we can say:
$\left[P\right]=\frac{\left[a\right]}{\left[V^2\right]}$
Here, $P$ is pressure and $V$ is volume.
So, $\left[P\right]=\left[M{L}^{-1}{T}^{-2}\right]$ and $\left[V\right]=\left[L^3\right]$

$\left[a\right]=\left[P\right].[V{]}^2$
$\left[a\right]=\left[M{L}^{-1}{T}^{-2}\right][L^3{]}^2$
$\left[a\right]=\left[M{L}^5{T}^{-2}\right]$