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 dimensional representation of $ab/RT$ is

• A. $M{L}^5{T}^{-2}$
• B. $M^0{L}^3{T}^0$
• C. $M{L}^{-1}{T}^{-2}$
• D. None of these

Answer 1

The correct option is D None of these

We already know,
$\left[a\right]=\left[M{L}^5{T}^{-2}\right]$
$\left[b\right]=\left[L^3\right]$
and
$\left[\frac{ab}{V^2}\right]=\left[RT\right]$
$\left[\frac{ab}{RT}\right]=\left[V^2\right]$

$\therefore \left[\frac{ab}{RT}\right]=\left[L^6\right]$