Question

The dimensional formula for $\frac{ab}{RT}$ is:

• A. $M{L}^5{T}^{-2}$
• B. $M^0{L}^3{T}^0$
• C. $M{L}^{-1}{T}^{-2}$
• D. $M^0{L}^6{T}^0$

Answer 1

The correct option is D $M^0{L}^6{T}^0$

The vander Waals gas equation is $\left(\begin{array}{c}P+\frac{a}{V^2}\end{array}\right)(V-b)=RT$,

where $P$ is the pressure, $V$ is molar volume and $T$ is the temperature of the given sample of gas. $R$ is called molar gas constant, $a$ and $b$ are called van der Waals constants.

$\left(\begin{array}{c}P+\frac{a}{V^2}\end{array}\right)(V-b)=RT$,

$PV+\frac{a}{V}-Pb-\frac{ab}{V^2}=RT$

So, $\left[PV\right]=\left[RT\right];\left[a/V\right]=\left[RT\right];\left[Pb\right]=\left[RT\right];\left[ab/V^2\right]=\left[RT\right]$

Thus, $\left[\frac{ab}{RT}\right]=\left[V^2\right]=M^0{L}^6{T}^0$