Question

The vander Waal's equation of a gas is $(P+\frac{a}{V^2})(V-b)=nRT$ where $P,V,R,T$ and $n$ represent the pressure, volume, universal gas constant, absolute temperature and number of moles of a gas respectively, $a$ and $b$ are constants. The ratio $\frac{b}{a}$ will have the following dimensional formula.

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

Answer 1

The correct option is A $M^{-1}{L}^{-2}{T}^2$

Vander's walls equation is given as $(P+\frac{a}{V^2})(v-b)=nRT$

According to the principle of homogeneity is dimension, $\frac{\alpha }{V^2}$ and $b$ should

have dimensional of pressure and volume respecting.

Thus,

$\frac{a}{V^2}=pressure,b=volume$

$a=pressure\times V^2,b=volume$

$\Rightarrow \frac{b}{a}=\frac{volume}{pressure\times V^2}$

$\Rightarrow \frac{b}{a}=\frac{\left[L^3\right]}{\left[M{L}^{-1}{T}^{-2}\right][L^3{]}^2}$

$\Rightarrow \frac{b}{a}=\frac{1}{\left[M{L}^{-1}{T}^{-2}\right]\left[L^3\right]}=\frac{1}{\left[M{L}^2{T}^{-2}\right]}$

$\Rightarrow \frac{b}{a}=\left[M^{-1}{L}^{-2}{T}^2\right]$