Question

The Van der Waal's equation of ${}^{\prime }{n}^{\prime }$ moles of a real gas is
$(P+\frac{a}{V^2})(V-b)=nRT$
Where $P$ is pressure, $V$ is volume, $T$ is absolute temperature, $R$ is molar gas constant and $a,b,c$ are Van der Waal constants. The dimensional formula for $ab$ is:

• A. [$M{L}^8{T}^{-2}$]
• B. [$M{L}^6{T}^{-2}$]
• C. [$M{L}^4{T}^{-2}$]
• D. [$M{L}^2{T}^{-2}$]

Answer 1

The correct option is A [$M{L}^8{T}^{-2}$]

Since, the dimensions of $P$ must be same as $\frac{a}{V^2}$,
Hence,

$\frac{\left[a\right]}{L^6}=\left[M{L}^{-1}{T}^{-2}\right]$

$\left[a\right]=\left[M{L}^5{T}^{-2}\right]$

Also, dimension of $b$ must be same as that of $V$. Hence, $\left[b\right]=L^3$.

Thus, $\left[ab\right]=\left[M{L}^8{T}^{-2}\right]$