Question

Vander Waal's gas equation is: $(P + \frac{a}{V^2})(V-b) = RT$. The dimensions of constant a as given above are:

• A. $[ML^4T^{-2}]$
• B. $[ML^5T^{-2}]$
• C. $[ML^3T^{-2}]$
• D. $[ML^2T^{-2}]$

Answer 1

Answer: (B)

(B) $[ML^5T^{-2}]$

Answer 2

The principle of dimensional homogeneity states that terms added or subtracted in an equation must have the same dimensions. In the Van der Waals equation, $(P + \frac{a}{V^2})$, the term $\frac{a}{V^2}$ is added to pressure $P$. Therefore, the dimensions of $\frac{a}{V^2}$ must be equal to the dimensions of pressure $P$.

Dimensions of Pressure ($P$) are $[ML^{-1}T^{-2}]$.

Dimensions of Volume ($V$) are $[L^3]$.

Thus, $[\frac{a}{V^2}] = [P]$ implies $\frac{[a]}{[L^3]^2} = [ML^{-1}T^{-2}]$.

Solving for $[a]$: $[a] = [ML^{-1}T^{-2}] \times [L^6] = [ML^5T^{-2}]$.