The dimensional formula of the constant ''a'' in Vanderwaals gas eqaution is `(P+(a)/(V^(2)))(V-b)=RT`:

Options

A. `ML^(-5)T^(2)`
B. `ML^(3)T^(-2)`
C. `ML^(2)T^(-1)`
D. `ML^(5)T^(-3)`

Answer

A

Explanation

From the principle of homogeneity, the dimensions of `(a)/(V^(2))="Dimension of P"`
`"Dimension of a"="Dimension of PV"^(2)`
Dimension of `a=[ML^(-1)T^(-2)][L^(3)]^(2)`
`=[ML^(-1)T^(-2)][L^(6)]`
Dimension of `a=[ML^(-5)T^(-2)]`