The vander waal's equation for a gas is `(p + 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, where a and b are constants. The ratio`b/a` will have the following dimensional formula

Options

A. `[M^(-1)L^(-2)T^(2)]`
B. `[M^(-1)L^(-1)T^(-1)]`
C. `[ML^(2)T^(2)]`
D. `[MLT^(-2)]`

Answer

A

Explanation

According to the principal of homogenity of dimensions, `P = a/V^(2) implies a = PV^(2) = [ML^(-1)T^(-2)][L^(3)]^(2) = [ML^(5)T^(-2)]`
`V = b = L^(3) implies b/a = [L^(3)]/ [ML^(5)T^(-2)] = [M^(-1)L^(-2)T^(2)]`