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Q.

The van der Waal's equation for 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 b/a will have the following dimensional formula

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a

$M^{- 1} L^{- 1} T^{- 1}$

b

${MLT}^{- 2}$

c

${ML}^{2} T^{2}$

d

$M^{- 1} L^{- 2} T^{2}$

answer is A.

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Detailed Solution

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$(P + \frac{a}{V^{2}}) (V - b) = nRT$
According to principle of Homogeneity 'b' has the same dimensions of 'V'
b = L³
similarly $\frac{a}{V^{2}}$ has same dimensions of 'P'

$\frac{a}{{[L^{3}]}^{2}} = [{ML}^{- 1} T^{- 2}] \Rightarrow a = [{ML}^{- 1} T^{- 2}] [L^{6}] a = [{ML}^{5} T^{- 2}] \Rightarrow \frac{b}{a} = \frac{L^{3}}{{ML}^{5} T^{- 2}} = [M^{- 1} L^{- 2} T^{2}]$

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