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Q.

The Vander 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

$(p + \frac{a}{v^{2}}) (v - b) = NRT p and \frac{a}{v^{2}} are same dimensional quantities. [v] = [b] [b] = [L^{3}] [p] = [\frac{a}{v^{2}}] [a] = [{ML}^{- 1} T^{- 2}] [L^{6}] [a] = [M^{1} L^{5} T^{- 2}] \frac{[b]}{[a]} = \frac{[L^{3}]}{[M^{1} L^{5} T^{- 2}]} = [M^{- 1} L^{- 2} T^{2}]$

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The Vander waal’s equation for a gas is p+av2v−b=nRTwhere 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