Q.

The units of rate constant for the reaction obeying rate expression, $r = k [A] [B]^{2 / 3}$ is

Moderate

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${mole}^{- 2 / 3} {lit}^{2 / 3} {time}^{- 1}$

${mole}^{2 / 3} {lit}^{- 2 / 3} {time}^{- 1}$

${mole}^{- 5 / 3} {lit}^{5 / 3} {time}^{- 1}$

${mole}^{2 / 3} {lit}^{2 / 3} {time}^{- 1}$

answer is A.

(Detailed Solution Below)

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Detailed Solution

Let us consider the problem:
Let the order $= 1 + \frac{2}{3} = \frac{5}{3}$
Hence,
Units of rate constant = mole

$= {mole}^{1 - \frac{5}{3}} {lit}^{\frac{5}{3} - 1} {time}^{- 1} = {mole}^{- 2 / 3} {litre}^{2 / 3} {time}^{- 1}$

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