Questions

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

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

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

c
${\mathrm{mole}}^{-5/3}{\mathrm{lit}}^{5/3}{time}^{-1}$
d
${\mathrm{mole}}^{2/3}{\mathrm{lit}}^{2/3}{\mathrm{time}}^{-1}$
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detailed solution

Correct option is A

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

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

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