The unit of rate constant for -2.5 order reaction is:

$ (\text{mol}\ \text{L}^{-1})^{7/2}\ \text{s}^{-1} $

The correct answer is Option (2) → $ (\text{mol}\ \text{L}^{-1})^{7/2}\ \text{s}^{-1} $

For an $n$-th order reaction, the unit of the rate constant $k$ is given by:

$\text{Unit of } k = (\text{concentration})^{1-n} \cdot (\text{time})^{-1}$

Since concentration is expressed in $\text{mol}\ \text{L}^{-1}$ and time in seconds ($\text{s}$):

$\text{Unit of } k = (\text{mol}\ \text{L}^{-1})^{1-n}\ \text{s}^{-1}$

Given $n = -2.5$:

$1 - n = 1 - (-2.5) = 1 + 2.5 = 3.5 = \frac{7}{2}$

$\text{Unit of } k = (\text{mol}\ \text{L}^{-1})^{7/2}\ \text{s}^{-1}$