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} $

Units of rate constant

For a general reaction

$\text{aA}+\text{bB}\rightarrow\text{cC}+\text{dD}$

$\text{Rate}=k[\text{A}]^{x}[\text{B}]^{y}$

Where $x+y=n$ = order of the reaction

$k=\frac{\text{Rate}}{[\text{A}]^{x}[\text{B}]^{y}}$

$=\frac{\text{concentration}}{\text{time}}\times\frac{1}{(\text{concentration})^{n}}\quad(\text{where }[\text{A}]=[\text{B}])$

For a -2.5 order reaction

$n = -2.5$

$k=(\text{concentration}/\text{time})\times(\text{concentration})^{2.5}=(\text{concentration})^{3.5}/\text{time}$

$\text{units}=(\text{mol}\ \text{L}^{-1})^{3.5}\ \text{s}^{-1}=(\text{mol}\ \text{L}^{-1})^{7/2}\ \text{s}^{-1}$