Write the unit of the rate constant for the following reactions:
$1.$ $\frac{1}{2}$ order
$2.$ $\frac{3}{2}$ order

The general formula for the unit of the rate constant $k$ for a reaction of order $n$ is given by:
Unit $= (mol \ L^{-1})^{1-n} \ s^{-1}$
$1.$ For a reaction of order $n = \frac{1}{2}$:
Unit $= (mol \ L^{-1})^{1 - 1/2} \ s^{-1} = (mol \ L^{-1})^{1/2} \ s^{-1} = mol^{1/2} \ L^{-1/2} \ s^{-1}$
$2.$ For a reaction of order $n = \frac{3}{2}$:
Unit $= (mol \ L^{-1})^{1 - 3/2} \ s^{-1} = (mol \ L^{-1})^{-1/2} \ s^{-1} = mol^{-1/2} \ L^{1/2} \ s^{-1}$