$(a)$ Write the general reaction and derive the units of the rate constant. $(b)$ Based on that,write the rate constant units for zero,first,and $2^{nd}$ order reactions.

(N/A) General Reaction: $aA + bB \rightarrow cC + dD$
The differential rate expression for the general reaction is:
Rate $= -\frac{d[R]}{dt} = k[A]^x[B]^y \quad \dots (i)$
$\therefore k = \frac{\text{Rate}}{[A]^x[B]^y}$
Where,the order of reaction $(x+y) = n$ and $n = 0, 1, 2, 3, \frac{1}{2}, \frac{3}{2}, \dots$ etc.
The $SI$ units of concentration are $mol \ L^{-1}$ and time is $s$.
Unit of $k = \frac{\text{concentration}}{\text{time}} \times \frac{1}{(\text{concentration})^n}$
$= \frac{mol \ L^{-1}}{s} \times \frac{1}{(mol \ L^{-1})^n}$
$\therefore$ Unit of $k = (mol \ L^{-1})^{(1-n)} \ s^{-1}$
Where,$n =$ order of the reaction.

$Order \ of \ reaction \ (n)$	$Unit \ of \ k \ (mol \ L^{-1})^{(1-n)} \ s^{-1}$
$Zero \ (0)$	$mol \ L^{-1} \ s^{-1}$
$First \ (1)$	$s^{-1}$
$Second \ (2)$	$mol^{-1} \ L \ s^{-1}$