For a reaction $2 \ A + B \rightarrow P$, when the concentration of $B$ alone is doubled, the rate does not change, and when the concentrations of both $A$ and $B$ are doubled, the rate increases by a factor of $4$. The unit of the rate constant is,

What is the order of reaction $A + B \to C$?

Observation	$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Rate $(mol \ L^{-1} \ sec^{-1})$
$1$	$0.1$	$0.1$	$2 \times 10^{-3}$
$2$	$0.4$	$0.1$	$3.2 \times 10^{-3}$
$3$	$0.1$	$0.2$	$8 \times 10^{-3}$

$(a)$ 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.

$t_{1/2} =$ constant confirms the first order reaction. If $a^2 t_{1/2} =$ constant,it confirms that the order of reaction is ($a =$ initial concentration of reactant).

For the reaction $Cl_{2(aq)} + H_2S_{(aq)} \to S_{(s)} + 2H^+_{(aq)} + 2Cl^-_{(aq)}$, the rate law is given by $\text{Rate} = K[Cl_2][H_2S]$. Which of the following mechanisms is consistent with this rate law?
$(A)$ $Cl_2 + H_2S \to H^+ + Cl^- + Cl^+ + HS^-$ (slow); $Cl^+ + HS^- \to H^+ + Cl^- + S$ (fast)
$(B)$ $H_2S \rightleftharpoons H^+ + HS^-$ (fast equilibrium); $Cl_2 + HS^- \to 2Cl^- + H^+ + S$ (slow)

Give two examples of zero-order reactions and two examples of first-order reactions.