The reaction,$X + 2Y + Z \to N$ occurs by the following mechanism:
$(i)$ $X + Y \rightleftharpoons M$ (very rapid equilibrium)
$(ii)$ $M + Z \to P$ (slow)
$(iii)$ $P + Y \to N$ (very fast)
What is the rate law for this reaction?

The hypothetical reaction : $2A + B \to C + D$ is catalyzed by $E$ as indicated in the possible mechanism below -
Step-$1$ : $A + E \rightleftharpoons AE$ (fast)
Step-$2$ : $AE + A \to A_2 + E$ (slow)
Step-$3$ : $A_2 + B \to C + D$ (fast)
What rate law best agrees with this mechanism?

How can you determine the rate law of the following reaction?
$2 \, NO \, (g) + O_2 \, (g) \to 2 \, NO_2 \, (g)$

Considering the reaction $aG + bH \rightarrow \text{Products}$,when the concentrations of both reactants $G$ and $H$ are doubled,the rate increases by $8$ times. However,when the concentration of $G$ is doubled while the concentration of $H$ remains constant,the rate doubles. What is the overall order of the reaction?

The three experimental data for determining the differential rate of reaction $Cl_{2(g)} + 2NO_{(g)} \rightarrow 2NOCl_{(g)}$ at $310 \ K$ temperature are provided. $(a)$ Derive the differential rate of reaction. $(b)$ Calculate the order of reaction. $(c)$ Calculate the value of the rate constant.

Consider a reaction $aG + bH \rightarrow$ Products. When the concentration of both reactants $G$ and $H$ is doubled,the rate increases by $8$ times. However,when the concentration of $G$ is doubled keeping the concentration of $H$ fixed,the rate is doubled. The overall order of the reaction is: