For a reaction $A + B \rightarrow \text{Product}$,the rate of reaction doubles when the concentration of $A$ is doubled. The rate becomes four times when the concentrations of both $A$ and $B$ are doubled. What is the order of the reaction with respect to $A$ and $B$ respectively?

For a reaction of order $(n - 1)$,what is the relationship between the half-life period $(t_{1/2})$ and the initial concentration of the reactant $([R]_0)$?

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

In a one-component second-order reaction,if the concentration of the reactant is reduced to half,the rate

The rate constants for the following reactions are:
Reaction $1$: $A \xrightarrow{\text{catalyst } 1} P_1, k_1 = 1 \ s^{-1}$
Reaction $2$: $A \xrightarrow{\text{catalyst } 2} P_2, k_2 = 0.1 \ L \ mol^{-1} \ s^{-1}$
Reaction $3$: $A \xrightarrow{\text{catalyst } 3} P_3, k_3 = 0.01 \ L^2 \ mol^{-2} \ s^{-1}$
What is the correct relation between the rates of the reactions at $[A] = 1 \ M$?

The rate constants for first-order and second-order reactions have units of ..... respectively.