The rate constant of esterification is given by $k = k^{\prime} [H_2O]$. If the rate constant $k = 2.0 \times 10^{-3} \ min^{-1}$,calculate $k^{\prime}$. (Assume $[H_2O] = 55.5 \ mol \ L^{-1}$)

If the half-life period of a reaction is inversely proportional to the initial concentration,the order of the reaction is:

For a second-order reaction where both reactants have the same initial concentration,it takes $500 \ s$ for the reaction to be $20\%$ complete. How many seconds will it take for the reaction to be $80\%$ complete (in $s$)?

For a reaction $A \rightarrow 2 B + C$ the half-lives are $100 \ s$ and $50 \ s$ when the concentration of reactant $A$ is $0.5 \ mol \ L^{-1}$ and $1.0 \ mol \ L^{-1}$ respectively. The order of the reaction is (Nearest Integer).

For the reaction,$2A + B \to \text{products}$,when the concentrations of $A$ and $B$ both were doubled,the rate of the reaction increased from $0.3 \ mol \ L^{-1} \ s^{-1}$ to $2.4 \ mol \ L^{-1} \ s^{-1}$. When the concentration of $A$ alone is doubled,the rate increased from $0.3 \ mol \ L^{-1} \ s^{-1}$ to $0.6 \ mol \ L^{-1} \ s^{-1}$. Which one of the following statements is correct?

Write the general reaction,its differential rate equation,and the rate law.