For the non-stoichiometric reaction $2A + B \rightarrow C + D,$ the following kinetic data were obtained in three separate experiments,all at $298 \, K.$
Initial Concentration $(A)$ Initial Concentration $(B)$ Initial rate of formation of $C$ $(mol \, L^{-1} \, s^{-1})$
$0.1 \, M$ $0.1 \, M$ $1.2 \times 10^{-3}$
$0.1 \, M$ $0.2 \, M$ $1.2 \times 10^{-3}$
$0.2 \, M$ $0.1 \, M$ $2.4 \times 10^{-3}$

The rate law for the formation of $C$ is:

  • A
    $\frac{d[C]}{dt} = k[A][B]$
  • B
    $\frac{d[C]}{dt} = k[A]^{2}[B]$
  • C
    $\frac{d[C]}{dt} = k[A][B]^{2}$
  • D
    $\frac{d[C]}{dt} = k[A]$

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The experimental data for the reaction $2A + B_2 \to 2AB$ is given below. Determine the rate equation for the reaction.
$Exp.$ $[A]_0$ $[B_2]_0$ $Rate \ (mol \ L^{-1} \ s^{-1})$
$(1)$ $0.50$ $0.50$ $1.6 \times 10^{-4}$
$(2)$ $0.50$ $1.00$ $3.2 \times 10^{-4}$
$(3)$ $1.00$ $1.00$ $3.2 \times 10^{-4}$

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 $[A] = 1 \ M$?

Select the rate law for the reaction $A + B \longrightarrow C$ based on the following data:
$Exp$ $[A]$ $[B]$ $Rate$
$1$ $0.012$ $0.035$ $0.10$
$2$ $0.024$ $0.070$ $0.80$
$3$ $0.024$ $0.035$ $0.10$
$4$ $0.012$ $0.070$ $0.80$

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