For the reaction $A + B \longrightarrow \text{product}$,the rate law equation is $\text{rate} = k[A]^2[B]$. If the rate of reaction is $0.22 \ mol \ L^{-1} \ s^{-1}$,calculate the rate constant $k$. Given: $[A] = 1 \ mol \ L^{-1}, [B] = 0.25 \ mol \ L^{-1}$.
- A$0.44 \ mol^{-2} \ L^2 \ s^{-1}$
- B$0.88 \ mol^{-2} \ L^2 \ s^{-1}$
- C$1.136 \ mol^{-2} \ L^2 \ s^{-1}$
- D$3.52 \ mol^{-2} \ L^2 \ s^{-1}$
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$Experiment$ $[X] / (mol \ L^{-1})$ $[Y] / (mol \ L^{-1})$ $\text{Initial rate} / (mol \ L^{-1} \ min^{-1})$ $I$ $0.1$ $0.1$ $2 \times 10^{-3}$ $II$ $0.2$ $0.2$ $4 \times 10^{-3}$ $III$ $0.4$ $0.4$ $M \times 10^{-3}$ $IV$ $0.1$ $0.2$ $2 \times 10^{-3}$
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| $Experiment$ | $[X] / (mol \ L^{-1})$ | $[Y] / (mol \ L^{-1})$ | $\text{Initial rate} / (mol \ L^{-1} \ min^{-1})$ |
| $I$ | $0.1$ | $0.1$ | $2 \times 10^{-3}$ |
| $II$ | $0.2$ | $0.2$ | $4 \times 10^{-3}$ |
| $III$ | $0.4$ | $0.4$ | $M \times 10^{-3}$ |
| $IV$ | $0.1$ | $0.2$ | $2 \times 10^{-3}$ |
Examine the data of the table and calculate the ratio of the numerical value of $M$ to $0.2$.
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