Medium
From the rate expression for the following reaction,determine its order of reaction and the dimensions of the rate constant.
$H_2 O_2+3 I^{-}+2 H^{+} \rightarrow 2 H_2 O+I_3^{-} \text { Rate }=k\left[H_2 O_2\right]\left[I^{-}\right]$
$H_2 O_2+3 I^{-}+2 H^{+} \rightarrow 2 H_2 O+I_3^{-} \text { Rate }=k\left[H_2 O_2\right]\left[I^{-}\right]$
(N/A) Given Rate $= k[H_2O_2][I^{-}]$
The order of reaction is the sum of the powers of the concentration terms in the rate law expression.
Order $= 1 + 1 = 2$
Dimension of $k = \frac{\text{Rate}}{[H_2O_2][I^{-}]}$
$= \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})(\text{mol L}^{-1})}$
$= \text{L mol}^{-1} \text{s}^{-1}$
The order of reaction is the sum of the powers of the concentration terms in the rate law expression.
Order $= 1 + 1 = 2$
Dimension of $k = \frac{\text{Rate}}{[H_2O_2][I^{-}]}$
$= \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})(\text{mol L}^{-1})}$
$= \text{L mol}^{-1} \text{s}^{-1}$
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The reaction between $X$ and $Y$ is first order with respect to $X$ and zero order with respect to $Y$.
$Experiment$ $[X] / (mol \ L^{-1})$ $[Y] / (mol \ L^{-1})$ $\text{Initial rate} / (mol \ L^{-1} \ min^{-1})$ $I$ $0.1$ $0.1$ $2 \times 10^{-3}$ $II$ $0.2$ $0.2$ $4 \times 10^{-3}$ $III$ $0.4$ $0.4$ $M \times 10^{-3}$ $IV$ $0.1$ $0.2$ $2 \times 10^{-3}$
Examine the data of the table and calculate the ratio of the numerical value of $M$ to $0.2$.
| $Experiment$ | $[X] / (mol \ L^{-1})$ | $[Y] / (mol \ L^{-1})$ | $\text{Initial rate} / (mol \ L^{-1} \ min^{-1})$ |
| $I$ | $0.1$ | $0.1$ | $2 \times 10^{-3}$ |
| $II$ | $0.2$ | $0.2$ | $4 \times 10^{-3}$ |
| $III$ | $0.4$ | $0.4$ | $M \times 10^{-3}$ |
| $IV$ | $0.1$ | $0.2$ | $2 \times 10^{-3}$ |
Examine the data of the table and calculate the ratio of the numerical value of $M$ to $0.2$.
Write the differential rate expression for the following reaction and determine its order of reaction:
$5 Br^{-} + BrO_3^{-} + 6 H^{+} \rightarrow 3 Br_2 + 3 H_2 O$
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