Medium
From the rate expression for the following reaction,determine its order of reaction and the dimensions of the rate constant.
$(i)$ $3 NO_{(g)} \rightarrow N_2O_{(g)}$ Rate $= k[NO]^2$
$(i)$ $3 NO_{(g)} \rightarrow N_2O_{(g)}$ Rate $= k[NO]^2$
(N/A) $(i)$ Given rate $= k[NO]^2$
Therefore,the order of the reaction $= 2$.
The dimension of $k = \frac{\text{Rate}}{[NO]^2}$
$= \frac{\text{mol} \ \text{L}^{-1} \ \text{s}^{-1}}{(\text{mol} \ \text{L}^{-1})^2}$
$= \frac{\text{mol} \ \text{L}^{-1} \ \text{s}^{-1}}{\text{mol}^2 \ \text{L}^{-2}}$
$= \text{L} \ \text{mol}^{-1} \ \text{s}^{-1}$
Therefore,the order of the reaction $= 2$.
The dimension of $k = \frac{\text{Rate}}{[NO]^2}$
$= \frac{\text{mol} \ \text{L}^{-1} \ \text{s}^{-1}}{(\text{mol} \ \text{L}^{-1})^2}$
$= \frac{\text{mol} \ \text{L}^{-1} \ \text{s}^{-1}}{\text{mol}^2 \ \text{L}^{-2}}$
$= \text{L} \ \text{mol}^{-1} \ \text{s}^{-1}$
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