From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.

$(i)$ $3 NO ( g ) \rightarrow N _{2} O$ $(g)$ Rate $=k[ NO ]^{2}$

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$(i)$ Given rate $=k[ NO ]^{2}$

Therefore, order of the reaction $=2$

Dimension of $k=\frac{\text { Rate }}{[ NO ]^{2}}$

$=\frac{\operatorname{mol}\, L^{-1} \,s^{-1}}{\left(\operatorname{mol}\, L^{-1}\right)^{2}}$

$=\frac{\operatorname{mol}\, L^{-1} \,s^{-1}}{\operatorname{mol}^{2} \,L^{-2}}$

$=L \,m o l^{-1}\, s^{-1}$

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