# From the rate expression for the following reactions,

Question:

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

(i) 3 NO(g) → N2O (g) Rate = k[NO]2

(ii) H2O(aq) + 3 I− (aq) + 2 H+ → 2 H2O (l) +  Rate = k[H2O2][I]

(iii) CH3CHO(g) → CH4(g) + CO(g) Rate = [CH3CHO]3/2

(iv) C2H5Cl(g) → C2H4(g) + HCl(g) Rate = [C2H5Cl]

Solution:

(i) Given rate = [NO]2

Therefore, order of the reaction = 2

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

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

$=\frac{\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}}{\mathrm{~mol}^{2} \mathrm{~L}^{-2}}$

$=\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}$

(ii) Given rate [H2O2] [I]

Therefore, order of the reaction = 2

Dimension of $k=\frac{\text { Rate }}{\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\left[\mathrm{I}^{-}\right]}$

$=\frac{\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}}{\left(\mathrm{~mol} \mathrm{~L}^{-1}\right)\left(\mathrm{mol} \mathrm{L}^{-1}\right)}$

$=\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}$

(iii) Given rate [CH3CHO]3/2

Therefore, order of reaction $=\frac{3}{2}$

Dimension of $k=\frac{\text { Rate }}{\left[\mathrm{CH}_{3} \mathrm{CHO}\right]^{\frac{3}{2}}}$

$=\frac{\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}}{\left(\mathrm{~mol} \mathrm{~L}^{-1}\right)^{\frac{3}{2}}}$

$=\frac{\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}}{\mathrm{~mol}^{\frac{3}{2}} \mathrm{~L}^{-\frac{3}{2}}}$

$=L^{\frac{1}{2}} \mathrm{~mol}^{-\frac{1}{2}} \mathrm{~s}^{-1}$

(iv) Given rate [C2H5Cl]

Therefore, order of the reaction = 1

Dimension of $k=\frac{\text { Rate }}{\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right]}$

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

$=\mathrm{s}^{-1}$