88. From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants
(i) 3NO(g) → N₂O (g) Rate = k[NO]²
(ii) H₂O₂ (aq) + 3I^– (aq) + 2H⁺ → 2H₂O (l) + I^-₃ Rate = k[H₂O₂][I^-]
(iii) CH₃CHO (g) → CH₄ (g) + CO(g) Rate = k [CH₃CHO]3/2
(iv) C₂H₅Cl (g) → C₂H₄ (g) + HCl (g) Rate = k [C₂H₅Cl]

(c) Rate = k[CH₃CHO]^3/2
Order w.r.t., CH₃CHO = 3/2 = 1.5
Overall order of reaction = 1.5
Rate constant,
$$\begin{gathered} \mathrm{k} = \frac{\mathrm{Rate}}{[{\mathrm{CH}}_3\mathrm{CHO}{]}^{3/2}} = \frac{\mathrm{conc}./\mathrm{time}}{\mathrm{conc}{.}^{3/2}} \\ = \frac{1}{\mathrm{conc}{.}^{1/2}\times \mathrm{s}} = \frac{1}{(\mathrm{mol} {\mathrm{L}}^{-1}{)}^{1/2}\mathrm{s}} \\ = {\mathrm{L}}^{1/2} {\mathrm{mol}}^{-1/2} {\mathrm{s}}^{-1} \end{gathered}$$   
The dimensions of rate constant, k are L^1/2 mol^–1/2 s^–1.

(d) Rate  = $\mathrm{k}\left[{\mathrm{CHCl}}_3\right] [{\mathrm{Cl}}_2{]}^{1/2}$
Order w.r.t. $\left[{\mathrm{CHCl}}_3\right] = 1$
Order w.r.t. ${\mathrm{Cl}}_2\left(\mathrm{g}\right) = \frac{1}{2}= 0.5$
Overall order of reaction  = 1+0.5 = 1.5
Rate constant,
$$\begin{gathered} \mathrm{k}= \frac{\mathrm{Conc}./\mathrm{time}}{\left[{\mathrm{CHCl}}_3\right] {\left[{\mathrm{Cl}}_2\right]}^{1/2}} =\frac{\mathrm{conc}./\mathrm{time}}{\mathrm{conc}{.}^{3/2}} \\ = \frac{1}{(\mathrm{mol} {\mathrm{L}}^{-1}{)}^{1/2} \mathrm{x} \mathrm{s}} \\ = {\mathrm{L}}^{1/2} {\mathrm{mol}}^{-1/2} {\mathrm{s}}^{-1} \end{gathered}$$
The dimensions of rate constant, k are L^1/2 mol^–1/2 s^–1.