In the reaction
2A + B + C → A₂B + C,
there is no change in C, therefore its conc. does not affect the rate of the reaction.
Initial rate = k[A] [B]²
But [A] = 0.1 M,
[B] = 0.2 M
and k = 2 x 10^–6 M^–2 s^–1

Therefore initial rate

Rate= [k] x [A] x [B]²

= 2 x 10^–6 M^–2 s^–1 x (0.1 M) (0.2 mol M)² = 8 x 10^–9 ms^–1

From the equation:

2A + B + C → A₂B + C,

it is clear that when 2 moles of A are used then 1 mol of B is used in the same time. Therefore, when A has been reduced to 0.06 M (due to its 0.04 M has been reacted to 0.02 of B). Thus,

Conc. of A left = [A] = 0.06 M
Conc. of B left = [B] = [0.02 M – 0.02 M]
= 0.018 M

Rate = k[A] [B]²
= 2 x 10^–6 M² S^–1 x (0.06 M) (0.18 M)
= 3.89 x 10^–9 Ms^–1.

(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.

The various factors which affect the rate of chemical reactions are:
(i) Concentration of reactants
(ii) Temperature of reaction
(iii) Presence of catalyst
(iv) Nature of reactants
(v) Surface area
(vi) Exposure to radiations.