Given the following steps in the mechanism for a chemical reaction
(a) $\mathrm{A}+\mathrm{B}\stackrel{ \mathrm{fast}}{⟶}\mathrm{C}$
(b) $\mathrm{B}+\mathrm{C}\stackrel{ \mathrm{slow}}{⟶}\mathrm{D}+\mathrm{E}$
(c) $\mathrm{D}+\mathrm{F}\stackrel{ \mathrm{fast} }{⟶}\mathrm{A}+\mathrm{E}$

Write the rate equation for the rate determining step.

Given the following steps in the mechanism for a chemical reaction
(a) $\mathrm{A}+\mathrm{B}\stackrel{ \mathrm{fast}}{⟶}\mathrm{C}$
(b) $\mathrm{B}+\mathrm{C}\stackrel{ \mathrm{slow}}{⟶}\mathrm{D}+\mathrm{E}$
(c) $\mathrm{D}+\mathrm{F}\stackrel{ \mathrm{fast} }{⟶}\mathrm{A}+\mathrm{E}$
Given that the concentration of $\mathrm{C}$ is directly proportional to the concentration of $\mathrm{A}$, rewrite the rate equation so that it includes the concentration terms for only reactants and products and not intermediates.

Given the following steps in the mechanism for a chemical reaction
(a) $\mathrm{A}+\mathrm{B}\stackrel{ \mathrm{fast}}{⟶}\mathrm{C}$
(b) $\mathrm{B}+\mathrm{C}\stackrel{ \mathrm{slow}}{⟶}\mathrm{D}+\mathrm{E}$
(c) $\mathrm{D}+\mathrm{F}\stackrel{ \mathrm{fast} }{⟶}\mathrm{A}+\mathrm{E}$
What is the overall order of the reaction?

Explain the following: Factors affecting rate of reaction.

Establish the following relation for a first-order reaction:

$\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{\mathrm{a}}{(\mathrm{a}-\mathrm{x})}$

Where the terms have their usual significance. Hence, show that the half-life $\left({\mathrm{t}}_{1/2}\right)$ of a first-order reaction is independent of initial concentration.