The branch of chemistry which deals with the study of the rate of the chemical reactions, the factors affecting the rate of reactions and the mechanism by which the reaction proceed is called chemical kinetics.

**Rate or Speed of reaction** – Rate of a chemical reaction can be defined as the change in concentration of reactants or products in unit time.

Rate or Speed = \frac {change in concentration of reactant or product}{time taken for change}

Rate of a reaction can be expressed in the terms of rate of disappearance of any of the reactant or rate of appearance of any of product. Rate of a reaction depends upon experimental conditions such as concentration of reactants, temperature and catalyst. It also depends upon the nature of reactant.

**Unit of the rate of reaction is ** mol {L}^{-1} {sec}^{-} or mol {L}^{-1} {min}^{-}

For a gaseous reactant or product, the unit is {atm sec}^{-} or {atm min}^{-}

**Rate Law**– Rate law for a chemical reaction cannot be decided from the balanced equation, i.e. theoretically. It has to be determined experimentally.

e.g. {2NO}+{O}_{2}→{2NO}_{2}

**Rate constant**– Rate constant may be defined as the rate of reaction when the concentration of each reactant is taken as unity.

{xA}+{yB}\longrightarrow {product}

\frac {dx}{dt} \alpha {[A]}^{x}{[B]}^{y} ;\frac{dx}{dt}=-K { [A] }^{ x }[{ B] }^{ y } \longleftarrow (rate constant)

**Order of a reaction**– The sum of the coefficients or powers of the reacting species that are involved in the rate law expression for the reaction represents.

e.g. {aA}+{bB}\longrightarrow {product}

Rate of reaction = {k}{[A]}^{x} {[B]}^{y} Order of reaction = {x} + {y}**Molecularity**– It is the number of reacting species taking part in an elementary reaction, which must collide simultaneously on order to bring about a chemical reaction. It is a theoretical concept. It always a whole number value. Its value can never be zero and fractional.

**Zero order reaction**– It means that the rate of reaction is directly proportional to the zero power of the concentration of reactant R, i.e. Rate= k[R_{0}]=k

For the reaction, R \longrightarrow P, k= \frac {[{R}_{0}]-[R]}{t}

where, [R_{0}] is initial concentration of reactant.

**First Order Reaction**– Reaction whose rate is determined by the change of one concentration term only, are known as first order reactions.

e.g. (a) {2N}_{2}{O}_{5} \longrightarrow {4NO}_{2} + {O}_{2}, Rate= k [{N}_{2}{O}_{5}]

According to rate law, rate =k[A] , where, constant k =rate constant

For such reactions, rate constant equations,

k = \frac {2.303}{t} {log}_{10} \frac {{[A]}_{0}}{[A]}= or k \frac {2.303}{t} {log}_{10} \frac {a}{(a-x)} = \frac{2.303}{t} {log}_{10} \frac {{V}_{0}}{{V}_{t}}

where,a=initial concentration, (a-x)=concentration after time (t)

V_{0}= initial volume, V_{t}= volume at time t.

**Characteristics of first order reaction-**

- Half life period of first order reaction is independent of initial concentration of reactants [A
_{0}]. It can be determined by following equation

{t}_{\frac{1}{2}}=\frac{0.693}{k}

- If we increase the concentration of reactant in a first order reaction by n times then rate of reaction also increases by n, but value of rate constant remains unchanged.

**Half-Life of reaction**– The time taken to reduced by 50% of the initial concentration of any reactant is known as half-life of that reactant.

For first order reaction {t}_{(\frac{1}{2})} = \frac {0.693}{k}

For zero order reaction {t}_{(\frac{1}{2})} =\frac{{[A]}_{0}}{2k}

**Pseudo First Order Reactions**– Pseudo first order reactions are not truly first order but show first order kinetics under certain conditions, e.g. acidic hydrolysis of an ester and inversion of sugar. These reactions are bi-molecular but have order one . In other words, we can say that when a reaction is first order with respect to each of the two reactants then, it becomes pseudo first order, when one of the reactants is taken in excess.

E.g. CH_{3}COOC_{2}H_{5} + H_{2}O \underrightarrow { { H }^{ + } } CH_{3}COOH + C_{2}H_{5}OH

**Temperature dependence of the rate of a reaction**– Most of the chemical reactions are accelerated by increases in temperature. It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant in nearly doubled. The effect of temperature is usually expressed in terms of temperature coefficient.

**Arrhenius equation**– It is the mathematical relationship between rate constant and temperature,

{K}={Ae}^{{-E}_{a} /RT}

where, A = frequency factor, E_{a} = activation energy (J/mol), R = gas constant

and T= temperature

**Activation energy (E _{a})** – Energy difference between threshold energy and energy actually possessed by the reacting molecule in normal condition known as activation energy. This can be calculated using Arrhenius equation as

{log} \frac {{k}_{2}}{{k}_{1}} = \frac {{E}_{a}}{2.303R} \left [\frac {{T}_{2}-{T}_{1}}{{T}_{1} \times {T}_{2}} \right]

**Threshold energy** – It is the minimum energy which the colliding molecules must have for effective collisions, i.e. those collisions which lead to the formation of product molecules.

**Effect of Catalyst** – A catalyst can alters the rate of reaction without going in any chemical change. It also decrease the requirement of activation energy by providing alternate path for the reaction.

**Collision Theory of Chemical Reactions**– According to this theory reactions occur due to

- requirement to achieve threshold energy.
- proper orientation if the reactant molecules.

Such collision are called effective collision and can be expressed by Arrhenus equation.

k = {Ae}^{{-E}_{a}/RT}

where, A= Arrhenius Factor of pre-exponential factor. E_{a}= activation energy, R= gas constant.

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