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Chemical kinetics

Fast/instantaneous reactions

Slow reactions

Moderately slow reactions

Rate of reaction

Instantaneous rate of reaction

Factors affecting rate of reaction

Rate law expressions

Characteristics of rate constant

Order of reaction

Molecularity of a reaction

Order vs molecularity

Integrated rate equation

Rate constant

Units of rate constant

Zero order reactions

First order reactions

Pseudo first order reaction

Rate of reaction of hydrolysis of ester

Rate of reaction of inversion of cane sugar

Temperature dependence of rate of a reaction

Arrhenius equation

Threshold energy (ET)

Activation energy (Ea)

Activated complex (or transition state)

Temperature coefficient for rate of reaction

Effect of catalyst on rate of reaction

Collision theory of reaction rates

Activated complex theory or transition state theory of reaction rates

Photochemical reactions



Chemical kinetics

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

We need to find out,

  1. the feasibility of a chemical reaction which can be predicted by thermodynamics (A reaction with ΔG < 0, at constant temperature and pressure is feasible);

  2. extent to which a reaction will proceed can be determined from chemical equilibrium;

  3. speed of a reaction i.e. time taken by a reaction to reach equilibrium.

Classification of chemical reactions on the basis of rate of reaction

Fast/instantaneous reactions

Chemical reaction which completes in less than 1 ps (10-12 s) time is known as fast reaction. It is practically impossible to measure the speed of such reactions, e.g., ionic reactions, organic substitution reactions.

Slow reactions

Chemical reactions which complete in a long time from some minutes to some years are called slow reactions, e.g., rusting of iron, transformation of carbon into diamond etc.

Moderately slow reactions

Chemical reactions which are intermediate between slow and fast reactions are called moderately slow reactions.

Rate of reaction

Rate of a chemical reaction is the change in the concentration of any one of the reactants or products per unit time. It is expressed in mol L-1 s-1 or Ms-1 or atm time-1 units.

It can be expressed in terms of

  1. the rate of decrease in concentration of any one of the reactants, or

  2. the rate of increase in concentration of any one of the products.

For the reaction

R  P

One mole of the reactant R produces one mole of the product P. If [R1] and [P1] are the concentrations of R and P respectively at time t1 and [R2] and [P2] are their concentrations at time t2 then,

Δt = t2  t1,  

ΔR= R2 R1,  

Δ [P] = [P2]  [P1]

The square brackets in the above expressions are used to express molar concentration.

Average rate of reaction rav=decrease in concentration of reactantstime taken

rav=-Δ[R]Δt= Δ[P]Δt

Instantaneous rate of reaction

Rate of a chemical reaction at a particular moment of time, is known as instantaneous rate of reaction. It is represented by the slope of the time vs concentration curve,

rinst = limΔt0-ΔRΔt= -dRdt


rinst = limΔt0Δ[P]Δt= d[P]dt

For the reaction,

aA + bB  cC + dD


Rate of disappearance of A = - Δ[A]Δt

Rate of disappearance of B = - Δ[B]Δt

Rate of appearance of C = Δ[C]Δt

Rate of appearance of D = Δ[D]Δt

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Factors affecting rate of reaction

  1. Nature and concentration of reactants

  2. Temperature

  3. Surface area of reactant

  4. Radiations and catalyst

  5. Pressure of gas

Rate law expressions

The rate of a chemical reaction at a given temperature may depend on the concentration of one or more reactants and products.

For the chemical reaction,

aA + bB  cC + dD 

where a, b, c and d are the stoichiometric coefficients of reactants and products.

The rate expression for this reaction is

Rate  [A]x [B]y 

Here exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants.

We can write,

Rate=k [A]x [B]y,

where ‘k’ is called the rate constant.


-dRdt=[A]x [B]y

The equation which relates the rate of a reaction to concentration of reactants is called rate law or rate expression.

“Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.”

Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation, i.e., theoretically but must be determined experimentally.

Characteristics of rate constant

  1. Greater the value of rate constant, faster is the reaction.

  2. Each reaction has a particular value of rate constant at a particular temperature.

  3. The value of rate constant for the same reaction changes with temperature.

  4. The value of rate constant for a reaction doesn’t depend upon the concentration of the reactants.

Order of reaction

The sum of powers of the concentration of the reactants in the rate law expression (x + y) is called the order of that chemical reaction.

Molecularity of a reaction

The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.

Unimolar reaction NH4NO2 → N2 + 2H2O
Bimolar reaction 2HI → H2 + I2
Trimolar reaction 2NO + O2 → 2NO2

The probability that more than three molecules can collide and react simultaneously is very small. Hence, reactions with the molecularity three are very rare and are slow to proceed.

Therefore, complex reactions involving more than three molecules in the stoichiometric equation must take place in more than one step.

The reactions taking place in one step are called elementary reactions. When a sequence of elementary reactions (called mechanism) gives us the products, the reactions are called complex reactions.

For example,

This reaction which seems to be of tenth order is actually a second order reaction. This shows that this reaction takes place in several steps.

Order vs molecularity

  1. Order of a reaction is an experimental quantity. It can be zero and even a fraction but molecularity is a theoretical concept and cannot be zero or a non integer.

  2. Order is applicable to elementary as well as complex reactions whereas molecularity is applicable only for elementary reactions. For complex reaction molecularity has no meaning.

  3. For complex reaction, order is given by the slowest step and molecularity of the slowest step is same as the order of the overall reaction.

Integrated rate equation

The concentration dependence of rate is called differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by determination of slope of the tangent at point, t in concentration vs time plot. This makes it difficult to determine the rate law and hence the order of the reaction.

If we integrate the differential rate equation to give a relation between directly measured experimental data, i.e., concentrations at different times and rate constant, the equation obtained is called integrated rate equation.

The integrated rate equations are different for the reactions of different reaction orders.

Rate constant may be defined as the specific rate of reaction when the molar concentrations of the reactants is taken to be unity, i.e.,

Units of rate constant or specific reaction rate for a nth order reaction is given as

k = 1Time× 1Conc.n-1

If concentration is measured in units of mol·L−1 (abbreviated as M), then

Zero order reactions

The rate of the reaction is proportional to zero power of the concentration of reactants.

Consider the reaction, R → P

Rate =-dRdt=kR0 

 d[R]dt=-k  dR= -k dt

Integrating both sides, we get,

where, C is the constant of integration.

Now, at t = 0, the concentration of the reactant R = [Ro] = initial concentration of the reactant.

Substituting the value, we get,

R= -kt + [Ro]     k=[Ro]-[R]t

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For t= t12 ;     R=Ro2

t12 =[Ro]2k

For zero order gaseous reactions,

k=po-pt and t12=po2k


2NH3(g)1130K + Pt Catalyst N2(g) + 3H2(g)

First order reactions

The reaction, whose rate is proportional to the concentration of reactants, is called first order reaction.

R  P 

 Rate=dRdt= -kR

Or Rate=dRR= -kdt

 ln [R] =  kt + C 

When t = 0, R = [Ro], where [Ro] is the initial concentration of the reactant.


Substituting the value of C

lnR=  kt +lnRo

 ln  R[Ro]= - kt

R= Roe-kt

and,  k=1t ln [Ro]R=2.303t log[Ro]R

 ln R1[R2]=kt2- t1

 t=2.303k logRo[R]

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For t= t12 ;     R=Ro2   

 t12 =2.303klogRo[Ro ]2

 t12 =0.693k

For first order gas phase reaction of type

Let pi be the initial pressure of A and pt the total pressure at time ‘t’.

Total pressure pt = pA + pB + pC (pressure units)

If x atm be the decrease in pressure of A at time t and one mole each of B and C is being formed, the increase in pressure of B and C will also be x atm each.

A(g) B(g) + C(g)
At t = 0 pi atm 0 atm 0 atm
At time t (pi – x) atm x atm x atm



k =2.303t log pipA


Hydrogenation of ethene is an example of first order reaction.

All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.

Ra88226  He24+ Rn86222

Pseudo first order reaction

Chemical reactions which appear to be of higher order but actually are of the lower order are called pseudo order reactions. In case of pseudo first order reaction, chemical reaction between two substances takes place when one of the reactants is present in excess, e.g., hydrolysis of ester.

Example – Hydrolysis of ethyl acetate

During the hydrolysis of 0.01 mol of ethyl acetate with 10 mol of water, amounts of the various constituents at the beginning (t = 0) and completion (t) of the reaction are given as under.








t = 0 0.01 mol 10 mol 0 mol 0 mol
t 0 mol 9.99 mol 0.01 mol 0.01 mol

The concentration of water does not get altered much during the course of the reaction.

So, in the rate equation

the term [H2O] can be taken as constant.

The equation, thus, becomes

where k = k′ [H2O] and the reaction behaves as first order reaction.

A reaction in which concentration of one of the reactants can be taken as constant and can be included in the rate constant, are called pseudo first order reactions.

For first order chemical reaction of type,


k =2.303t log V-VoV-Vt

where Vo, Vt, and V are the volumes of NaOH solution used for the titration of same volume of the reaction mixture after times 0, t and ∞ respectively.

Inversion of cane sugar is another pseudo first order reaction.

C12H22O11Cansugar+H2O    H+   C6H12O6Glucose+ C6H12O6Fructose


k =2.303t log ro-rrt-r

Where ro, rt, and r are the polarimetric readings (angle of rotation of polarized light) at t = 0, t and ∞, respectively.

Comparision of zero and first order rections


Reaction type

Differential rate law

Integrated rate law

Straight line plot

Half life

Units of k



dRdt= - k

kt = [R]0 - [R]

[R] vs t


Conc time-1 or mol L–1 s–1



dRdt=- kR



kt =lnR0R

ln [R] vs t


time-1 or s–1


For a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.

The temperature dependence of the rate of a chemical reaction is given by Arrhenius equation,

k = A e-Ea/RT


Taking log on both sides, we get,

lnk =lnA-EaRT

logk =logA-Ea2.303RT

In the Arrhenius equation, when T → ∞ or Ea = 0 then

and the rate of reaction becomes independent of temperature

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Threshold energy (ET) - The minimum amount of energy which the reactant must possess in order to convert into products is known as threshold energy.

Activation energy (Ea)

The additional amount of energy, required by the reactant so that their energy (ER) becomes equal to the threshold value is known as activation energy.Ea = ET - ER

Lower the activation energy, faster is the reaction.

Different reactions have different rates because their activation energies are different.

Larger the value of Ea, smaller the value of rate constant and greater is the effect of a given temperature rise on k.

Activated complex (or transition state)

Activated complex is the highest energy unstable intermediate between the reactants and products and gets decomposed immediately (having very short life), to give the products. In this state, bonds of reactant are not completely broken while the bonds of products are not completely formed.


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Distribution of kinetic energy

The distribution of kinetic energy may be described by plotting the fraction of molecules (NE/NT) with a given kinetic energy (E) vs kinetic energy.

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Here NE is the number of molecules with energy E and NT is total number of molecules.

The peak of the curve corresponds to the most probable kinetic energy.

Temperature coefficient is the ratio of rate constant of a reaction at two temperatures differing by 10oC. Temperatures selected are usually 298 K and 308 K.

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  1. If k2 and k1 are rate constatnts at temperatures T2 and T1, then,

    logk2k1= Ea2.303RT2-T1T1T2

  2. Fraction of molecules with energy equal to or greater than the activation energy is called Boltzmann factor and is given by

    χ =nN= e-EaRT

    Or,   log χ= -Ea2.303 RT

  3. Ea is constant for a particular reaction.

  4. Ea does’t depend on temperature, volume, pressure, etc., but gets affected by catalyst

Effect of catalyst on rate of reaction

A catalyst is a substance which increases the rate of a reaction without itself undergoing any permanent chemical change.

For example MnO2 catalyses the following reaction so as to increase its rate considerably,

When the added substance reduces the rate of reaction, it is called inhibitor.

The action of the catalyst can be explained by intermediate complex theory.

According to this theory, a catalyst participates in a chemical reaction by forming temporary bonds with the reactants resulting in an intermediate complex. This has a transitory existence and decomposes to yield products and the catalyst.

It is believed that the catalyst provides an alternate pathway or reaction mechanism by reducing the activation energy between reactants and products and hence lowering the potential energy barrier.

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As per Arrhenius equation, lower the value of activation energy, faster will be the rate of reaction.

For a reaction being catalysed

kpka=eEa-Ep/RT= eΔE/RT

where, ‘p’ denotes presence of catalyst and ‘a’ denotes absence of catalyst.


Collision theory

According to this theory, the reactant molecules are assumed to be hard spheres and the reaction occurs when molecules collide with each other.

The number of collisions between the reacting molecules taking place per second per unit volume is known as collision frequency (ZAB

But only those collisions in which the colliding species have certain minimum amount of energy and collide in proper orientation, result in the product formation. Such collisions are called fruitful collisions or effective collisions.

Here, rate =  dVdt

= collision frequency × fraction of effective collision

where, ZAB represents the collision frequency of reactants, A and B, e-Ea/RT represents the fraction of molecules with energies equal to or greater than Ea.

The proper orientation of reactant molecules leads to bond formation whereas improper orientation makes them simply bounce back and no products are formed.


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So, to account for effective collisions, another factor, P called the probability or steric factor is introduced.

Drawback of collision theory: It considers the atoms/molecules to be hard spheres and ignores their structural aspect.

Activated complex theory or transition state theory

This theory is based on the fact that bond cleavage and bond formation, involved in a chemical reaction, must occur simultaneously.

Hence, the reactants are not converted directly into the products. There is an energy barrier or activated complex [intermediate product with partially formed bond] between the reactants and products. The reactants must cross this energy barrier before converting into products. The height of the barrier determines the threshold energy.

Photochemical reactions

Chemical reactions that occur on exposure to visible radiation are called photochemical reactions.

  1. The rate of a photochemical reactions is affected by the intensity of light.

  2. Temperature has little effect on photochemical reactions.

Quantum yield or quantum efficiency of a photochemical reaction,

Φ=number of reactant molecules reacting in a given timenumber of photons of light absorbed in the same time