 # Chemical Kinetics

It’s of great importance to know the feasibility, extent and rate of a chemical reaction to use it for our benefits. Feasibility of a chemical reaction can be predicted by thermodynamics while its extent can be predicted by chemical equilibrium. The speed or rate of a reaction to reach the equilibrium is calculated by using another branch of chemistry that is Chemical Kinetics.

The word chemical means interaction of substances or chemical change. The word kinetics comes from the Greek language word ‘kinesis’ which means movement. Chemical kinetics tells us about the rate of reaction. Chemical kinetics is an important aspect of a chemical reaction as it predicts at what rate the reaction will attain equilibrium which helps us to know how we can use this chemical change in a better way. For example, we can know how rapidly food material get spoiled by predicting the rate of the chemical change which is taking place in the food material.

Rate of a Chemical Reaction

Rate of a chemical reaction depends on the concentrations of reactants or products and the time required to complete the chemical change.

Rate of a chemical reaction can be defined as the change in concentration of a reactant or product in unit time. Thus, rate of a chemical reaction can be expressed on the basis of following points –

• The rate of decrease in concentration of any one of the reactants or the rate of increase in concentration of any one of the products

• Time taken in the change in concentration

Suppose one mole of a reactant A produces one mole of product B and their concentration at time t1 is [A]1 and [B]1 respectively. While their concentration at time t2 is [A]2 and [B]2 respectively.

A 🡪 B -------------------(1)

Δt = t2 – t1

Δ[A] = [A]2 – [A]1 , it will be a negative value as the concentration of reactant will decrease with time. Here, square brackets are used to express molar concentration.

Δ[B] = [B]2 – [B]1

Rate of Disappearance of A = $\frac{\text{Decrease in Concentration of A}}{\text{Time taken}}$ = $\frac{Δ[A]}{Δt}$

Rate of Appearance of B = $\frac{\text{Increase in Concentration of B}}{\text{Time taken}}$ = + $\frac{Δ[B]}{Δt}$

The average rate of reaction – The change in concentration of any of the reactants or products per unit time over a specific time period is called average rate of reaction. It is denoted by rav. Thus, average rate of reaction depends upon the following two factors –

• Concentration of reactants or products

• Time taken to for the change to occur

In the above equations - $\frac{Δ[A]}{Δt}$ and  $\frac{Δ[B]}{Δt}$ expresses the average rate of reaction.

Instantaneous rate of reaction – It is used to express the rate of reaction at a particular moment of time. In instantaneous rate of reaction, the time period is very short and due to this change in concentration of reactants and products is very small or negligible. Thus, the instantaneous rate is the rate of a reaction at any specific point of time. It is denoted by rinst. It is obtained by considering the average rate at the smallest time interval. For infinitesimally small - time interval (dt), instantaneous rate of reaction (reaction of equation 1) is given as –

rinst = - $\frac{d[A]}{dt}$ = $\frac{d[B]}{dt}$

Average Rate of a Reaction

Instantaneous Rate of Reaction

Unit of rate of a reaction – mol/L/s or mol L-1s-1 (if concentration = mol/L and time is in seconds)

Factors Influencing Rate of a Reaction

Following factors influence the rate of reaction –

• Concentration – Rate of a reaction at given temperature may depend upon the concentration of one or more reactants or products. When rate of a reaction is expressed in terms of change in concentration of reactants with time is called rate law.  It is also known as rate equation or rate expression.

• Rate law -  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 the same as the stoichiometric coefficient of the reacting species in a balanced chemical equation. Suppose a general reaction is –

aA + bB 🡪 cC + dD

where a, b, c and d are the stoichiometric coefficients of reactants and products. Rate expression for the above reaction will be –

rate [A]x [B]y

rate = k[A]x [B]y

- $\frac{Δ[R]}{Δt}$  = k[A]x [B]y

Where k = rate constant

• Order of a reaction - Order of a chemical reaction can be defined as the sum of power of concentration of reactants in the rate law expression is called the order of that chemical reaction. Reactions can be first order reaction, second order reaction, pseudo first order reaction etc. depends on the concentration of the reactants. Order of a reaction is an experimental value. It means it is an experimentally determined parameter. It can have fractional value as well.

If the experimental rate law expression is given for a reaction, then we can deduce the order of that reaction as well. For example, consider a reaction –

aA + bB 🡪 P

And rate law is given as –

rate = k[A]x[B]y

order of reaction for the above reaction on the basis of given rate law can be written as follows –

order of reaction = x + y

How to Find Order of Reaction?

Order of reaction is determined by experiment. Although if we know rate law expression determined experimentally then we can determine order of reaction using rate law. Order of reaction can be an integer or fractional value. Following orders of reactions are possible –

• Order of reaction can be zero – In zero order reaction the concentration of reactant/s doesn’t affect the rate of a reaction.

• Order of reaction can be negative integer – Negative integer value of order of reaction indicates that the concentration of the reactants inversely affect the rate of a reaction.

• Order of reaction can be positive integer – Positive integer value of order of reaction indicates that the concentration of the reactants directly affect the rate of a reaction.

• Order of reaction can be fractional value – Fractional value of order of reaction indicates more intricate relationship between concentration of reactants and rate of reaction. Generally, complex reactions possess fractional value of order of reaction.

Following Methods can be Used for Determination of Order of Reaction –

• Differential Method – It is also called initial rates method. In this method concentration of one reactant varies while others are kept in constant concentration and initial rate of reaction is determined. Suppose if three reactants A, B and C are taking part in the reaction then in this method we keep varying the concentration of one reactant (for example reactant A) while concentration of other reactants such B and C constant.

• Graphical Method – This method is used when only one reactant takes part in the reaction. In this method if we draw a graph between log[A] (where A is a reactant and [A] is concentration of reactant A) and t (time) and it’s a straight line then reaction follows a first order.  In the same way if we draw a graph between $\frac{1}{[A]}$ and t and get a straight line then reaction follows second order. While if we draw a graph between $\frac{1}{[A]^{2}}$ and t and get a straight line then the reaction is a third order reaction.

• Integral Method – In this method concentrations of the reactants are compared with the integral form of the rate law. It is used for verification of initial rate method.

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.

## Difference Between Molecularity and Order of Reaction –

 S.No. Molecularity Order of Reaction 1. It is the number of molecules taking part in the rate determining step. It shows the relation between concentration of reactants and rate of reaction. 2. For determination of molecularity only rate determining step is considered. For determination of order of reaction all steps of a reaction are considered. 3. It doesn’t depend on pressure and temperature. It depends on pressure, temperature and concentration. 4. It is always a whole number. It can be zero, integer or even a fractional value. 5. We can determine molecularity by looking at reaction mechanism. Order of reaction can be determined by experiments. 6. Molecularity cannot be a negative number. Order of reaction can be a negative number.

Zero Order Reaction

In these reactions the rate of reaction doesn’t depend upon the concentration of reactants. It means change in concentration of reactants doesn't affect the rate of reaction.

Example - 2NH₃(g) $\overset{\text{Fe or W as catalyst}}{\rightarrow}$ N₂(g) + 3H₂(g)

In zero order reactions, the rate of reaction is proportional to zero power of the concentration of reactants. Suppose the reaction is –

R 🡪 P

Then, Rate = k[R]o = - $\frac{d[R]}{dt}$

As [R]o  = 1,

So, Rate = k 1 =  - $\frac{d[R]}{dt}$

d[R] = -k dt

on integration - [R] = -k t + I

where, I = constant of integration

At t = 0, [R] = [R]0

[R]0 =   I

On substituting the value of I in the above equation –

[R] = -k t + [R]0

Above equation is similar to the equation of a straight line (y = mx + c). So, if we plot [R] against t, we get a straight line.

k = $\frac{[R]_{0} - [R]}{t}$

Half life of zero order reaction – [R]0/2k

Unit of k – mol/L/s

First Order Reaction

In these reactions the rate of reaction depends on the concentration of one reactant only. There can be many reactants in the reaction but concentration of only one reactant will affect the rate of reaction. Concentration of other reactants will have no effect on order of reaction.

Example – N2O5 🡪 N2O3 + O2

Rate = k[N2O5]

For 1st order reactions – In[R] = -kt + In[R]0

k = $\frac{1}{t_{2} - t_{1}}$ ln$\frac{[R]_{1}}{[R]_{2}}$

where, R1 and R2 are concentrations of the reactants at time t1 and t2 respectively.

Half life of first order reaction – In 2/k

Unit of k – time-1 or per second

Half life of first order reaction is independent of [R]0 while for zero order reaction t1/2 [R]0

Second Order Reaction

In these reactions the rate of reaction depends on the concentration of two different reactants or square of concentration of one reactant.

Example – 2NO2 🡪 2NO + O2

Rate = k[NO2]2

CH3COOC2H5 + OH- 🡪 CH3COO- + C2H5OH

Rate = k[CH3COOC2H5] [OH-]

A reaction is called a second order reaction when the overall order is two. Suppose if the reaction is as follows –

A + A 🡪 P

Or 2A 🡪 P

In these reactions rate is proportional to the square of the concentration of one reactant. The differential rate law for the above second order reaction can be written as follows –

$\frac{d[A]}{dt}$ = - K[A]2

Rate of such reactions can also be written as r = k[A]2

Here k is rate constant for second order reaction. Unit of reaction rate (r) is moles per liter per second (mol.L-1.s-1) and the unit of second order rate constant is M-1.s-1 (M is molarity which can be expressed as mol/L).

If both the reactants are different in the reaction –

A + B 🡪 P

Rate for the above reaction can be written as follows –

R = k[A]x[B]y

Where the sum of x and y is equal to two.

Other Examples of Second Order Reactions

Few examples of second order reaction are given below –

• Nitrogen dioxide decomposes into nitrogen monoxide and oxygen. Reaction is given below-

2NO2 🡪 2NO + O2

• Decomposition of hydrogen iodide – Hydrogen iodide breaks down into iodine and hydrogen. Reaction is given below –

2HI 🡪 I2 + H2

• Decomposition of nitrosyl bromide –

2NOBr 🡪 2NO + Br2

• Hydrolysis of an ester in presence of a base –

CH3COOC2H5 + NaOH 🡪 CH3COONa + C2H5OH

• Combustion Reaction –

O2 + C 🡪 O + CO

Integrated and differential Rate Equation for Second Order Reactions

We are considering here that equation where chemical reaction can be represented as follows –

A + A 🡪 P _ _ _ _ _ (1)

Generally, polymerization reactions follow the same as in them two monomer units combine and form a polymer.

The differential rate law equation for the chemical equation (1) can be written as follows –

- $\frac{d[A]}{dt}$ = k[A]2 _ _ _ _ _ (2)

On rearranging the above equation (2), we get –

$\frac{d[A]}{[A]^{2}}$ = -kdt _ _ _ _ _ (3)

On integrating the above equation (3) considering that concentration of the reactant changes between time 0 and time t, we get –

[A]$_{0}$[A]$_{t}$∫$\frac{d[A]}{[A]^{2}}$ = - k0t∫dt _ _ _ _(4)

Applying the power rule of integration in equation (4), we get –

[-$\frac{1}{[A]}$ ]$_{[A]_{0}}^{[A]_{t}}$ = k [t]$_{0}^{t}$  _ _ _ _ _ (5) (Power rule of Integration - ∫$\frac{dx}{x^{2}}$ = - $\frac{1}{x}$ + C)

On simplifying equation (5), we get –

- [- $\frac{1}{[A]_{t}}$ - (-$\frac{1}{[A]_{0}}$)] = kt

= $\frac{1}{[A]_{t}}$ - $\frac{1}{[A]_{0}}$ = kt_ _ _ _(6)

Equation (6) is the required integrated rate expression of second order reactions.

Second Order Reaction Graph

On rearranging the equation (6), we get –

$\frac{1}{[A]_{t}}$ = kt + $\frac{1}{[A]_{0}}$ _ _ _ _(7)

On comparing equation (7) with straight line equation or linear equation y = mx + c, we can write –

Y = 1/[A]t (on y-axis)

X = t (on x-axis)

m = k (Slope)

c = 1/[A]0 (Intercept)

so, graph can be drawn as follows –

It is clear from the graph that slope is equal to the value of rate constant k.

Half Life of Second Order Reactions

The amount of time required by reactant/s in a reaction for undergoing decay by half is called half life of that reaction. In the same way the amount of time required by reactant/s to undergo decay by half in second order reaction is called half life of second order reaction. So, while calculating the half life of a reaction t becomes t1/2 and as t=t1/2 then [A]t becomes [A]0/2.

Now putting the values of t and [A] in equation (6), we get –

$\frac{1}{\frac{[A]_{0}}{2}}$ - $\frac{1}{[A]_{0}}$ = kt$_{\frac{1}{2}}$ _ _ _ _ _ (8)

On solving equation (8), we get –

$\frac{2}{[A]_{0}}$ - $\frac{1}{[A]_{0}}$ = kt$_{\frac{1}{2}}$ _ _ _ _ _(9)

On simplifying equation (9), we get –

$\frac{1}{[A]_{0}}$ =kt$_{\frac{1}{2}}$  _ _ _ _ _(10)

On rearranging the equation (10), to get t1/2

t1/2  =  $\frac{1}{k[A]_{0}}$ _ _ _ _ _(11)

Equation (11) is the equation for half life of second order reaction.

As we can see t1/2 is inversely proportional to the concentration of the reactant in second order reactions. Graph is given below for half life of second order reactions which is drawn between [A] and t.

Although the graph looks very similar to first order plots but it decreases at a much faster rate as the graph shows above and length of half life increases while the concentration of the reactant decreases. This is the reason generally students find the concept of half life for second order reactions more difficult than first and zero order reactions. Value of the rate constant of second order reactions cannot be calculated directly from the half life equation unless the initial concentration is known.

Importance of determining the Half – life of reactions - Determination of Half-life of reactions is largely used in the pharma field. For example, drug dosage interval is determined on the basis of the half life period of the reaction of the drug. When chemical kinetics is used in pharma, it is called pharmacokinetics. It can also be defined as the branch of pharmacology concerned with the movement of drugs within the body. Another vital application of half life in pharmacokinetics is that half – life for the drug reaction shows how tightly drugs bind to each ligand before it is undergoing decay. It is very important for drug design to know how tightly it binds with ligands.

Pseudo First Order Reaction

Suppose a reaction is – aA + bB 🡪 cC + dD

Rate according to rate law expression = k [A]$^{x}$ [B]$^{y}$

Where x and y are concentrations of A and B respectively.

So, order of reaction will be = x + y

We can say x is the order of reaction with respect to A and y is the order of reaction with respect to B.

Now if suppose x=1 and y = 1 then the reaction will be a 2nd order reaction. But if the concentration of B is much more than the concentration of A then change in concentration of B will be very less so its concentration can be assumed constant. So, in this condition although the reaction is of 2nd order in nature but can be approximated as 1st order reaction with respect to A and known as pseudo 1st order reaction.

Thus, pseudo first order reaction is actually of higher order reaction but can be approximated or appears to be pseudo first order reaction. We can say in general pseudo order reactions are those reactions which appears to be of xth order reaction but can be approximated or are of some different order.

Pseudo first order reaction definition

Those reactions which are not of 1st order but approximated or appears to be of 1st order due to higher concentration of the reactant/s than other reactant are known as pseudo first order reactions.

Pseudo First Order Reaction Example

Pseudo first order reaction can be well explained by following examples –

1. Hydration of Alkyl Halide

CH3I + H2O 🡪 CH3OH + H+ + I-

Rate of reaction = k [CH3I] [ H2O]

As methyl iodide is also used in aqueous solution form so the concentration of water is far higher than methyl iodide.

[CH3I] <<< [ H2O]

So, concentration of water doesn’t change much and can be approximated as no change or constant.

Now we can write – Rate of reaction = k [CH3I]

Where k’ = k [H2O]

Thus, the reaction appears to be first order, but it is actually of second order that’s why it is known as pseudo first order reaction.

2. Hydrolysis of Cane Sugar

C12H22O11 + H2O 🡪 C6H12O6 + C6H12O6

Sucrose      Water     Glucose   Fructose

Rate of reaction = k [C12H22O11] [H2O]

But [H2O] >>> [C12H22O11]

So, concentration of water can be approximated as constant as its concentration doesn’t change a lot during the reaction.

Now rate of reaction can be written as –

r = k’ [C12H22O11]

where k’ = k [H2O]

Thus, hydrolysis of cane sugar is a pseudo first order reaction.

3. Hydrolysis of Ester

Reaction – CH3COOC2H5 + H2O         🡪           CH3COOH      +     C2H5OH

Ethyl ethanoate  Water                    Ethanoic acid        Ethanol

Rate of reaction = k [CH3COOC2H5] [H2O]

But [H2O] >>> [CH3COOC2H5]

So, we can say concentration of water remains almost constant during the reaction.

So, we can write –

Rate of reaction = k’ [CH3COOC2H5]

K’ = k [H2O]

Thus, hydrolysis of ester is a pseudo first order reaction.

Temperature Dependence of the Rate of a Reaction

As we know, the rate of a reaction gets influenced by the change in temperature. That’s why when we cook food at low temperature (low gas), it takes time to cook while at high temperature (high gas), it cooks faster. It is found that the rate constant gets doubled when temperature gets increased by 10o in a chemical reaction. Change in rate of reaction can be easily explained by the Arrhenius equation.

The Arrhenius equation was first proposed by Dutch Chemist J. H. van’t Hoff in 1884 but it was explained and interpreted by Swedish Chemist Svante Arrhenius in 1889.

k = A e$^{-\frac{Ea}{RT}}$

where, k = rate constant

A = Arrhenius factor or frequency factor or pre- exponential factor; It is a constant which is specific to a particular reaction.

e = Mathematical quantity

Ea = Activation energy (Unit – J mol-1)

R = Gas constant

T = Temperature (in K)

According to the Arrhenius equation, a reaction can only take place if molecules of one substance collide with the molecules of another substance and form an unstable intermediate. This unstable intermediate is called an activated complex. This activated complex exists for a very short time interval and gets converted into a product. The energy required to form an unstable intermediate or activated complex is called activation energy which is denoted by Ea

Effect of catalyst on rate of reaction

What is a Catalyst?

A catalyst is a substance which increases the rate of a reaction without taking part in it. It means it increases the rate of reaction without itself undergoing any permanent chemical change.

• For example, in nitration of benzene, benzene reacts with concentrated nitric acid in presence of catalyst concentrated sulphuric acid and forms nitrobenzene and water. Reaction is given below –

• Another example is halogenation of benzene. Halogenation of benzene is an electrophilic substitution reaction of benzene. In this reaction benzene reacts with halogen in presence of catalyst Lewis acid such as anhydrous AlCl3, AlBr3, FeCl3, FeBr3 etc. and forms aryl halides. For example, in Bromination of Benzene, benzene reacts with bromine in presence of Lewis acid and forms bromobenzene. In this reaction Br+ (bromonium ion) acts as an electrophile. Reaction is given below –

If a substance is added to a reaction and its rate of reaction decreases, then it is called an inhibitor.

Action of catalyst – Action of catalyst is based on intermediate complex theory. Catalyst forms temporary bonds with the reactants and forms an intermediate complex which soon decomposes to yield products and the catalyst used remains the same or chemically unchanged.

Catalyst provides an alternate pathway for the reaction to take place which requires less amount of activation energy. It does not change the Gibbs energy of reactions. It also does not change the equilibrium constant of a reaction but helps in attaining the equilibrium quickly.

Thus, a small quantity of catalyst increases the rate of a reaction.

Collision Theory of Chemical Reactions

Collision theory was developed by Max Trautz and William Lewis in 1917-18. This theory is based on the kinetic theory of gases.

According to collision theory, the reactant molecules are assumed to be hard spheres and the molecules must collide with each other for a chemical reaction to occur. Product is the result of successful collisions between reactant molecules.

The number of collisions per second per unit volume of the reaction mixture is known as collision frequency which is denoted by Z. Rate of a reaction depends on the frequency of collisions.

For a successful collision, following conditions must be followed –

• Reactant molecules must collide with each other

• Sufficient energy is required

• Molecules should collide in the proper orientation

Collision theory explains why various chemical reactions occur at different rates.

For a bimolecular reaction – A + B 🡪 P

Rate of reaction = Z$_{AB e^{-\frac{Ea}{RT}}}$

Where, Z$_{AB}$ = Collision frequency of reactants A and B

e$^{-\frac{Ea}{RT}}$ = Energy of fraction of molecules ≥ Ea (Activation energy)

As successful collision or effective collision is a result of collision between reactant molecules in proper orientation. So, factor P is also introduced in the equation.

Rate of reaction = PZ$_{AB e^{-\frac{Ea}{RT}}}$

P is called probability or steric factor.

This ends our coverage on the summary of the unit “Chemical Kinetics”. We hope you enjoyed learning and were able to grasp the concepts. You can get separate articles as well on various subtopics of this unit such as effect of catalyst, collision theory etc. on Vedantu website. We hope after reading this article you will be able to solve problems based on the topic. We have already provided detailed study notes or revision notes for this unit, which you can easily download by registering yourself on Vedantu website. Here in this article we have discussed the unit in a summarized way with the emphasis on important topics of the unit.  If you are looking for solutions of NCERT Textbook problems based on this topic, then log on to Vedantu website or download Vedantu Learning App. By doing so, you will be able to access free PDFs of NCERT Solutions as well as Revision notes, Mock Tests and much more.