## Introduction

**In this chapter**, we will discuss about **rate of a reaction** and outlines the basic concepts in terms of **order** and **molecularity** of reactions. This is followed by the **rate laws**. Then we will discuss integrated rate equations which includes kinetics of zero and first order reactions with their characteristics **half-life** and parallel reactions. Finally we will see the kinetics of nuclear reactions including their types, **radioactive decay** and **carbon-dating**.

## Chemical Kinetics

**Chemical kinetics** is the branch of chemistry that deals with rate of a reaction, factors affecting the rate and the reaction mechanism. Once a reaction starts, how fast and how far it will go. Ionic reactions in
solution such as that between HCl (aqueous) and AgNO_{3} (aqueous) giving a
white precipitate of AgCl take place within twinkling of eye. Hence, chemical kinetics helps us to describe reaction rates and examine how they are affected by catalyst, concentration and temperature.

A **chemical reaction** involves breaking of bonds in reactant molecules and
making of bonds in product molecules. Different reactions differ in respect of the strength of bonds to be broken and hence they occur at different rates.

## Rates of Chemical Reaction

It is defined as the rate of change in concentration of either reactants or products per unit mole. “**Rate of change of concentration of reactant or product**” means the disappearance of amount of reactants or appearance of the amount of product in a unit interval of time. Unit of rate of reaction is mole L^{-1} sec^{-1}.

For a reaction, A ⟶ B

Rate =`-\frac{∆[A]}{∆t}=+\frac{∆[B]}{∆t}`

For a reaction, H_{2} + I_{2} ⟶ 2HI

Rate =`-\frac{∆[H_{2}]}{∆t}=-\frac{∆[I_{2}]}{∆t}=+\frac{1}{2}\frac{∆[HI]}{∆t}`

**Read also:** Surface Chemistry Class 12 Chemistry Notes Chapter 5

## Rate Law

It states that the rate of a chemical reaction is **proportional** to the product of the active masses of the reacting substances, raised to the power, equal to the respective number of their molecules taking part in a reaction as represented by the balanced chemical equation.

The theoretical rate of a reaction is given by **rate law**. Thus, for the general chemical change, mA + nB ⟶ Products

rate = `\frac{dx}{dt}\propto [A]^{m}\times [B]^{n}`

rate = `\frac{dx}{dt}=k[A]^{m}\times [B]^{n}`

Here, [A] = active mass of substance A

k = rate constant

**Read also:** Moving Charges and Magnetism Class 12 Physics Notes Chapter 4

## Factors Affecting Rate of a Chemical Reaction

**Rate of reaction** depends upon the experimental conditions such as concentration of reactants (pressure in case of gases), temperature and catalyst.

### i). Concentration of Reactant

The **rate of a reaction** depends on the concentration of reactant(s) according to the rate law expression. Hence, the rate of a reaction decreases as the reaction moves in the forward direction because the concentration of reactant(s) decreases.

### ii). Nature of Reactant and Product

**Chemical reactions** which involve complex molecules as reactants and in which complex molecules are formed as products, proceed at a slower rate. Greater number of bond rearrangements are involved in complex reactants and products which make the reaction slower. Reactions involving lesser number of bond rearrangements are fast.

### iii). Exposure to Radiations

**Rates** of certain reactions increase by absorption of photons of a particular radiation. Such reactions are called photochemical reactions. For example, photosynthesis in plants; formation of ozone in the stratosphere.

### iv). Temperature

For most of the reactions, the rate of reaction increases two to three times, with every 10°C rise in temperature. This rate of increase factor is known as **temperature coefficient**.

Temperature coefficient `=\frac{K_{T+10}}{K_T}=` 2 to 3

**Read also:** Conceptual Questions for Class 12 Physics Chapter 4 Moving Charges and Magnetism

### v). Presence of a Catalyst

Generally, a positive catalyst enhances the rate of a reaction by decreasing the activation energy, but negative catalyst retards a chemical reaction.

### vi). Surface Area of Solid Reactant

The rate of a reaction increases with increasing surface area of solid reactant, i.e.,

Rate of reaction ∝ Surface area of solid reactant

i.e.,Wood shavings burn more rapidly than a log of wood of same mass. Coal dust burns at a faster rate than a large piece of coal.

## Order and Molecularity

### i). Order of Reaction

The sum of powers of the concentration of the reactants in the rate law expression is called the **order** of that chemical reaction. It can be fraction, zero or any whole number.

By the equation of rate law,

Rate = k [A]^{x} [B]^{y}

Order of Reaction = x + y

Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero order reaction means that the rate of reaction is independent of the concentration of reactants.

#### a). Zero order reaction

Those reactions in which rate of reaction does not change with concentration of the reactants.

For a general reaction,

aA ⟶ bB

Rate law for such a reaction is expressed as.

Rate = k [A]°

Unit of rate constant for zero order reaction

`\frac{∆[A]}{∆t}=k[A]°`

Unit `=\frac{mol-L^{-1}}{sec}\times\frac{1}{(mol-L^{-1})°}=` mol L^{-1} sec^{-1}

#### b). First order reaction

A reaction is said to be first order if its reaction rate is determined by the variation of one concentration term only. Rate law for such a reaction is expressed as.

Rate = k [A]^{1}

Units of rate constant for first order reaction

`\frac{∆[A]}{∆t}=k[A]^1`

Unit `=\frac{mol-L^{-1}}{sec}\times\frac{1}{(mol-L^{-1})^1}=` sec^{-1}

#### c). Second order reaction

The reaction in which sum of powers of concentration terms in rate law equation is two. Rate law for such a reaction is expressed as.

Rate = k [A]^{2}

Units of rate constant for first order reaction

`\frac{∆[A]}{∆t}=k[A]^2`

Unit `=\frac{mol-L^{-1}}{sec}\times\frac{1}{(mol-L^{-1})^2}=` mol^{-1} L sec^{-1}

### ii). Molecularity of a Reaction

**Modularity** of reaction is defined as the number of reacting particles (atoms or molecules or any other species), which collides simultaneously to bring about the chemical change. It is a theoretical concept. Its value is always a whole number. It is never more than three. It cannot be zero.

For example, order of reaction and molecularity of electrolysis of water of Ethyl Acetate is given by

CH_{3}COOC_{2}H_{5} + H_{2}O ⟶ CH_{3}COOH + C_{2}H_{5}OH

**Order** = 1 (Because concentration of H_{2}O does not change duering the reaction)

**Molecularity** = 2

## Integrated Rate Equations

### i). Zero Order Reaction

The reaction whose rate does not depend upon the concentration of reactants is called a zero order reaction.

A ⟶ B is a zero order reaction, then

`-\frac{d[A]}{dt}=k[A]^{0}`

`-\frac{d[A]}{dt}=k`

`d[A]=-kdt`

Integrating both side of the equation,

`\int d[A]=-k\int dt`

`[A]=-k.t+C` .....(1)

At initial time t=0, putting [A]=[A]_{0} in eq. (1)

`[A]_{0}=-k\times 0+C`

`C=[A]_{0}`

Putting the value of C in the eq. (1)

`[A]=-k.t+[A]_{0}`

`[A]-[A]_{0}=-k.t`

`k.t=[A]_{0}-[A]`

`k=\frac{[A]_{0}-[A]}{t}`

This is the integrated form of equation of rate of zero order reaction.

### ii). First Order Reaction

If a general reaction A ⟶ B follows first order kinetics, then its rate law is,

`-\frac{d[A]}{dt}=k[A]`

`\frac{d[A]}{[A]}=-kdt`

Integrating both side of the equation,

`\int\frac{d[A]}{[A]}=-k\int dt`

`ln[A]=-kt+C` .....(1)

At initial time t=0, putting [A]=[A]_{0} in eq. (1)

`ln[A]_{0}=-k\times 0+C`

`C=ln[A]_{0}`

Putting the value of C in the eq. (1)

`ln[A]=-kt+ln[A]_{0}`

`kt=ln[A]_{0}-ln[A]`

`kt=ln\frac{[A]_{0}}{[A]}`

`k=\frac{2.303}{t}log\frac{[A]_{0}}{[A]}` .....[ln x = 2.303 log x]

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

This is the integrated form of equation of rate of zero order reaction.

## Half Life Period (t_{1/2})

The time in which half of the initial amount of reactants is converted to products or the time taken for 50% completion of reaction is known as **half life period**.

For first order reaction, A ⟶ Products

`k=\frac{2.303}{t}log\frac{a}{a-x}`

For t_{1/2}, x = `\frac{a}{2}`

`k=\frac{2.303}{t_{1/2}}log\frac{a}{a-a/2}`

`t_{1/2}=\frac{2.303}{k}log\frac{a}{a/2}`

`t_{1/2}=\frac{2.303}{k}log2`

`t_{1/2}=\frac{2.303}{k}\times 0.3010`

`t_{1/2}=\frac{0.693}{k}`

## Collision thoery

According to the collision theory, “the molecules of reactants are assumed to be hard spheres and the reactions are assumed to occur only when these spheres (molecules) collide with each other”. In collision theory **activation energy** and proper orientation of the molecules together determine the criteria for an **effective collision** and hence the rate of a chemical reaction.

### Effective Collisions

The number of collisions per second per unit volume of the reaction mixture is called **collision frequency** (z).

### Collision Frequency

The molecules which have sufficient energy and proper orientation collide to give product, such collisions are called effective collisions.

### Activation Energy

The **activation energy** is the minimum amount of energy needed by the reacting particles in any particular reaction for that reaction to take place. Unless particles collide with sufficient energy to supply the activation energy they simply don’t react.

### Arrhenius equation

The actual dependence of rate constant on temperature is represented by the Arrhenius equation:

`k=Ae^{{E_a}/{RT}}`

k/A is defined as the fraction of molecules undergoing effective collisions per unit time.

A ⟶ Arrhenius constant or frequency factor.

E_{a} ⟶ Activation energy

R ⟶ Gas constant

## Radio Carbon Dating

C^{14} dating is based on the fundamental assumption that intensity of cosmic rays and hence of C^{14} in the atmosphere has been constant over thousands of years. This gives the initial activity of C^{14} corresponding to the time when a plant or an animal died and further assimilation of radiocarbon ceased.

_{7}N^{14} + _{0}n^{1} ⟶ _{6}C^{14} + _{1}H^{1}

_{6}C^{14} ⟶ _{7}N^{14} + _{-1}e^{0}

time period can be calculated by

`t=\frac{2.303}{\lambda}log\frac{N_0}{N_t}`

t_{1/2} of C^{14} = 5770 years

## Summary

**Chemical kinetics**is the study of chemical reactions with respect to reaction rates, effect of various, variables rearrangement of atoms and formation of intermediates.The

**rate of a reaction**is concerned with decrease in concentration of reactants or increase in concentration of products per unit time.**Rate law**is the mathematical representation for rate of reaction. It can be determined experimentally and cannot be predicted.**Order of a reaction**with respect to a reactant is the power of its concentration term which appears in the rate law. It is an experimentally determined quantity.**Molecularity**of a reaction is the number of reacting species taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction.Rate constant is the proportionality constant in rate law.

Intergrated rate equations can be determined by intergrating the differential rate equations.

**Half life**is the time in which half of the initial amount of reactants is converted into products (time taken for 50% completion of reactions).A number of factors such as nature of reactants and products, exposure to radiations, temperature, concentration of reactants, catalyst and surface area of solid reactants affect the rate of a reaction.

In

**collision theory**, activation energy and proper orientation of the molecules together determine the criteria for an effective collision and hence rate of a reaction.**Nuclear chemistry**is the study of chemical reactions involving changes in nuclei of atoms. It provides information about kinetics of radioactive decay and time period.