## Chapter:4

# What are Chemical Kinetics ?

## Rate Of Reaction

- The average rate is defined as the ratio of the change in the concentration of the reactants or products of reaction to the time interval.
- The rate of reaction at a given time is called an instantaneous rate of reaction.
- The instantaneous rate at the beginning of a reaction is called the initial rate of reaction.
- Instantaneous rate is determined from a graph of concentration vs time by drawing a line tangent to the curve at that particular time.

## Reaction Rate Law

_{m}[Y]

_{n}[X] and [Y] = molar concentrations of X and Y m and n = powers to which the concentrations must be raised (can only be determined empirically) k = constant of proportionality known as the rate constant (determined empirically, only valid for a specific reaction at a specific temperature.

## Instantaneous Rate Of Chemical Reaction

The rate of reaction changes from time to time as the reaction happens.

The rate of reaction at a particular time is called the instantaneous rate.

The instantaneous rate of a reaction is equal to the gradient of tangent at a particular time.

Rate of reaction =𐤃(Product)/𐤃(Time)

𐤃(Product) = Change of the amount of product

𐤃(Time) = Change of the time

## Average Rate Of Chemical Reaction

It may be defined as the change in concentration of a reactant or product of a chemical reaction in a given interval of time.

So,

Average rate of reaction

=Change in concentration of reactants or products/Time interval

We can rewrite the equation as :

rateA=𐤃[A]/𐤃t

Where 𐤃 indicates the change in quantity,

chemical symbols in square brackets, [ ],

indicate the entity’s concentration, in mol/L.

## Factors Affecting The Rate Of Reaction

**Total Surface Area:**For some amount of reactant, particles with smaller size has bigger total surface area. The bigger the total surface area, higher is the rate of reaction.**Concentration of Solution:**The higher the concentration, higher is the rate of reaction.

**Factors**

**Temperature:**The higher the temperature, higher is the rate of reaction.**Catalyst:**1. Positive catalyst- Increases the rate of reaction.

2. Negative catalyst- Reduces the rate of reaction**Pressure:**The higher the pressure, higher is the rate of reaction.

## Order And Molecularity Of A Reaction

The sum of the powers of concentration terms in rate equation is known as order of reaction. The order of a reaction is determined experimentally and it can be zero, fractional or integer. The number of ions, atoms or molecules involve in the rate determining step or rate limiting step is known as molecularity of a reaction. The molecularity of a reaction is determined theoretically and it can never be zero or fraction.

Reaction | Order | Units of rate constant |

Zero order reaction | 0 | mol L ^{–1}/s × 1/(mol L ^{–1})0= mol L ^{–1}s ^{–1} |

First order | 1 | mol L ^{–1} × 1/(mol L ^{–1})1 = s ^{–1} |

Second order reaction | 2 | mol L ^{–1}/s × 1/(mol L ^{–1})2= L mol ^{–1}s ^{–1} |

## Half-life Equations

For a zero-order reaction, t1/2 is directly proportional to the initial concentration :

t1/2 =[A]0/2k (zero order process; rate = k)

For a first-order reaction, t1/2 does not depend on the initial concentration.

## Half-life Of A Reaction

The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as t1/2.

t1/2 for a Zero Order Reaction

For a zero order reaction, rate constant is given by equation

k =([R]0 – [R])/t

At t = t1/2. [R] =1[R]0/2

The rate constant at t1/2 becomes

k =([R]0 – 1/2[R]0)/t1/2

t1/2 =[R]0/2k

It is clear that t1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.

## Half-life Of First Order Reaction

The half-life, t1/2, is the time required for the concentration of a reactant to decrease to half of its initial concentration.

t1/2 = t when [A] = [A]0/2 = ln([A]0/[A]0/2)/k=ln 2/k=0.693/k

**Determining Rate law and Integrated Rate law for Zero and first order reaction**

Order | Rate law | Integrated Rate Law | Linear plot | Slope | Units |

0 | rate = k | [A] _{0} – [A] _{t} = kt | [A] vs t | –k | mol L ^{–1}s ^{–1} |

1st | rate = k[A] | ln[A] _{t}/[A] _{0}= –kt | ln[A] vs t | –k | s ^{–1} |

## Concept Of Collision Theory

(Max Trautz and william Lewis gave this theory in 1916-1918)

- 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.
- Let the reaction is : P + Q → Product now as per collision theory, Rate = ZPQ→e-Ea/RT
- Note : Collision frequency is calculated by number of collisions per second per unit volume of the reacting mixture.

$$\text{Where :}\\ \begin{dcases} \text{Z}_{\text{PQ}} = \text{Collision frequency of P Q}\\ \text{E}_\text{a} = \text{activation energy,}\\ \text{R} = \text{universal gas constant.}\\ \text{T} = \text{Temperature in absolute scale}\\ \text{ρ}= \text{Steric factor.} \end{dcases}$$

## Activation Energy (E A)

Activation energy is the minimum amount of extra energy needed by the reacting molecule to get converted into product. It is usually measured in joules or kilojoules/mole or K.Cal/mol.

**For exothermic reaction :**(Ea) forward reaction < (Ea) backward reaction.**For endothermic reaction :**(Ea) forward reaction > (Ea) backward reaction.

## Arrhenius E Quation (Given By S Vante Arrhenius In 1889)

It is an expression that provides a relationship known the rate constant absolute temperature and the A factor (Also known pre exponential factor or frequency factors).

K ∞ e^{-Ea/RT} = A e^{-Ea/RT}

Where A is frequency factor, Ea = activation energy, T = absolute temperature R is universal gas constant and K is rate constant of the reaction.