The rate of a chemical reaction is a measure of how quickly reactants are converted into products in a given time. It quantifies the speed of the reaction, typically expressed in terms of the change in concentration of a reactant or product per unit time. Here are some key points about the rate of reaction:

4.1. introduction of chemical kinetics

Every chemical reaction proceeds at a diferent rate or speed. Some reactions proceed very slowly and may take a number of days to complete; while others are very rapid, requiring only a few seconds. For example, rusting of iron could start quickly, while ripening of fruits may be completed in a few days. On the other hand, weathering of stone may take more than a decade and the breakdown of plastics in the environment takes more than hundred years. However, other reactions, like the combustion of gasoline or the explosion of gunpowder occur in a few seconds. Can you add more examples from your experience?

To be useful reactions must occur at a reasonable rate. The area of chemistry that is concerned with reaction rates is called chemical kinetics. The word “kinetic”suggests movement or change.

Chemical kinetics refers to the rate of reaction, which is the change over time in the concentration of reactants and products.

Chemical kinetics studies the rate at which a chemical process occurs. Besides information about the speed at which reactions occur, chemical kinetics also sheds light on the reaction mechanism, which focuses on how the reaction occurs . (exactly how the reaction occurs).

4.2.The Rate of Reaction

The rate of a chemical reaction measures the change in concentration of a reactant or a product per unit time.This means that the rate of a reaction determines how fast the concentration of a reactant or product changes with time.
For example, for a general reaction: Reactants ➔ Products
This equation tells us that, during the course of a reaction, reactant molecules are consumed while product molecules are formed. As a result an, we can follow the progress of are action by monitoring either the decrease in concentration of the reactants or the increase in concentration of the products.
Consider the progress of a simple reaction : A ➔ B
The decrease in the number of A molecules and the increase in the number of B molecules with time are shown in figure

In general, it is more convenient to express the rate in terms of change in concentration with time.

Rate of reaction = Change in concentration of substance /change in time

R= $\frac{\Delta C}{\Delta t}$

Reaction rate and Stoichiometry

• Consider the general equation:- aA + bB ➔ cC + dD

Where a, b, c, and d are coefficients of the respective chemical species A, B, C and D.

• The relationships between the various rates is given by:

$\text{Rate} = -\frac{\Delta A}{a \Delta t} = -\frac{\Delta B}{b \Delta t} = \frac{\Delta C}{c \Delta t} = \frac{\Delta D}{d \Delta t}$

EXAMPLES

1. For the Reaction:- 2HI(g) ➔ H₂(g) + I₂(g) . Express the rate of reaction in terms of the concentration of:
   a) H₂
   • b) HI

Solution:-
a) R_H2 = $\frac{\Delta [H_2]}{\Delta t}$

b) R_HI= $-\frac{\Delta [HI]}{\Delta t}$

2. What is the valid rate expression for each molecule of the reaction; 2NO + 2H₂ ↔ N₂ +2H₂O

Solution:-
R_NO = $\frac{\Delta [NO]}{2 \Delta t}$
R_H2 = $\frac{\Delta [H_2]}{2 \Delta t}$
R_N2 = $\frac{\Delta [N_2]}{\Delta t}$
R_H2O = $\frac{\Delta [H_2O]}{2 \Delta t}$

3. In the reaction of nitric oxide with hydrogen : 2NO(g) + 2H₂(g) → N₂(g) + 2H₂O (g)
If the rate of disappearance of NO is 5.0 × 10^–5 mol L^–1s^–1, what is the rate of reaction for the formation of N₂?
Solution:
The rate of reaction for the formation of N₂ = $ \frac{[N_2]}{t} = \frac{[NO]}{2t}$

$\frac{R_{NO}}{2}$ = RN₂ = $\frac{5.0}{2}$ x10^-5 mol L^–1s^–1 = 2.5 × 10^–5 mol L^–1s^–1

Note that A denotes the difference between the final and initial state. Thus, for the preceding reaction we can express the rate as:

2A ➔ B
Rate =Δ [A]/ 2 Δt = 1 [B]÷ Δt


inwhich,[A]and[B]are the changes in concentration(mol/L)over aperiodic ΔC/Δt, [A]is a negative quantity. The rate of a reaction is a positive quantity, so a minus sign is needed in the rate expression to make the rate positive. On the other hand, the rate of product formation does not require a minus sign because [B] is a positive quantity (the concentration of B increases with time).

Writr the rate expression interms of disappearance of the reactants and the appearance of the products:

a. I−(aq) + OCl− (aq) → Cl− (aq) + OI− (aq)
b. 3O2(g) → 2O3(g)
c. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g)
Solution:
a. Because each of the stoichiometric coefcients equals 1,

r = Δ[I^–]/Δt =Δ[OCl-]/Δt = Δ[Cl-]/Δt= ΔC[OI-]/Δt

Determination of Rate of Reaction

To determine the rate of a chemical reaction, you need to measure how the concentration of a reactant or product changes over time. There are several methods used depending on the nature of the reaction and the substances involved.

1. Measurement of Concentration Changes

titration: You can take samples from the reaction mixture at different times and titrate them to find the concentration of a reactant or product.

2. Measurement of Volume

Changes gas Volume: For reactions that produce a gas, you can measure the volume of gas produced over time using a gas syringe or an inverted measuring cylinder.

3. Pressure Measurement: If the reaction involves gases and is carried out in a closed system, changes in pressure can be used to determine the rate of reaction.

4. Measurement of Mass Changes ( Mass Loss) : If a gas is produced and escapes the reaction vessel, you can measure the rate of mass loss using a balance.

5. Measurement of Color Change colorimetry: For reactions that involve a change in color, a colorimeter can be used to track the rate of reaction by measuring changes in color intensity.

for the reaction A ➔ B , the Concentration of Reactant ( A ) Over Time is given in the following table

Time (s)	Concentration of ( A ) (M)
0	0.100
10	0.08
20	0.072
30	0.060
40	0.050
50	0.042
60	0.035

To determine the change in concentration over time, for example, between 0 and 10 seconds, the concentration of ( A ) decreases from 0.100 M to 0.085 M.

Change in concentration: −∆[A] = 0.100M- 0.085M = 0.015M

Time interval: ∆t = 0- 10s = 10sec

To calculate the rate of reaction: Rate = −∆A/∆t = -0.015 M/10s = -0.0015 M/s

To repeat for other intervals, from 10seconds to 20 seconds:

-∆[A] = 0.085M – 0.072M = 0.013M

Rate = -0.013M/10s = -0.0013 M/s …..and so on for each interval.

Summary of Rate Calculation

Time(s) (Δt[A](M) Rate of Reaction (M/s) 0 – 10 0.015 0.0015

10 – 20 0.013 0.0013

_{20 – 30 0.012 0.0012}

30 – 40 0.010 0.0010

40 – 50 0.008 0.0008

50 – 60 0.007 0.0007

Plotting concentration vs. time:

The table above and its resulting analysis help illustrate how the concentration of a reactant changes over time and how to calculate the rate of reaction from that data.The rate of reaction decreases over time as the concentration of [A] decreases. so graphically a decreasing curve shows how the rate of the reaction decreases over time .

Conditions needed for a chemical reaction

For a chemical reaction to occur, several conditions must be met. These conditions ensure that the reactants interact in a way that allows for the breaking and forming of chemical bonds, leading to the production of products.

Primary conditions needed for a chemical reaction:

1. Reactant Contact (Collision Theory)

Molecules Must Collide: For a reaction to take place, the reactant molecules must physically collide with each other.Sufficient Energy: These collisions must occur with enough kinetic energy to overcome the activation energy barrier, allowing bonds to break and new bonds to form.

2. Proper Orientation or Correct Alignment: The reactant molecules must be oriented in a specific way when they collide so that the parts of the molecules that need to react come into contact. Incorrect orientation can lead to ineffective collisions where no reaction occurs.

3. Activation Energy (Minimum Energy Requirement) : Activation energy is the minimum amount of energy required to initiate a chemical reaction. If the reacting particles do not have sufficient energy to overcome this barrier, the reaction will not occur.

Catalysts: Catalysts lower the activation energy required, making it easier for a reaction to occur at a given temperature.