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Chemical Kinetics

“Chemical Kinetics involves the study of the rates and mechanism of chemical reactions.” 

Rate of Reaction

The rate of reaction refers to the speed at which the products are formed from the reactants in a chemical reaction.

Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Consider a reaction of the form
A + 2B  → 3C + D...........(1)
in which the molar concentration of participants are [A], [B], [C] & [D].
The rate of consumption or decomposition of one of the reactants at a given time is Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry where R is A or B. The rate of formation of one of the products is  Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistrywhere P is C or D.
The rate of reaction can be expressed with respect to any species in equation (1).
 

Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Thus, the rate of reaction can be defined with respect to both reactants and products.
For example:
4NO2 (g) + O2 (g)  → 2N 2O2 (g)
Q.1. Find the expression for the Rate of Reaction.
4NO2 (g) + O2 (g)  → 2N 2O2 (g)

Sol:

Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Question for Introduction to Chemical Kinetics: Rate, Rate Law & Order
Try yourself:
Which of the following expressions represents the rate of reaction for the given chemical equation?

4NO2 (g) + O2 (g) ? 2N2O2 (g)
View Solution

Rate Law and Rate Constant

The rate of a reaction will generally depend on temperature pressure and the concentration of species involving in the reaction.
The rate of reaction is proportional to the molar concentration of reacting species.
i.e. A + B + C + D + ……. → Product
then, rate of reaction = k[A][B]b [C]c [D]d ………..

where [A] is the concentration of reactant A, [B] is the concentration of reactant B and so on. The constant a is known as the reaction order with respect to species A, b the reaction order with respect to species B, and so on.
The overall reaction order is equal to the sum of the individual reaction orders (a + b + c + d + ……..). Finally, the constant k is the rate constant for the reaction.
The rate constant is not only dependent on concentration but also on temperature & pressure.

This relationship is known as a rate law. 

Order of the Reaction

A + B + C + ………  → Product
The rate law = v = k[A]a [B]b [C]c ……..
The order of reaction = a + b + c + ……
For example: if rate law = v = k[A]1/2 [B]
Then, it is half order in A, first-order in B, and three half Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistryorder overall.

Molecularity of a Reaction

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

Question for Introduction to Chemical Kinetics: Rate, Rate Law & Order
Try yourself:
What is the rate law for a reaction involving species A, B, and C?
View Solution

Relationship between Rate law, Order, and the Rate Constant:

Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Then, rate of reaction =  Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

The unit of rate of reaction is mol liter–1 sec–1 i.e. mol L–1 s–1.
where M represents mol L–1 or moles per liter & n is the order of reaction.
The unit of rate constant (k)
Rate of reaction = k[A]n
unit of rate of reaction = unit of k × [unit of concentration]
MS–1 = unit of k × [M]n

 ⇒  unit of k = Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

i.e., unit of k     = M1 - n S-1 = mol1 - n Ln - 1 S-1

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Q.2. Find the order of the reaction if unit of rate constant or the reaction is (dm3)3/2 mol–3/2 s–1.
 Sol. 
Unit of rate constant = (dm3)3/2 mol–3/2 s–1 (given)
We know that,
Unit of rate constant = M1 – n s–1
For nth order
i.e. M1 - n s -1 = (dm3 )3 / 2 (mol)-3 / 2 s -1

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

∵      1 L = 1 dm3
&  Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry
Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

i.e. it is 5/2 order reaction.
 

Determination of Order of Reaction 

Using the following data for the reaction, we determine the order of the reaction with respect to A and B, over all order and rate constant for the reaction

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

Sol. A + B  → Product
rate of react ion = k[A]a [B]b
5.25 × 10–4 = k[2.30 × 10–4]a [3.10 × 10–5]b ...(1)
4.20 × 10–3 = k[4.60 × 10–4]a [6.20 × 10–5]...(2)
1.70 × 10–2 = k[9.20 × 10–4]a [6.20 × 10–5]b ...(3)

Divide equation (2) by equation (3), we get

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry

2.47 × 10–1 = (0.5)a
(0.247) = (0.5)a
(0.5 × 0.5) ≈ (0.5)a
(0.5)a ≈ (0.5)a
or taking log we can find the value of a.
a = 2
Divide equation (1) by equation (2) we get

 Introduction to Chemical Kinetics: Rate, Rate Law & Order | Physical Chemistry
1.25 × 10–1 = [0.5]a [0.5]b = [0.5]2 [0.5]b
= 0.25 [0.5]b
5 × 10–1 = [0.5]b
⇒ 0.5 = [0.5]b
⇒ b = 1 

Therefore, the reaction is second order in A and first order in B, and third-order overall.

rate = k[A]2 [B]
5.2 × 10–4 Ms–1 = k(2.3 × 10–4 M)2 (3.1 × 10–5]M
⇒ k = 3.17 × 108 M–2 s–1
i.e. the over all rate law is
rate = (3.17 × 108 M–2 s–1) [A][B]

Question for Introduction to Chemical Kinetics: Rate, Rate Law & Order
Try yourself:Which of the following represents the unit of the rate constant (k) in a reaction?
View Solution

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FAQs on Introduction to Chemical Kinetics: Rate, Rate Law & Order - Physical Chemistry

1. What is chemical kinetics?
Ans. Chemical kinetics is the study of the rates at which chemical reactions occur, the factors that influence these rates, and the mechanisms by which reactions proceed.
2. What is the rate of a chemical reaction?
Ans. The rate of a chemical reaction is the speed at which reactants are converted into products. It is typically expressed as the change in concentration of a reactant or product per unit time.
3. What is the rate law of a chemical reaction?
Ans. The rate law of a chemical reaction is an equation that relates the rate of the reaction to the concentrations of the reactants. It is determined experimentally and can provide insight into the reaction mechanism.
4. What is the rate constant of a chemical reaction?
Ans. The rate constant is a proportionality constant in the rate law equation that reflects the specific reaction rate at a given temperature. It is unique to each reaction and is influenced by factors such as temperature and the presence of catalysts.
5. What is the order of a chemical reaction?
Ans. The order of a chemical reaction refers to the sum of the exponents in the rate law equation. It indicates how the rate of the reaction is affected by changes in the concentrations of the reactants.
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