Chemical Kinetics Class 12: Rate Law, Integrated Equations, and Arrhenius Theory by PW

Chemical Kinetics focuses on how fast chemical reactions take place and the factors responsible for changes in their rates. It provides a basis for studying the dependence of reaction rates on concentration, temperature, activation energy, and catalysts, along with the steps through which reactions occur.

For revision, you should understand how rate expressions are formulated and how integrated equations are applied to reactions of different orders. This PW Class 12 Chemical Kinetics notes covers zero-order and first-order reactions, half-life, general order kinetics, Arrhenius theory, and the effect of catalysts on reaction rates.

Rate Of Reaction And Stoichiometry

The rate of reaction indicates how quickly the concentration of a reactant or product changes with time.

Rate = Change in concentration / Change in time

Since reactants are consumed during a reaction, their concentration decreases with time. In contrast, the concentration of products generally increases. Therefore, different signs are used when writing rate expressions.

The rate of reaction is expressed as a positive quantity. The negative sign in the reactant expression compensates for the decrease in reactant concentration.

Stoichiometric Relationships

Consider the general reaction:

aA + bB → cC + dD

The concentrations of different reactants and products may change at different rates because their stoichiometric coefficients are different. To obtain a common rate of reaction, the individual rates are divided by their respective stoichiometric coefficients.

Rate = −(1/a)(d[A]/dt) = −(1/b)(d[B]/dt) = (1/c)(d[C]/dt) = (1/d)(d[D]/dt)

This relationship connects the rates of consumption and formation of all the species involved in the reaction.

Classification Of Reactions

Based on the number of steps involved, reactions can be classified into elementary and complex reactions.

• Elementary Reactions: These occur in a single step without involving a sequence of simpler reactions.

• Complex Reactions: These proceed through two or more elementary steps and may involve intermediate species.

In a complex reaction, one of the elementary steps may proceed more slowly than the others. This slow step can determine the overall reaction rate and is called the Rate Determining Step (RDS).

Rate Law And Order Of Reaction

The rate law represents the dependence of reaction rate on the concentrations of the reactants. It is determined experimentally.

For a reaction involving A and B:

Rate = k[A]ˣ[B]ʸ

Here:

• k = rate constant

• [A] and [B] = concentrations of the reactants

• x and y = experimentally determined powers

Rate Constant

The rate constant (k) is the proportionality constant in the rate law. Its value depends on factors such as:

• Nature of the reactants

• Temperature

• Presence of a catalyst

For a given reaction under specified conditions, the rate constant is independent of the concentrations of the reactants.

Order Of Reaction

The overall order of a reaction is the sum of the powers of the concentration terms in its rate law.

n = x + y

The order of reaction is an experimental quantity. It can be zero, positive, negative, fractional or an integer.

For an elementary reaction, the order with respect to a reactant is equal to its stoichiometric coefficient.

Units Of Rate Constant

For an overall reaction order n, the units of the rate constant can be represented as:

Units of k = (mol/L)^(1−n) s⁻¹

Common examples are:

Quick Recall: The units of k can help identify the order of a reaction. For example, s⁻¹ indicates a first-order reaction, while mol L⁻¹ s⁻¹ indicates a zero-order reaction.

Molecularity Of A Reaction

Molecularity is the number of reacting species that participate simultaneously in a single elementary reaction step.

It is a theoretical concept and is applicable only to elementary reactions.

Depending on the number of reacting species, molecularity may be:

1. Unimolecular → Molecularity = 1

2. Bimolecular → Molecularity = 2

3. Trimolecular → Molecularity = 3

Molecularity cannot be zero, negative or fractional because it represents an actual number of reacting particles involved in an elementary step. Molecularity generally does not exceed three because simultaneous collisions involving more particles are highly unlikely.

Order Of Reaction Vs Molecularity

Zero-Order Reactions

A zero-order reaction is one in which the rate remains independent of the concentration of the reactant.

The differential rate equation is:

Rate = −d[A]/dt = k[A]⁰ = k

Integrated Rate Law

For an initial concentration [A]₀ and concentration [A]ₜ after time t, the integrated rate equation is:

[A]ₜ = [A]₀ − kt

A graph of [A]ₜ versus t is a straight line.

• Slope = −k

• Y-intercept = [A]₀

Half-Life Period

The half-life (t₁/₂) is the time required for the concentration of a reactant to become half of its initial value.

For a zero-order reaction:

t₁/₂ = [A]₀/(2k)

Therefore:

t₁/₂ ∝ [A]₀

This shows that the half-life of a zero-order reaction increases with an increase in the initial concentration.

First-Order Reactions

In a first-order reaction, the rate depends directly on the first power of the reactant concentration.

Rate = −d[A]/dt = k[A]

Integrated Rate Law

For a first-order reaction, the integrated rate equation is:

ln([A]₀/[A]ₜ) = kt

Using common logarithms, the equation becomes:

k = (2.303/t) log₁₀([A]₀/[A]ₜ)

The concentration at time t can also be represented in exponential form:

[A]ₜ = [A]₀e⁻ᵏᵗ

Degree Of Dissociation

If α represents the degree of dissociation, then:

α = Moles reacted / Moles taken

The integrated equation can then be written as:

ln[1/(1 − α)] = kt

Half-Life Period

For a first-order reaction:

t₁/₂ = 0.693/k

The important feature of a first-order reaction is that its half-life does not depend on the initial concentration.

Comparison: Zero-Order Vs First-Order Kinetics

General Nth-Order Kinetics

For a reaction of order n, where n ≠ 1, the integrated rate equation is:

[1/(n − 1)] [1/[A]ₜ⁽ⁿ⁻¹⁾ − 1/[A]₀⁽ⁿ⁻¹⁾] = kt

The general relationship for half-life is:

t₁/₂ ∝ 1/[A]₀⁽ⁿ⁻¹⁾

or

t₁/₂ ∝ [A]₀⁽¹⁻ⁿ⁾

Second-Order Reaction

For a second-order reaction, n = 2. The integrated rate equation becomes:

1/[A]ₜ − 1/[A]₀ = kt

Its half-life follows the relationship:

t₁/₂ ∝ 1/[A]₀

Thus, increasing the initial concentration decreases the half-life of a second-order reaction.

Temperature Dependence And Arrhenius Equation

Temperature can significantly influence the rate constant of a chemical reaction. The Arrhenius equation describes the relationship between the rate constant, temperature and activation energy.

k = Ae⁻ᴱᵃ/ᴿᵀ

Here:

• k = rate constant

• A = Arrhenius pre-exponential factor or frequency factor

• Eₐ = activation energy

• R = universal gas constant

• T = absolute temperature in Kelvin

The activation energy (Eₐ) is the minimum energy required for reactant molecules to reach the transition state and undergo the reaction.

Logarithmic Form Of Arrhenius Equation

Taking the natural logarithm of the Arrhenius equation gives:

ln k = −(Eₐ/R)(1/T) + ln A

Therefore, a plot of ln k versus 1/T gives a straight line.

• Slope = −Eₐ/R

• Y-intercept = ln A

Two-Temperature Form

When the rate constants at two different temperatures are known, the following equation can be used:

ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂)

Here, k₁ and k₂ are the rate constants at temperatures T₁ and T₂, respectively.

Role Of A Catalyst

A catalyst increases the rate of a reaction by providing an alternative reaction pathway with a lower activation energy.

Important effects of a catalyst include:

• It lowers the activation energy (Eₐ) of the reaction pathway.

• It does not change the initial and final energy states of the reaction.

• It does not alter thermodynamic quantities such as ΔH and ΔG.

• It increases the rates of both forward and backward reactions.

• It does not change the equilibrium position.

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