Chapter 3: Chemical Kinetics

Rate of Chemical Reaction

Definition and Measurement

Chemical kinetics is the branch of chemistry that studies the speed or rate of chemical reactions and the mechanisms by which they occur. The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time.

Rate Expressions

For a reaction A + B → C, the rate of disappearance of reactant A is given by Rate = -Δ[A]/Δt. Similarly, the rate of appearance of product C is Rate = Δ[C]/Δt. Concentrations are expressed in molarity (mol L⁻¹).

Units and Types of Rates

The unit of rate of reaction is mol L⁻¹ s⁻¹ or mol L⁻¹ min⁻¹ for reactions in solution, and atm s⁻¹ or atm min⁻¹ for gaseous reactions. Instantaneous rate refers to the rate at a specific moment, while average rate is measured over a time interval.

Factors Affecting Rate

• Concentration: Increasing reactant concentration generally increases the reaction rate.
• Temperature: Higher temperatures increase molecular kinetic energy, increasing reaction rates.
• Pressure: For gases, increased pressure increases concentration and rate.
• Catalysts: Substances that lower activation energy and increase reaction rate without being consumed.
• Nature of Reactants: Simpler molecules react faster due to fewer bonds to break.
• Surface Area: Greater surface area of solids increases reaction rate.
• Radiation: Photochemical reactions are initiated by light and often proceed faster.
• Physical State: Reactivity depends on whether substances are solid, liquid, or gas.

Solved Examples

Example 1

For the reaction R → P, the concentration of R changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction in mol L⁻¹ min⁻¹ and mol L⁻¹ s⁻¹.

Solution:

Average rate = -Δ[R]/Δt = -(0.02 - 0.03)/25 = 4 × 10⁻⁴ mol L⁻¹ min⁻¹

Converting to seconds: 4 × 10⁻⁴/60 = 6.67 × 10⁻⁶ mol L⁻¹ s⁻¹

Example 1

For the reaction R → P, the concentration of R changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction in mol L⁻¹ min⁻¹ and mol L⁻¹ s⁻¹.

Solution:

Average rate = -Δ[R]/Δt = -(0.02 - 0.03)/25 = 4 × 10⁻⁴ mol L⁻¹ min⁻¹

Converting to seconds: 4 × 10⁻⁴/60 = 6.67 × 10⁻⁶ mol L⁻¹ s⁻¹

Example 1

For the reaction R → P, the concentration of R changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction in mol L⁻¹ min⁻¹ and mol L⁻¹ s⁻¹.

Solution:

Average rate = -Δ[R]/Δt = -(0.02 - 0.03)/25 = 4 × 10⁻⁴ mol L⁻¹ min⁻¹

Converting to seconds: 4 × 10⁻⁴/60 = 6.67 × 10⁻⁶ mol L⁻¹ s⁻¹

Example 1

For the reaction R → P, the concentration of R changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction in mol L⁻¹ min⁻¹ and mol L⁻¹ s⁻¹.

Solution:

Average rate = -Δ[R]/Δt = -(0.02 - 0.03)/25 = 4 × 10⁻⁴ mol L⁻¹ min⁻¹

Converting to seconds: 4 × 10⁻⁴/60 = 6.67 × 10⁻⁶ mol L⁻¹ s⁻¹

Practice Set

• Level 1: Define the rate of a chemical reaction and state its units.
• Level 2: Explain how temperature affects the rate of a chemical reaction.
• Level 3: A reaction has a rate of disappearance of reactant A as 0.005 mol L⁻¹ s⁻¹. Calculate the rate of appearance of product if the reaction is A + B → C.
• Answer: The rate of disappearance of A is 0.005 mol L⁻¹ s⁻¹. For the reaction A + B → C, the stoichiometric ratio of A to C is 1:1, so the rate of appearance of C is also 0.005 mol L⁻¹ s⁻¹.

Answer Key

• Level 1: Rate of reaction is the change in concentration of reactants or products per unit time. Units are mol L⁻¹ s⁻¹ or mol L⁻¹ min⁻¹.
• Level 2: Increasing temperature increases molecular kinetic energy, leading to more frequent and energetic collisions, thus increasing reaction rate.
• Level 3: Rate of appearance of product C = rate of disappearance of A = 0.005 mol L⁻¹ s⁻¹.

Order of Reaction

Definition and Determination

The order of a reaction is the sum of the powers of the concentration terms in the experimentally determined rate law. It indicates how the rate depends on reactant concentrations and can be zero, whole number, or fractional. The order is determined only from experiment and may differ from the stoichiometric coefficients of the balanced chemical equation.

The molecularity of a reaction is not the same as order. Molecularity is the number of reacting species taking part in a single elementary step, whereas order is obtained from the rate law for the overall reaction.

Types of Reaction Orders

• Zero Order: Rate is independent of reactant concentration. Rate = k.
• First Order: Rate is directly proportional to concentration. Rate = k[A].
• Pseudo First Order: A reaction that is actually of higher order but behaves like first order because one reactant is taken in large excess, so its concentration remains nearly constant.
• Second Order: Rate depends on the square of one reactant or the product of two reactants. Rate = k[A][B] or k[A]².

Higher-order reactions may also occur, but in Class 12 chemistry the above orders are the most commonly discussed in rate laws and half-life calculations.

Rate Constant and Units

The rate constant k varies with temperature and is characteristic of a particular reaction at a given temperature. Its units depend on the overall order of the reaction: mol L⁻¹ s⁻¹ for zero order, s⁻¹ for first order, and L mol⁻¹ s⁻¹ for second order.

More generally, the units of k change so that the rate always has the units of concentration per unit time.

Half-life

Half-life is the time required for the concentration of a reactant to reduce to half its initial value. For first order reactions, half-life is independent of concentration and is given by t_1/2 = 0.693/k.

For zero order reactions, t_1/2 = [A]₀/2k, and for second order reactions, t_1/2 = 1/k[A]₀.

Thus, the dependence of half-life on initial concentration is different for different orders: it is constant for first order, proportional to [A]₀ for zero order, and inversely proportional to [A]₀ for second order.

Solved Examples

Example 2

A first-order reaction is 20% complete in 40 minutes. Calculate the time required for 60% completion.

Solution:

For a first-order reaction, t = 2.303/k log(a/(a - x))

For 20% completion, x = 20 and a - x = 80:

40 = 2.303/k log(100/80)

k = 2.303 × log(100/80) / 40 = 0.00279 min⁻¹

For 60% completion, x = 60 and a - x = 40:

t = 2.303/k log(100/40) = 164.42 minutes

Practice Set

• Level 1: Define the order of a reaction.
• Level 2: Write the rate law for a second-order reaction involving two reactants.
• Level 3: Calculate the half-life of a first-order reaction with rate constant k = 0.02 s⁻¹.

Answer Key

• Level 1: Order is the sum of the powers of the concentration terms in the rate law.
• Level 2: Rate = k[A][B]
• Level 3: t_1/2 = 0.693 / 0.02 = 34.65 seconds

Collision Theory

Concept and Activation Energy

Collision theory states that chemical reactions occur when reactant molecules collide with sufficient energy and proper orientation. The minimum energy required for a collision to be effective is called activation energy (E_a).

A collision is effective only if the colliding particles can overcome the energy barrier and form the activated complex, after which products are formed. Higher activation energy means fewer molecules have enough energy to react at a given temperature, so the reaction is slower.

Effective Collisions and Rate

Only collisions with energy equal to or greater than E_a and correct orientation lead to product formation. The rate of reaction depends on collision frequency (Z) and the fraction of effective collisions (f): Rate = f × Z.

At higher temperature, the number of effective collisions increases because more molecules possess energy greater than or equal to E_a. A catalyst also increases the rate by lowering E_a, thereby increasing the fraction of effective collisions.

Arrhenius Equation

The Arrhenius equation relates the rate constant k to temperature T and activation energy E_a:

k = A e^{−E_a / RT}

where A is the frequency factor, R is the gas constant, and T is temperature in kelvin.

The equation shows that k increases rapidly when temperature rises or when E_a decreases. In logarithmic form, it becomes ln k = ln A − E_a / RT, which is useful for comparing rate constants at different temperatures.

Solved Examples

Example 3

(i) For the reaction A → B, the rate increases 27 times when concentration of A is tripled. Find the order of the reaction.

Solution:

Rate = k[A]ⁿ

27 = 3ⁿ

n = 3

Therefore, the order of the reaction is 3.

(ii) Activation energy decreases from 75.2 kJ mol⁻¹ to 50.14 kJ mol⁻¹ with catalyst at 25°C. Calculate rate increase.

Solution:

Decrease in activation energy, ΔEₐ = 75.2 - 50.14 = 25.06 kJ mol⁻¹

At 25°C, T = 298 K

Using Arrhenius equation, the rate increases by 2.46 × 10⁴ times.

Practice Set

• Level 1: Define activation energy.
• Answer: Activation energy is the minimum amount of energy that reacting molecules must possess to undergo a chemical reaction.
• Level 2: Explain the role of a catalyst in a chemical reaction.
• Answer: A catalyst increases the rate of a reaction by providing an alternative pathway with lower activation energy. It is not consumed in the reaction and does not change the equilibrium position.
• Level 3: Calculate the factor by which rate increases if activation energy decreases from 80 kJ mol⁻¹ to 60 kJ mol⁻¹ at 298 K.
• Answer: According to the Arrhenius equation, k ∝ e^-Eₐ/RT. So, rate increases by a factor of e^{(80-60)000/(8.314×298)} = e^8.08 ≈ 3.2 × 10³. Thus, the rate increases by about 3200 times.

Answer Key

• Level 1: Activation energy is the minimum energy required for reactant molecules to undergo a reaction.
• Level 2: A catalyst lowers activation energy, increasing the rate without being consumed.
• Level 3: Use the Arrhenius equation to calculate the rate increase factor. For two temperatures, k₂/k₁ = e^{−E_a/R(1/T₂ − 1/T₁)}, where E_a is activation energy, R is the gas constant, and T is temperature in kelvin.

Quick Reference Table

• Rate of chemical reaction: The change in concentration of a reactant or product per unit time.
• Rate of disappearance: For a reactant A, rate = -Δ[A]/Δt.
• Rate of appearance: For a product C, rate = Δ[C]/Δt.
• Concentration: Usually expressed in molarity (mol L⁻¹).
• Unit of rate: mol L⁻¹ s⁻¹ or mol L⁻¹ min⁻¹ for reactions in solution; atm s⁻¹ or atm min⁻¹ for gaseous reactions.
• Average rate: Rate measured over a time interval.
• Instantaneous rate: Rate at a specific moment.
• Effect of concentration: Increasing reactant concentration generally increases the reaction rate.
• Effect of temperature: Higher temperature increases kinetic energy and reaction rate.
• Effect of pressure: For gases, increased pressure increases concentration and rate.
• Effect of catalyst: A catalyst lowers activation energy and increases rate without being consumed.
• Effect of nature of reactants: Simpler molecules generally react faster because fewer bonds need to be broken.
• Effect of surface area: Greater surface area of a solid increases the reaction rate.
• Effect of radiation: Photochemical reactions are initiated by light and often proceed faster.
• Effect of physical state: Reactivity depends on whether substances are solid, liquid or gas.
• Order of reaction: The sum of the powers of concentration terms in the experimentally determined rate law.
• Zero-order reaction: Rate = k; rate is independent of reactant concentration.
• First-order reaction: Rate = k[A]; rate is directly proportional to concentration.
• Pseudo first-order reaction: A reaction that behaves like first order under certain conditions.
• Second-order reaction: Rate = k[A][B] or k[A]².
• Rate constant: k varies with temperature and its unit depends on the order of reaction.
• Unit of k for zero order: mol L⁻¹ s⁻¹.
• Unit of k for first order: s⁻¹.
• Unit of k for second order: L mol⁻¹ s⁻¹.
• Half-life: Time required for the concentration of a reactant to become half of its initial value.
• Half-life of first-order reaction: t₁/₂ = 0.693/k and is independent of concentration.
• Half-life of zero-order reaction: t₁/₂ = [A]₀/2k.
• Half-life of second-order reaction: t₁/₂ = 1/k[A]₀.
• Collision theory: Reactions occur when molecules collide with sufficient energy and proper orientation.
• Activation energy: The minimum energy required for a collision to be effective.
• Effective collision: A collision with energy equal to or greater than activation energy and correct orientation.
• Collision frequency: Z, the number of collisions occurring per unit time.
• Fraction of effective collisions: f, the fraction of collisions that lead to product formation.
• Arrhenius equation: k = Ae⁻ᴱᵃ/RT, where A is the frequency factor, R is the gas constant and T is temperature in kelvin.
• Frequency factor: A, a constant related to the frequency of effective collisions.
• Catalyst and rate: A catalyst decreases activation energy and increases the rate of reaction.

Common Mistakes and Misconceptions

• Assuming that rate of reaction and extent of reaction mean the same thing; rate tells how fast a reaction occurs, not how much product is finally formed.
• Using the sign of rate incorrectly; rate of disappearance is written with a negative sign, while rate of appearance is positive.
• Mixing up average rate and instantaneous rate; average rate is measured over a time interval, while instantaneous rate is at a particular moment.
• Applying the same half-life relation to every order of reaction; half-life formulas are different for zero, first and second order reactions.
• Assuming reaction order must always be a whole number; order can be zero, fractional or even pseudo first order under suitable conditions.
• Thinking that a catalyst is consumed during the reaction; a catalyst is regenerated and remains chemically unchanged overall.
• Believing that a decrease in activation energy changes the products of a reaction; it changes the pathway and speed, not the final products.
• Confusing rate of reaction with equilibrium position; a catalyst only helps the reaction reach equilibrium faster and does not change the equilibrium position.

Glossary

• Rate of reaction: the change in concentration of a reactant or product per unit time.
• Average rate: rate measured over a time interval.
• Instantaneous rate: rate at a specific moment.
• Rate law: the experimentally determined expression showing how reaction rate depends on reactant concentrations.
• Order of reaction: the sum of the powers of concentration terms in the rate law.
• Rate constant (k): the proportionality constant in the rate law; its value depends on temperature and reaction conditions.
• Zero-order reaction: a reaction whose rate is independent of reactant concentration.
• First-order reaction: a reaction whose rate is directly proportional to the concentration of one reactant.
• Pseudo first-order reaction: a reaction that behaves like a first-order reaction under certain conditions.
• Second-order reaction: a reaction whose rate depends on the square of one reactant or on the product of two reactant concentrations.
• Half-life: the time required for the concentration of a reactant to become half of its initial value.
• Activation energy: the minimum energy required for reactant molecules to undergo a chemical reaction.
• Collision theory: the theory that reactions occur when reactant particles collide with sufficient energy and proper orientation.
• Effective collision: a collision that leads to product formation.
• Frequency factor (A): the factor in the Arrhenius equation related to collision frequency and proper orientation.
• Arrhenius equation: the equation that relates the rate constant to temperature and activation energy.
• Catalyst: a substance that increases the rate of a reaction without being consumed and by lowering activation energy.
• Temperature effect: higher temperature generally increases reaction rate by increasing kinetic energy and the number of effective collisions.
• Concentration effect: higher reactant concentration generally increases reaction rate.
• Pressure effect: for gases, higher pressure increases concentration and usually increases reaction rate.
• Surface area effect: greater surface area of a solid generally increases reaction rate.
• Nature of reactants: the chemical nature and bond strength of substances that influence how fast they react.
• Photochemical reaction: a reaction initiated by light.