Chemical kinetics in chemistry: Class 12 Notes, Formulas, and Solutions

The rate of a chemical reaction or the speed of reaction is defined as how much concentration change in a specific time period. Essentially how fast reactants disappear or how quickly products appear. Just like we measure the speed of a car by how much distance it covers in a given time, we measure reaction rate by.

Average and Instantaneous Rate

When chemical reactions take place, they keep changing speed, and usually the speed of the reaction slows down as reactants are used up. So, there are two types of rate of reaction- Average Rate and Instantaneous Rate.

Average Rate

The average rate of reaction is the speed at which the reaction occurs in the given time.

For a reaction R → P:

• Rate of disappearance of R = -Δ[R]/Δt
• Rate of appearance of P = +Δ[P]/Δt

The negative sign ensures that the rate is always positive, even though the reactant concentration decreases.

Instantaneous Rate

Instantaneous Rate gives the exact rate (speed of a reaction) at a particular instant. It's like checking your speedometer at a specific moment.

- r_inst = -d[R]/dt = +d[P]/dt

This is found by drawing a tangent to the concentration-time curve at the desired point and calculating its slope.

Units of Reaction Rate

The units of rate depend on how we present concentration:

• For molarity: mol L⁻¹ s⁻¹ or M s⁻¹
• For gaseous reactions: atm s⁻¹ or bar s⁻¹

Several factors can affect how fast or slow a chemical reaction proceeds. These factors help us control reactions in different settings. Some of the factors affecting the rate of reactions are: concentration of the reactant, temperature, and catalyst.

Dependence of Rate on Concentration

Most reactions speed up when we increase the concentration of reactants. More molecules in a given space means more frequent collisions and faster reactions.

Rate Law

The mathematical relationship between the rate of reaction and concentration is called the rate law or rate expression.

For a general reaction: aA + bB → products
Rate law: Rate = k[A]ˣ[B]ʸ
-d[R]/dt = k[A]ˣ[B]ʸ  (this form of the rate law equation is known as the differential rate equation)

Where,

• k = rate constant (specific for each reaction at a given temperature)
• x, y = orders with respect to A and B, respectively

The exponents x and y are not necessarily equal to the stoichiometric coefficients a and b. They must be determined experimentally.

The differential rate equation relates the speed of reaction to the concentration of the reactant, which is known as the rate law.

Order of a Reaction

The order indicates how sensitive the reaction rate (speed of reaction) is to concentration changes. It’s the sum of all exponents in the rate law.
In the rate law,
Rate = k[A]ˣ[B]ʸ

• x and y are the orders of reaction 
• Change in concentration will be in the A and B
• x + y = overall order of reaction

Types of orders:

• Zero order: Rate independent of reactant concentration
• First order: Rate directly proportional to [reactant]
• Second order: Rate proportional to [reactant]²
• Fractional order: Possible in complex reactions

Elementary Reaction- when a reaction occurs in a single step without involving any intermediate to form a product. There are three types of elementary reactions: Unimolecular, Bimolecular, and Termolecular.

Complex Reaction- when a reaction occurs in multiple steps with intermediates involved. Each step in a complex reaction is an elementary reaction.

Molecularity of a Reaction

Molecularity refers to the number of molecules that actually participate in an elementary reaction step.

Difference between Order and Molecularity:

Examples:

• Unimolecular: NH₄NO₂ → N₂ + 2H₂O (one molecule decomposes)
• Bimolecular: 2HI → H₂ + I₂ (two molecules collide)
• Termolecular: 2NO + O₂ → 2NO₂ (three molecules collide simultaneously)

Reactions with molecularity greater than three are extremely rare because the probability of more than three molecules colliding simultaneously is very low.

Rate Determining Step

In complex reactions involving multiple steps, the overall rate is controlled by the slowest step, called the rate-determining step. It’s like a traffic bottleneck; no matter how fast other lanes move, the overall speed is limited by the slowest lane.

Example: Decomposition of H₂O₂ catalyzed by I⁻
Overall reaction: 2H₂O₂ → 2H₂O + O₂

Mechanism:
Step 1: H₂O₂ + I⁻ → H₂O + IO⁻ (slow)
Step 2: H₂O₂ + IO⁻ → H₂O + I⁻ + O₂ (fast)

The rate law is determined by step 1: Rate = k[H₂O₂][I⁻]

Pseudo First Order Reactions

Sometimes higher-order reactions behave as if they are first order due to experimental conditions.

Example: Hydrolysis of ethyl acetate
CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH

This is actually a second-order reaction, but when water is in large excess, its concentration doesn’t change during the reaction. The reaction then appears to be first order with respect to ethyl acetate only.

Rate = k’[CH₃COOC₂H₅] where k’ = k[H₂O]

Through differential rate equations, we get the rate of reaction at any instant, and integrated rate equations connect concentrations at different times with the rate constant. 

The integrated rate equation is different for different reaction orders. For example:

Zero Order Reactions

In zero-order reactions, the reaction rate remains constant throughout the whole process, regardless of reactant concentration. It happens under special conditions, like when a catalyst surface becomes saturated.

For the reaction R → P with zero-order kinetics:

Rate equation: Rate = k[R]⁰ = k

Integrated form: [R] = [R]₀ - kt

Where.
[R]₀ is the initial concentration at t = 0.

 

Examples:

• Decomposition of NH₃ on the platinum surface at high pressure
• Some enzyme-catalyzed reactions occur when the enzyme is saturated

First Order Reactions

First-order reactions are most common in chemistry. In first order reaction, the rate is directly proportional to the concentration of one reactant.

For the reaction R → P:
Rate equation: Rate = k[R]

Integrated forms:

• Exponential form: [R] = [R]₀e^(-kt)
• Logarithmic form: ln[R] = ln[R]₀ - kt
• Common log form: log([R]₀/[R]) = kt/2.303

Examples:

• Radioactive decay: ²²⁶Ra → ²²²Rn + ⁴He
• Decomposition of N₂O₅: 2N₂O₅ → 4NO₂ + O₂
• Many organic reactions in dilute solutions

First Order Gas Phase Reactions

Integrated rate law expressed as partial pressures for the gaseous reaction at the same temperatures.

For A(g) → B(g) + C(g):

If pᵢ = initial pressure of A and pₜ = total pressure at time t:

• Pressure of A at time t: pₐ = 2pᵢ - pₜ
• Integrated equation: k = (2.303/t) log(pᵢ/pₐ)

Half-Life of Reactions

The time required for the concentration of a reactant to come down to half its initial value is called the half-life. It’s useful for comparing reaction rates.

For zero order: t₁/₂ = [R]₀/2k

• Half-life decreases as the reaction proceeds
• Depends on initial concentration

For first order: t₁/₂ = 0.693/k = ln2/k

• Half-life remains constant throughout the reaction
• Independent of initial concentration

Most chemical reactions increase their rate or speed with even a small increase in temperature. A general thumb rule is that reaction rates approximately double for every 10°C increase in temperature.

The Arrhenius Equation

The relationship between reaction rate and temperature was quantitatively described by Svante Arrhenius. His equation connects the rate constant with temperature.

k = Ae^(-Eₐ/RT)

Where,

• k = rate constant
• A = Arrhenius factor (frequency factor)
• Eₐ = activation energy (J/mol)
• R = gas constant (8.314 J mol⁻¹ K⁻¹)
• T = absolute temperature (K)

Activation Energy
Activation energy is the minimum energy required for reactant molecules to form products. 

• Higher Eₐ → slower reaction (few molecules have enough energy)
• Lower Eₐ → faster reaction (more molecules can overcome)
• Catalysts work by providing an alternative path with lower Eₐ

Maxwell-Boltzmann Distribution

The reason temperature affects the rate of reaction highly is because of how molecular energies are distributed.

• At any temperature, molecules have a range of kinetic energies
• Only molecules with energy ≥ Eₐ can react
• Higher temperature shifts the energy distribution to higher values
• Small temperature increases dramatically increase the fraction of molecules with energy ≥ Eₐ

The exponential term e^(-Eₐ/RT) in the Arrhenius equation represents the fraction of molecules with sufficient energy to react.

Effect of Catalyst

Catalysts a substances that increase reaction speed by providing an alternative reaction pathway with lower activation energy. Catalyst can affect the speed of reaction, but can’t change the occurring reaction.

How catalysts work:

• Provide an alternative mechanism with a smaller energy barrier
• Sometimes, increase the frequency of successful collisions
• Speed up forward and reverse reactions equally
• Doesn’t affect the final equilibrium position

There are three types of catalysis: Homogeneous, Heterogeneous, and Enzyme catalysis.

• Homogeneous: Catalyst in the same phase as the reactants
• Heterogeneous: Catalyst in a different phase (often a solid catalyst, liquid/gas reactants)
• Enzyme catalysis: Biological catalysts with extreme specificity and efficiency

Read More: Temperature Dependence of the Rate of Reaction

Now, let’s understand the mechanical explanation of how a reaction takes place and why factors like temperature and concentration affect the speed of a reaction through collision theory.

The Collison theory is developed on the following assumptions:

• Chemical reactions happen when molecules of reactant collide with each other.
• Not all collisions make a reaction. Only collisions with energy higher than or equal to the activation energy (Eₐ) can result in a chemical reaction.
• Even high-energy collisions won’t result in a reaction until the molecules are oriented correctly.

For a bimolecular reaction A + B → Products:

Rate = Z_AB × P × e^(-Eₐ/RT)

Where:

• Z_AB = collision frequency between A and B molecules
• P = steric factor (probability of proper orientation)
• e^(-Eₐ/RT) = fraction of collisions with sufficient energy

Collision Frequency

The collision frequency depends on Concentration, Temperature, Molecular size, and Relative velocity.

Steric Factor
The steric factor or Probability Factor (P) accounts for the geometric requirements of the reaction. Not all collisions, even high-energy ones, lead to a reaction.

Factors affecting P:

• Molecular complexity, simple atoms/molecules have P ≈ 1, complex molecules have P << 1
• Some reactions require very specific orientations
• The arrangement of atoms during a collision affects success

Effective Collisions

For a collision to be effective, which results in a chemical reaction, two conditions must be met:

First is Threshold Energy, the total kinetic energy of colliding molecules must surpass the activation energy.

Threshold Energy = Activation Energy + Average kinetic energy of reactants

And second, proper orientation.

• Breaking bonds is weakened during a collision
• New bonds can form efficiently
• The reaction pathway is energetically favorable

Temperature Dependence Explained

Collision theory explains why temperature has such a strong effect on reaction rates. Higher temperature results in more collisions, more energetic collisions, higher average energy of reactants, and a greater fraction of molecules with E ≥ Eₐ.

Limitations of Collision Theory

Here are some limitations of collision theory.

• Treats molecules as hard spheres, ignoring their internal structure and flexibility.
• Works best for gas-phase reactions between small molecules.
• Doesn’t fully address reactions involving intermediates or multiple steps.
• Doesn’t explain how solvents affect reaction rates in solution.

You can check all the important formulas of chemical kinetics in the table below:

Read more: Chemical Kinetics NCERT PDF