Rates of Reaction in Chemistry

Welcome to this comprehensive lesson on Rates of Reaction, designed for CXC Chemistry students. This lesson covers all aspects of reaction rates required for the 2024-2025 syllabus.

Introduction to Rates of Reaction

The rate of a chemical reaction refers to how quickly reactants are converted into products. Understanding reaction rates is crucial in chemistry as it helps explain why some reactions occur rapidly while others are slow, and how we can control these rates for practical applications.

Definition: The rate of reaction is the change in concentration of reactants or products per unit time.

There are several ways to measure the rate of a reaction:

Change in mass per unit time
Volume of gas produced per unit time
Change in color intensity per unit time
Change in concentration per unit time

Expressing Rate of Reaction

The rate of reaction can be expressed mathematically as:

Rate of reaction = Change in concentration / Time taken

For a general reaction: aA + bB → cC + dD

The rate can be expressed as:

Rate = -1/a × Δ[A]/Δt = -1/b × Δ[B]/Δt = 1/c × Δ[C]/Δt = 1/d × Δ[D]/Δt

Where:

Δ[A] represents the change in concentration of reactant A
Δt represents the time interval
The negative sign for reactants indicates their concentration decreases with time

Collision Theory and Reaction Rates

Collision theory explains how chemical reactions occur and helps us understand the factors affecting reaction rates.

Basic Principles of Collision Theory

Particles must collide with each other for a reaction to occur
Collisions must have sufficient energy (equal to or greater than the activation energy)
Particles must collide with the correct orientation

Energy profile diagram showing activation energy (Ea) and enthalpy change (ΔH)

Activation Energy (Ea): The minimum energy required for a reaction to occur.

Factors Affecting Rates of Reaction

Several factors can influence how quickly a chemical reaction proceeds:

1. Nature of Reactants

Different substances react at different rates due to:

Bond strength – stronger bonds require more energy to break
Physical state – reactions between gases or solutions are typically faster than reactions involving solids
Molecular complexity – complex molecules typically react more slowly

2. Concentration (Pressure for Gases)

Higher concentration of reactants leads to increased frequency of collisions between particles, resulting in a faster reaction rate.

Example: The reaction between hydrochloric acid and magnesium:

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

Increasing the concentration of HCl will increase the rate of hydrogen gas production.

3. Temperature

Increasing temperature accelerates reaction rates because:

Particles move faster, increasing collision frequency
More particles possess energy equal to or greater than the activation energy

As a rule of thumb, for many reactions, a 10°C increase in temperature approximately doubles the reaction rate.

Maxwell-Boltzmann distribution showing the effect of temperature on the number of molecules with energy greater than activation energy

4. Surface Area

Increasing the surface area of solid reactants increases the area of contact between reactants, resulting in more collisions and a faster reaction rate.

Example: A powdered calcium carbonate tablet will react faster with acid than a whole tablet.

5. Catalysts

Catalysts increase reaction rates by providing an alternative reaction pathway with lower activation energy.

A catalyst is not consumed in the reaction
It does not change the energy difference between reactants and products
It only affects the rate of the reaction, not the position of equilibrium

Energy profile showing how a catalyst lowers the activation energy

Common examples of catalysts:

Manganese dioxide (MnO₂) in the decomposition of hydrogen peroxide
Iron in the Haber process
Vanadium(V) oxide in the Contact process
Enzymes in biological systems

6. Light and Radiation

Some reactions are initiated or accelerated by light or radiation, particularly in photochemical reactions.

Example: The reaction between hydrogen and chlorine is very slow in the dark but occurs explosively in sunlight.

H₂(g) + Cl₂(g) → 2HCl(g)

Measuring Rates of Reaction

Various experimental methods can be used to measure reaction rates:

1. Measuring Mass Change

For reactions where a gas is produced or consumed, the change in mass over time can be measured using a balance.

Experiment: Calcium Carbonate and Hydrochloric Acid

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)

Method:

Place a conical flask containing dilute hydrochloric acid on a balance
Add calcium carbonate and quickly stopper the flask with cotton wool
Record the mass at regular time intervals
The decrease in mass corresponds to the carbon dioxide escaping
Calculate the rate of reaction by determining the gradient of the mass vs. time graph

2. Measuring Volume of Gas

For reactions where a gas is produced, the volume of gas can be measured over time using a gas syringe or by water displacement.

Experiment: Magnesium and Hydrochloric Acid

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

Method:

Set up a gas syringe connected to a conical flask
Add hydrochloric acid to the flask
Add magnesium ribbon and quickly stopper the flask
Record the volume of hydrogen gas collected at regular time intervals
Plot a graph of volume vs. time and calculate the gradient to determine the rate

Experimental setup for measuring gas production using a gas syringe

3. Colorimetry

For reactions involving a color change, the rate can be measured by monitoring the intensity of color using a colorimeter or by observing the time taken for a mark to disappear.

Experiment: Iodine Clock Reaction

Method:

Mix solutions of potassium iodate, sodium metabisulfite, and starch
The reaction initially produces iodide ions which are colorless
Once all the sodium metabisulfite is consumed, iodine forms and reacts with starch to form a blue-black complex
Measure the time taken for the color change to occur
Varying concentrations or temperature will change this time

4. Using a pH Meter or Conductivity Meter

For reactions where pH or conductivity changes, these properties can be monitored over time.

Order of Reaction

The order of a reaction describes how the rate depends on the concentration of reactants.

Zero-Order Reactions

Rate = k
The rate is independent of concentration
Often occurs when a reactant is in excess or a catalyst surface is fully saturated

First-Order Reactions

Rate = k[A]
The rate is directly proportional to the concentration of one reactant
Examples: Radioactive decay, many hydrolysis reactions

Second-Order Reactions

Rate = k[A][B] or Rate = k[A]²
The rate depends on the product of two concentrations

Rate Constant (k): The proportionality constant in the rate equation. Its units depend on the overall order of the reaction.

Determining Order of Reaction

Various methods can be used to determine the order of a reaction:

Initial Rate Method: Measure initial rates for different initial concentrations
Half-Life Method: For first-order reactions, the half-life is constant
Graphical Method: Plot concentration vs. time and analyze the shape

Order	Rate Law	Integrated Rate Law	Half-Life	Graph Characteristics
Zero	Rate = k	[A] = -kt + [A]₀	t₁/₂ = [A]₀/2k	Linear plot of [A] vs. t with negative slope
First	Rate = k[A]	ln[A] = -kt + ln[A]₀	t₁/₂ = ln(2)/k	Linear plot of ln[A] vs. t with negative slope
Second	Rate = k[A]²	1/[A] = kt + 1/[A]₀	t₁/₂ = 1/(k[A]₀)	Linear plot of 1/[A] vs. t with positive slope

Rate-Determining Step

Many chemical reactions occur through a series of elementary steps:

The slowest step in the reaction mechanism is called the rate-determining step
This step controls the overall rate of the reaction
The rate equation often reflects the molecularity of this step

Arrhenius Equation

The Arrhenius equation quantifies the relationship between temperature and reaction rate:

k = Ae^(-Ea/RT)

Or in logarithmic form:

ln(k) = ln(A) - Ea/RT

Where:

k is the rate constant
A is the pre-exponential factor (frequency factor)
Ea is the activation energy (J/mol)
R is the gas constant (8.314 J/mol·K)
T is the absolute temperature (K)

The Arrhenius equation can be used to calculate activation energy by measuring rate constants at different temperatures.

Applications of Reaction Rates

Understanding and controlling reaction rates have numerous practical applications:

Industrial Applications

Manufacturing: Optimizing conditions for maximum yield and efficiency
Catalysts: Using catalysts to reduce energy costs (e.g., Haber Process, Contact Process)
Food preservation: Slowing unwanted reactions through refrigeration

Environmental Applications

Catalytic converters: Reducing harmful emissions by catalyzing their conversion
Ozone depletion: Understanding the kinetics of ozone destroying reactions
Climate change: Studying reaction rates in atmospheric chemistry

Biological Applications

Enzyme kinetics: Understanding how enzymes catalyze biological reactions
Drug metabolism: Predicting how quickly drugs will be broken down in the body
Food spoilage: Controlling factors that affect the rate of food deterioration

Glossary of Terms

Activation Energy (Ea): The minimum energy required for a reaction to occur.

Catalyst: A substance that increases the rate of a reaction without being consumed in the process.

Collision Theory: A theory explaining that for a reaction to occur, particles must collide with sufficient energy and correct orientation.