Chapter 2: Rate of Reaction

Overview

The rate of reaction is a fundamental concept in chemical kinetics that describes how quickly reactants are converted into products. Understanding reaction rates is crucial for industrial processes, biological systems, and everyday applications. This chapter explores how to measure reaction rates, the collision theory that explains why reactions occur at different rates, and the various factors that influence reaction kinetics. From cooking food to industrial manufacturing, reaction rate principles are applied worldwide to optimize chemical processes.

Learning Objectives

After studying this chapter, you should be able to:

Define and calculate reaction rates using different methods
Apply collision theory to explain reaction mechanisms
Identify and explain factors affecting reaction rates (surface area, concentration, temperature, catalysts)
Understand the role of activation energy in chemical reactions
Analyze real-world applications of reaction rate principles
Perform experimental investigations of reaction rates

2.1 Determining the Rate of Reaction

What is Reaction Rate?

Reaction rate is defined as the change in amount of reactant or product per unit time. It measures how fast a chemical reaction occurs.

\text{Reaction rate} = \frac{\Delta \text{amount of reactant or product}}{\Delta \text{time}}

Units of Reaction Rate

Reaction rates can be expressed in various units:

g s⁻¹ (grams per second) - for mass changes
c $m^3$ s⁻¹ (cubic centimeters per second) - for gas volume changes
mol s⁻¹ (moles per second) - for molar changes
mol dm⁻³ s⁻¹ (moles per cubic decimeter per second) - for concentration changes

Rate of Reaction Visualization

Methods for Measuring Reaction Rates

1. Mass Loss Method

Used for reactions producing gases. The total mass of the apparatus is measured at regular time intervals.

Example: $\text{Zn(s)} + 2\text{HCl(aq)} \rightarrow \text{ZnCl}_2\text{(aq)} + \text{H}_2\text{(g)}$

As hydrogen gas is produced, the total mass decreases
Mass loss rate = Reaction rate

Setup Diagram:

2. Gas Volume Collection

Gas produced is collected in gas burettes or gas syringes, and volume is recorded at regular time intervals.

Example: $\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}$

C $O_2$ gas is collected and measured over time
Volume increase rate = Reaction rate

Setup Diagram:

3. Precipitation Formation

The time taken for a cross mark to become invisible beneath a precipitate is measured.

Example: $\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + \text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{Na}_2\text{SO}_4\text{(aq)} + \text{H}_2\text{O(l)} + \text{SO}_2\text{(g)} + \text{S(s)}$

Sulfur precipitate forms gradually
Time measurement relates to reaction rate

Experimental Setup:

4. Color Change Intensity

The intensity of color change is measured using colorimetry or visual observation.

Example: $2\text{KMnO}_4\text{(aq)} + 5\text{H}_2\text{C}_2\text{O}_4\text{(aq)} + 3\text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{K}_2\text{SO}_4\text{(aq)} + 2\text{MnSO}_4\text{(aq)} + 10\text{CO}_2\text{(g)} + 8\text{H}_2\text{O(l)}$

Purple color fades as reaction proceeds
Color intensity relates to concentration changes

Colorimetry Process:

Reaction Rate from Concentration-Time Graphs

From a concentration vs. time graph:

Instantaneous rate: Slope of the tangent at any point
Average rate: Total change ÷ Total time

Mathematical representation:

\text{Average rate} = -\frac{\Delta[\text{A}]}{\Delta t} = \frac{\Delta[\text{C}]}{\Delta t}

\text{Instantaneous rate} = -\frac{d[\text{A}]}{dt} = \frac{d[\text{C}]}{dt}

Key insight: The steeper the curve, the faster the reaction rate.

Concentration-Time Graph Analysis:

Did You Know?

The fastest chemical reactions occur on the femtosecond timescale (10⁻¹⁵ seconds), such as the breaking of chemical bonds in photochemical reactions. The slowest reactions can take billions of years, like radioactive decay of uranium-238.

2.2 Factors Affecting Reaction Rates

Collision Theory

Collision theory explains how reactions occur:

Molecules must collide to react
Collisions must have sufficient energy (≥ activation energy, Ea)
Collisions must have proper orientation for reaction to occur

Effective collision: A collision that results in a chemical reaction Activation energy (Ea): Minimum energy required for a successful reaction

Collision Theory Visualization:

Key Factors Influencing Reaction Rates

1. Surface Area (For Solids)

Effect: Smaller particle size = Larger surface area = Faster reaction rate

Explanation: More surface area available for collisions between reactants

Surface Area Effect:

\text{Reaction rate} \propto \text{Surface area}

Examples:

Powdered calcium carbonate reacts faster with acid than lumps of calcium carbonate
Granulated sugar dissolves faster than sugar cubes
Refrigerator ice cubes melt faster when crushed

Surface Area Comparison Diagram:

Practical applications:

Medicines are often powdered for faster absorption
Catalysts are made with high surface area (porous structures)
Foods are cut into smaller pieces for faster cooking

2. Concentration (For Solutions and Gases)

Effect: Higher concentration = Faster reaction rate

Explanation: More particles per unit volume = More frequent collisions

Concentration Effect:

\text{Reaction rate} \propto \text{Particle concentration}

Examples:

Concentrated acid reacts faster with magnesium than dilute acid
High-pressure oxygen supports faster combustion than low-pressure oxygen

Mathematical relationship: For reaction: $a\text{A} + b\text{B} \rightarrow \text{products}$ $\text{Rate} = k[\text{A}]^m[\text{B}]^n$ (where k is rate constant, m and n are orders)

Concentration Effect Diagram:

Collision Frequency Graph:

3. Temperature

Effect: Higher temperature = Faster reaction rate

Explanation:

Particles move faster and collide more frequently
More particles have energy ≥ activation energy
Exponential increase in reaction rate (approximately doubles for every 10°C rise)

Temperature Effect Equation:

\text{Rate} \propto e^{-E_a/RT}

Energy Distribution Diagram:

Maxwell-Boltzmann Distribution:

Examples:

Food cooking faster at higher temperatures
Refrigeration slows down spoilage by lowering temperature
Incubators maintain optimal temperature for bacterial growth

4. Pressure (For Gases Only)

Effect: Higher pressure = Faster reaction rate

Explanation: Higher pressure = Higher concentration = More frequent collisions

Pressure Effect Equation:

\text{Pressure} \propto \text{Concentration}

Examples:

High-pressure Haber process for ammonia synthesis
Pressure cookers increase reaction rates for faster cooking
Compressed gas cylinders increase reaction rates when valves are opened

Pressure Effect Diagram:

Pressure vs. Volume Relationship:

Note: Pressure changes only affect reactions involving gases

5. Catalysts

Effect: Catalysts increase reaction rate without being consumed

Mechanism: Catalysts provide an alternative reaction pathway with lower activation energy

Catalyst Effect Equation:

k_{\text{catalyzed}} > k_{\text{uncatalyzed}}

Energy Diagram with Catalyst:

Characteristics of catalysts:

Not consumed in the reaction
Speed up both forward and reverse reactions
Do not affect equilibrium position (only speed up attainment of equilibrium)
Can be recovered and reused

Catalyst Mechanism Diagram:

Examples:

Iron catalyst in Haber process ( $\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3$ )
Vanadium(V) oxide in Contact process ( $2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3$ )
Platinum/rhodium in catalytic converters
Enzymes in biological systems

SPM Exam Tips

When explaining collision theory, always mention ALL three requirements:

Particles must collide

Collisions must have sufficient energy (≥ Ea)

Collisions must have proper orientation

For surface area effects, explain the relationship between particle size and available surface area

Temperature affects both collision frequency AND the fraction of collisions with sufficient energy

Catalysts lower activation energy but are NOT used up in reactions

2.3 Industrial Applications of Reaction Rate Principles

1. Haber Process for Ammonia Synthesis

Reaction: $\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)} \quad \Delta H = -92 \text{kJ/mol}$

Optimization for rate and yield:

High temperature (450°C): Increases rate but favors reactants (compromise with equilibrium)
High pressure (200 atm): Increases rate and favors products
Iron catalyst: Increases rate by lowering activation energy
Recycling unreacted gases: Increases overall efficiency

Haber Process Optimization Diagram:

2. Contact Process for Sulfuric Acid

Reaction: $2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\text{SO}_3\text{(g)} \quad \Delta H = -197 \text{kJ/mol}$

Optimization:

Vanadium(V) oxide catalyst: $\text{V}_2\text{O}_5$ provides low activation energy pathway
Moderate temperature (400-450°C): Rate vs. equilibrium compromise
Sufficient oxygen: Ensures high reactant concentration

Contact Process Flow:

3. Catalytic Converters in Vehicles

Reactions:

$2\text{CO(g)} + 2\text{NO(g)} \rightarrow 2\text{CO}_2\text{(g)} + \text{N}_2\text{(g)}$
$2\text{CO(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{CO}_2\text{(g)}$
$2\text{C}_2\text{H}_6\text{(g)} + 7\text{O}_2\text{(g)} \rightarrow 4\text{CO}_2\text{(g)} + 6\text{H}_2\text{O(g)}$

Catalyst: Platinum (Pt) and Rhodium (Rh) gauze

Function: Converts harmful exhaust gases to less harmful products at lower temperatures

Catalytic Converter Process:

4. Biological Catalysts (Enzymes)

Characteristics:

Specific: Each enzyme catalyzes specific reactions
Efficient: Can increase reaction rates by factors of $10^6$ to $10^{12}$
Mild conditions: Work at body temperature and neutral pH
Denatured: Lose function at high temperatures or extreme pH

Enzyme Catalysis Process:

Examples:

Amylase: Breaks down starch to sugars
Protease: Breaks down proteins to amino acids
Catalase: Breaks down hydrogen peroxide to water and oxygen

Enzyme Examples:

Safety Reminder

When working with reaction rate experiments:

Use proper eye protection and lab coats

Be careful with concentrated acids and bases

Handle hot equipment with tongs or heat-resistant gloves

Ensure proper ventilation when dealing with gases

Follow waste disposal procedures for chemicals

Never mix chemicals without knowing the reaction

2.4 Experimental Investigations of Reaction Rates

Example 1: Reaction Between Marble Chips and Hydrochloric Acid

Aim: To investigate how surface area affects reaction rate

Materials:

Marble chips (CaC $O_3$ ) - large and small pieces
Dilute hydrochloric acid (HCl)
Conical flask, delivery tube, measuring cylinder, stopwatch

Procedure:

Place large marble chips in flask with acid
Collect C $O_2$ gas in measuring cylinder
Record gas volume every 10 seconds for 2 minutes
Repeat with small marble chips

Expected results: Small chips produce gas faster than large chips

Example 2: Effect of Temperature on Reaction Rate

Aim: To investigate how temperature affects the reaction between sodium thiosulfate and acid

Reaction: N$a_2S_2O_3$(aq) + $H_2$S$O_4$(aq) → N$a_2$S$O_4$(aq) + $H_2$O(l) + S$O_2$(g) + S(s)

Materials:

Sodium thiosulfate solution
Dilute sulfuric acid
Water baths at different temperatures
Stopwatch, white tile with cross mark

Procedure:

Heat sodium thiosulfate to different temperatures
Add acid and start stopwatch when cross disappears
Record time for each temperature

Expected results: Higher temperature = Shorter time = Faster reaction

Example 3: Catalytic Decomposition of Hydrogen Peroxide

Aim: To investigate the effect of manganese dioxide as a catalyst

Reaction: 2$H_2O_2$(aq) → 2$H_2$O(l) + $O_2$(g)

Materials:

Hydrogen peroxide solution
Manganese dioxide powder (catalyst)
Gas collection apparatus

Procedure:

Measure oxygen produced from pure $H_2O_2$
Repeat with Mn $O_2$ added
Compare gas collection rates

Expected results: Mn $O_2$ increases oxygen production rate

2.5 Reaction Rate Calculations

Rate Expression and Rate Law

For a general reaction: $a\text{A} + b\text{B} \rightarrow c\text{C} + d\text{D}$

The rate law is: Rate = $k[\text{A}]^m[\text{B}]^n$

Where:

k = rate constant (depends on temperature)
m = order with respect to A
n = order with respect to B
m + n = overall reaction order

Rate Law Formula:

\text{Rate} = k[\text{A}]^m[\text{B}]^n

Determining Reaction Order

1. Zero Order (m = 0)

Rate = $k[\text{A}]^0 = k$
Rate is independent of [A]
Graph: Rate vs. [A] = horizontal line

Zero Order Graph:

2. First Order (m = 1)

Rate = $k[\text{A}]^1 = k[\text{A}]$
Rate proportional to [A]
Graph: Rate vs. [A] = straight line through origin

First Order Graph:

3. Second Order (m = 2)

Rate = $k[\text{A}]^2$
Rate proportional to [A]²
Graph: Rate vs. [A] = parabola

Second Order Graph:

Reaction Order Summary:

Example Calculation

Problem: For the reaction $\text{A} + 2\text{B} \rightarrow \text{products}$ , the following data was obtained:

[A] (mol dm⁻³)	[B] (mol dm⁻³)	Rate (mol dm⁻³ s⁻¹)
0.10	0.10	0.0080
0.20	0.10	0.0160
0.10	0.20	0.0080

Determine:

Order with respect to A
Order with respect to B
Rate constant k

Solution:

When [A] doubles (0.10 → 0.20) and [B] constant, rate doubles (0.0080 → 0.0160)
- Therefore, first order with respect to A
When [B] doubles (0.10 → 0.20) and [A] constant, rate stays constant (0.0080 → 0.0080)
- Therefore, zero order with respect to B
Rate = $k[\text{A}]^1[\text{B}]^0 = k[\text{A}]$ Using first set of data: $0.0080 = k \times 0.10$ k = 0.080 d $m^3$ mol⁻¹ s⁻¹

Method Summary Diagram:

Summary

Key Concepts

Reaction rate measures how fast reactants are converted to products
Collision theory requires three conditions: collision, sufficient energy, proper orientation
Factors affecting reaction rates:
- Surface area: More surface area = faster rate
- Concentration: Higher concentration = faster rate
- Temperature: Higher temperature = faster rate
- Catalysts: Lower activation energy = faster rate
- Pressure (gases only): Higher pressure = faster rate
Catalysts speed up reactions without being consumed
Industrial applications optimize conditions for maximum rate and yield

Summary Diagram:

Experimental Skills

Measure reaction rates using various methods (mass loss, gas collection, precipitation, color change)
Investigate factors affecting reaction rates systematically
Plot and interpret concentration-time graphs
Calculate reaction rates from experimental data

Problem-Solving Strategy

Identify the type of reaction and measurable quantity
Choose appropriate method for measuring rate
Control variables while testing one factor at a time
Record data systematically and plot graphs
Analyze resultsi and draw conclusions

Experimental Workflow:

Practice Questions

Explain why powdered calcium carbonate reacts faster with acid than lumps of calcium carbonate.
A reaction is found to be first order with respect to reactant A and zero order with respect to reactant B. Write the rate law and explain what happens to the rate when: a) [A] is doubled b) [B] is doubled c) Both [A] and [B] are doubled
Describe an experiment to investigate the effect of temperature on the reaction between magnesium ribbon and hydrochloric acid.

Related Topics: