5.1 Rates of Reactions

Introduction

Chemical reactions are processes in which mass and energy are constantly changing. These reactions can take place at a range of speeds, from very fast to very slow.

• Fermentation is a slow reaction, taking several weeks to make enough products, and digestion is a slow reaction.
• Acid-base neutralization is a fast reaction, taking only a few microseconds.
• Other reactions take place at a moderate speed, such as those that contract muscles, send impulses along nerves, and capture photographic images.

For industry, it is important to understand the conditions under which a reaction will be most cost-effective.

Kinetics, also known as chemical kinetics, is the study of the rate of chemical reactions, their mechanisms, and the factors that influence them.

Definition

Rate of a Chemical Reaction: The rate of a chemical reaction tells us how quickly the reactants are used up or how quickly the products are formed over time. It is the change in the concentration of reactants or products in a given amount of time.

In simple words: The rate of reaction tells us how fast a reaction happens.

Mathematically:

Rate = Change in concentration of a substanceTime taken for change

Main Idea

• The rate of a reaction is the change in concentration of a reactant or product over time.
• As a reaction happens, the amount of reactants decreases, and the amount of products increases.
• Concentration is measured in moles per cubic decimeter (mol dm⁻³).
• Time is measured in seconds (s).
• So, the unit for the rate of reaction is mol dm⁻³ s⁻¹.

Core Concept

Rate of reaction:

Rate = Change in concentration of a substanceTime taken for change

Units:

• Concentration: mol dm⁻³
• Time: s
• Rate: mol dm⁻³ s⁻¹

Key point: The rate of reaction is not constant. It changes as the reaction progresses.

Detailed Explanation

Understanding the Rate of Reaction

As a reaction happens:

• The amount of reactants decreases.
• The amount of products increases.

For example, in a reaction:

A → B

• The concentration of A decreases over time.
• The concentration of B increases over time.

Rate of reaction can be expressed as:

Rate of reaction = -d[A]dt

Rate of reaction = +d[B]dt

Where:

• d[A] and d[B] are the changes in the concentration of A and B respectively.
• The negative sign indicates a decrease in the concentration of the reactant A.
• The positive sign indicates the increase in the concentration of product B.

Graphical Representation of the Rate of a Chemical Reaction

The rate of reaction can be understood using a graph of concentration vs. time.

What the graph shows:

• This means the reaction slows down because there are fewer reactant particles to react.
• This means the reaction has stopped because all the reactants are used up or the system has reached equilibrium.

Key point: The rate of reaction is not constant. It changes as the reaction progresses.

Average Rate of Reaction

Consider a general reaction:

A → B

The rate of reaction can be expressed in terms of:

• The rate of disappearance of reactant A.
• The rate of appearance of product B.

Rate of reaction:

Rate of reaction = -d[A]dt

Rate of reaction = +d[B]dt

Where:

• d[A] and d[B] are the changes in the concentration of A and B respectively.
• The negative sign indicates a decrease in the concentration of the reactant A.
• The positive sign indicates the increase in the concentration of product B.

Interpreting Data

Suppose a student is carrying out a chemical reaction where substance A reacts with another substance B to produce substance C. He followed the rate of reaction by determining the concentration of C produced at regular intervals.

The following data was obtained:

From this graph, you can determine the rate of reaction at any moment by determining the gradient at that moment.

Suppose you want to calculate the rate of reaction at 20 minutes.

For this purpose, draw a tangent to the curve at 20 minutes.

From the graph:

Δ C = 27 - 3 = 24\ mol dm^-3

Δ t = 40 - 0 = 40\ min

Rate of reaction (or gradient):

Rate = Δ CΔ t

Rate = 24\ mol dm^-340 × 60\ s

Rate = 0.01\ mol dm^-3\ s^-1

Thus, the rate of reaction at 20 min = 0.01\ mol dm^-3\ s^-1

Average rate of reaction:

Average rate = Total amount of C producedTotal time taken

Average rate = 25\ mol dm^-3100 × 60\ s

Average rate = 0.0042\ mol dm^-3\ s^-1

Conclusion

From this experiment, you can see that the reaction rate isn't constant. The amount of substance C formed increases more quickly at first and then slows down. This is a common pattern in chemical reactions, where the rate can change as reactants are consumed.

Intermediate Level

Rate of reaction:

Rate = Δ CΔ t

For reactant A:

Rate = -d[A]dt

For product B:

Rate = +d[B]dt

Graph interpretation:

• The curve becomes less steep as time goes on (reaction slows down).
• The curve becomes flat when the reaction stops (or reaches equilibrium).

Average rate:

Average rate = Total amount of product producedTotal time taken

Instantaneous rate:

• Determined by drawing a tangent to the curve at a specific time.
• The gradient of the tangent gives the rate at that moment.

Formula / Mathematical Form

Rate of reaction = Change in concentration of a substanceTime taken for change

Rate = Δ CΔ t

Units:

mol dm^-3\ s^-1

For reactant A:

Rate = -d[A]dt

For product B:

Rate = +d[B]dt

Solved Example

Example: Calculating Rate of Reaction

Given: From the data table:

Required: Rate of reaction at 20 minutes.

Formula:

Rate = Δ CΔ t

From the tangent at 20 minutes:

Δ C = 27 - 3 = 24\ mol dm^-3

Δ t = 40 - 0 = 40\ min

Substitution:

Rate = 2440 × 60

Calculation:

Rate = 0.01\ mol dm^-3\ s^-1

Final Answer: The rate of reaction at 20 minutes is 0.01\ mol dm^-3\ s^-1.

Example: Calculating Average Rate of Reaction

Given: Total amount of C produced = 25\ mol dm^-3 Total time taken = 100\ minutes

Required: Average rate of reaction.

Formula:

Average rate = Total amount of C producedTotal time taken

Substitution:

Average rate = 25100 × 60

Calculation:

Average rate = 0.0042\ mol dm^-3\ s^-1

Final Answer: The average rate of reaction is 0.0042\ mol dm^-3\ s^-1.

Important Points

• - Rate of reaction = change in concentration of a substance over time.
• - Unit: mol dm⁻³ s⁻¹.
• - Formula:
• Rate = Δ CΔ t
• - For reactants: Rate = -d[A]dt.
• - For products: Rate = +d[B]dt.
• - The rate of reaction is not constant.
• - The reaction is fast at first, then slows down.
• - Eventually, the reaction stops (or reaches equilibrium).
• - Average rate = total amount of product / total time.
• - Instantaneous rate = gradient of the tangent at a specific time.
• - Chemical kinetics = study of the rate of chemical reactions, their mechanisms, and the factors that influence them.

Remember

• - Rate of reaction = change in concentration over time.
• - Unit: mol dm⁻³ s⁻¹.
• - Rate = Δ C / Δ t.
• - Reactants decrease; products increase.
• - Rate is not constant.
• - Fast at first, slows down, then stops.
• - Average rate = total product / total time.
• - Instantaneous rate = gradient of tangent.
• - Chemical kinetics = study of reaction rates.

Common Mistakes

Quick Revision

Rate of Reactions:

The rate of a chemical reaction tells us how quickly the reactants are used up or how quickly the products are formed over time. It is the change in the concentration of reactants or products in a given amount of time.

Mathematically:

• Rate = Change in concentration of a substanceTime taken for change

As a reaction happens, the amount of reactants decreases, and the amount of products increases. For example, we measure concentration in moles per cubic decimeter (mol dm⁻³) and time in seconds (s). So, the unit for the rate of reaction is mol dm⁻³ s⁻¹.

Graphical Representation:

• As time goes on, the curves become less steep. This means the reaction slows down because there are fewer reactant particles to react.
• Eventually, the curves become flat. This means the reaction has stopped because all the reactants are used up or the system has reached equilibrium.

This shows that the rate of reaction is not constant. It changes as the reaction progresses.

Average Rate of Reaction:

Consider a general reaction:

• A → B

The rate of reaction can be expressed in terms of the rate of disappearance of reactant A or the rate of appearance of product B.

• Rate of reaction = -d[A]dt

• Rate of reaction = +d[B]dt

Where d[A] and d[B] are the changes in the concentration of A and B respectively. The negative sign indicates a decrease in the concentration of the reactant A whereas the positive sign indicates the increase in the concentration of product B.

Interpreting Data:

Suppose a student is carrying out a chemical reaction where substance A reacts with another substance B to produce substance C. He followed the rate of reaction by determining the concentration of C produced at regular intervals. The following data was obtained.

From this graph you can determine the rate of reaction at any moment by determining the gradient at that moment. Suppose you want to calculate the rate of reaction at 20 minutes. For this purpose, draw a tangent to the curve at 20 minutes.

• Rate of reaction (or gradient) = Δ CΔ t

• Rate of reaction (or gradient) = 24\ mol dm^-340 × 60\ s

Thus, the rate of reaction at 20 min = 0.01\ mol dm^-3\ s^-1

Average rate of reaction:

• Average rate of reaction = Total amount of C producedTotal time taken

• Average rate of reaction = 25\ mol dm^-3100 × 60\ s = 0.0042\ mol dm^-3\ s^-1

Conclusion:

From this experiment, you can see that the reaction rate isn't constant. The amount of substance C formed increases more quickly at first and then slows down. This is a common pattern in chemical reactions, where the rate can change as reactants are consumed.

60-Second Revision

• Rate of reaction = change in concentration over time.
• Unit: mol dm⁻³ s⁻¹.
• Rate = Δ C / Δ t.
• Reactants decrease; products increase.
• Rate is not constant.
• Fast at first, slows down, then stops.
• Average rate = total product / total time.
• Instantaneous rate = gradient of tangent.
• Chemical kinetics = study of reaction rates.
• ⚠️ Warning: the rate of reaction is not constant — it changes as the reaction progresses.