Calculating rates of reactions

Introduction

The rate of reaction measures how quickly reactants are used up or products are formed over time.
It is calculated using the formula: Rate = (amount of reactant used or product formed) / time taken For example, producing 1,200 cm³ of hydrogen in 4 minutes (240 seconds) gives a rate of 1200 / 240 = 5 cm³/s.

The Limitation of Mean Rate Calculations

A simple rate calculation only gives the average (mean) rate over the entire time period measured.
In reality, reactions are fastest at the start and slow down as reactants are used up, so the rate is constantly changing.
Using a graph allows us to see how the rate of reaction changes throughout the entire reaction.

2. The Limitation of Mean Rate Calculations AQA

Notes

A simple rate calculation only gives the average (mean) rate over the entire time period measured.
In reality, reactions are fastest at the start and slow down as reactants are used up, so the rate is constantly changing.
Using a graph allows us to see how the rate of reaction changes throughout the entire reaction.

Plotting a Volume–Time Graph

When monitoring a gas-producing reaction, time is plotted on the x-axis and the volume of gas produced is plotted on the y-axis.
At the start, the curve is very steep, indicating a high rate of reaction because there are plenty of reactants present.
As reactants are used up, the curve becomes less steep, and eventually the graph plateaus when the reaction has finished.

3. Plotting a Volume–Time Graph AQA

Notes

When monitoring a gas-producing reaction, time is plotted on the x-axis and the volume of gas produced is plotted on the y-axis.
At the start, the curve is very steep, indicating a high rate of reaction because there are plenty of reactants present.
As reactants are used up, the curve becomes less steep, and eventually the graph plateaus when the reaction has finished.

Calculating the Mean Rate from a Graph

To find the mean rate over a specific period, read off the volume of product produced at the end of that time period from the graph.
Draw a dashed vertical line from the chosen time on the x-axis up to the curve, then a horizontal line across to the y-axis to read the volume.
Divide the volume of gas produced by the time taken (in seconds) to calculate the mean rate, e.g. 1200 / 180 = 6.67 cm³/s.

4. Calculating the Mean Rate from a Graph AQA

Notes

To find the mean rate over a specific period, read off the volume of product produced at the end of that time period from the graph.
Draw a dashed vertical line from the chosen time on the x-axis up to the curve, then a horizontal line across to the y-axis to read the volume.
Divide the volume of gas produced by the time taken (in seconds) to calculate the mean rate, e.g. 1200 / 180 = 6.67 cm³/s.

Calculating the Rate at a Specific Time Using a Tangent

To find the instantaneous rate at a specific time, you must calculate the gradient of the curve at that point by drawing a tangent.
A tangent is a straight line that just touches the curve at one point and has the same gradient as the curve at that point.
Draw the tangent as long as possible to improve accuracy, then use the change in y and change in x values to calculate the gradient.
The gradient is calculated as: Rate = Δy / Δx = change in volume / change in time For example, a tangent giving a change in volume of 600 cm³ over 170 seconds gives a rate of 600 / 170 ≈ 3.53 cm³/s.

5. Calculating the Rate at a Specific Time Using a Tangent AQA

Notes

To find the instantaneous rate at a specific time, you must calculate the gradient of the curve at that point by drawing a tangent.
A tangent is a straight line that just touches the curve at one point and has the same gradient as the curve at that point.
Draw the tangent as long as possible to improve accuracy, then use the change in y and change in x values to calculate the gradient.
The gradient is calculated as: Rate = Δy / Δx = change in volume / change in time For example, a tangent giving a change in volume of 600 cm³ over 170 seconds gives a rate of 600 / 170 ≈ 3.53 cm³/s.

Examiner Guidance on Drawing Tangents

Examiners understand that drawing a tangent is a judgement by eye, so a range of acceptable answers is allowed.
You should aim to draw your tangent as accurately as possible, but you will not be penalised for small errors.
As long as your tangent has the correct steepness at the chosen point, different lengths of tangent line will give the same gradient.

6. Examiner Guidance on Drawing Tangents AQA

Notes

Examiners understand that drawing a tangent is a judgement by eye, so a range of acceptable answers is allowed.
You should aim to draw your tangent as accurately as possible, but you will not be penalised for small errors.
As long as your tangent has the correct steepness at the chosen point, different lengths of tangent line will give the same gradient.

Using a Mass–Time Graph Instead

Alternatively, the mass of a reactant remaining can be plotted against time, with the graph starting at the initial mass and declining over time.
The graph decreases steeply at first and then levels off as the reaction slows and eventually stops.
The same tangent method is used to find the rate at a specific time, dividing the change in mass (in grams) by the change in time (in seconds).
For example, a change in mass of 0.72 g over 100 seconds gives a rate of 0.72 / 100 = 0.0072 g/s.

7. Using a Mass–Time Graph Instead AQA

Notes

Alternatively, the mass of a reactant remaining can be plotted against time, with the graph starting at the initial mass and declining over time.
The graph decreases steeply at first and then levels off as the reaction slows and eventually stops.
The same tangent method is used to find the rate at a specific time, dividing the change in mass (in grams) by the change in time (in seconds).
For example, a change in mass of 0.72 g over 100 seconds gives a rate of 0.72 / 100 = 0.0072 g/s.

Key Differences: Mean Rate vs Instantaneous Rate

The mean rate gives an overall average across a time period and is found by dividing total change in product or reactant by total time.
The instantaneous rate gives the rate at one specific moment and is found by calculating the gradient of the tangent to the curve at that point.
Both methods require careful reading of values from the graph to ensure accurate calculations.

8. Key Differences: Mean Rate vs Instantaneous Rate AQA

Notes

The mean rate gives an overall average across a time period and is found by dividing total change in product or reactant by total time.
The instantaneous rate gives the rate at one specific moment and is found by calculating the gradient of the tangent to the curve at that point.
Both methods require careful reading of values from the graph to ensure accurate calculations.

Summary / Key Terms

A steep gradient on a rate-of-reaction graph indicates a fast rate of reaction, whilst a shallow gradient indicates a slow rate.
A plateau on the graph shows that the reaction has stopped, usually because one reactant has been completely used up.
Practising drawing tangents and reading graph values accurately are essential skills for GCSE Chemistry exam questions on rates of reaction.

9. Summary / Key Terms AQA

Notes

A steep gradient on a rate-of-reaction graph indicates a fast rate of reaction, whilst a shallow gradient indicates a slow rate.
A plateau on the graph shows that the reaction has stopped, usually because one reactant has been completely used up.
Practising drawing tangents and reading graph values accurately are essential skills for GCSE Chemistry exam questions on rates of reaction.

AQA student objectives

All · Most · Some

Key knowledge

Introduction

Notes

The Limitation of Mean Rate Calculations

Notes

Plotting a Volume–Time Graph

Notes

Calculating the Mean Rate from a Graph

Notes

Calculating the Rate at a Specific Time Using a Tangent

Notes

Examiner Guidance on Drawing Tangents

Notes

Using a Mass–Time Graph Instead

Notes

Key Differences: Mean Rate vs Instantaneous Rate

Notes

Summary / Key Terms

Notes