Revision notes for AQA GCSE Chemistry Calculating rates of reactions. Open the guide for explanations and worked examples. Written against the AQA GCSE Chemistry (8462) specification, so the content matches what's examinable rather than general Chemistry background.
Calculating rates of reactions
What you'll learn
- How to calculate the mean rate of reaction from data.
- How to choose the correct rate units, such as g/s or cm³/s.
- How to interpret reaction rate graphs.
- How to use a tangent to find rate at a specific time.
What does “rate of reaction” mean?
In chemistry, rate means how fast something changes. For a reaction, that change could be:
- a reactant being used up
- a product being formed
A fast reaction makes products quickly. A slow reaction makes products more gradually.
Definition
Rate of reaction
The rate of reaction tells you how quickly reactants are used up or products are formed. It is a change in quantity per unit time.
For example, if a reaction produces hydrogen gas, you could measure the volume of hydrogen made every few seconds. If lots of gas is made in a short time, the rate is high.
What quantity can you measure?
At GCSE, the “quantity” in a rate calculation is usually measured as:
- mass in grams, g
- volume in cubic centimetres, cm³
For Higher Tier, you may also use amount of substance in moles, mol.
You can calculate rate using either the reactant disappearing or the product appearing. Both describe the same reaction, just from different viewpoints.
Mean rate of reaction
Most basic calculations ask for the mean rate. “Mean” means average over a time interval.
Definition
Mean rate of reaction
The mean rate of reaction is the average rate over a chosen time period. It does not show every small change during the reaction; it gives one overall value.
The two key formulae are:
mean rate of reaction=quantity of reactant usedtime taken\text{mean rate of reaction} = \frac{\text{quantity of reactant used}}{\text{time taken}}mean rate of reaction=time takenquantity of reactant used mean rate of reaction=quantity of product formedtime taken\text{mean rate of reaction} = \frac{\text{quantity of product formed}}{\text{time taken}}mean rate of reaction=time takenquantity of product formedKey Idea
The core idea
Rate is always a quantity divided by a time. The units come from whatever quantity you measured, divided by the time unit.
Choosing the correct units
If the quantity is a mass in grams and time is in seconds, the rate is in g/s.
If the quantity is a volume in cm³ and time is in seconds, the rate is in cm³/s.
If the quantity is in moles and time is in seconds, the rate is in mol/s.
Example
Calculating mean rate from gas volume
A reaction produces 48 cm³ of gas in 120 s. Calculate the mean rate of reaction.
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The quantity measured is product formed, so use:
mean rate=volume of gas formedtime taken\text{mean rate} = \frac{\text{volume of gas formed}}{\text{time taken}}mean rate=time takenvolume of gas formed -
Substitute the values, keeping the units attached:
mean rate=48 cm3120 s\text{mean rate} = \frac{48\ \text{cm}^3}{120\ \text{s}}mean rate=120 s48 cm3 -
Calculate the rate:
mean rate=0.40 cm3/s\text{mean rate} = 0.40\ \text{cm}^3\text{/s}mean rate=0.40 cm3/s
Common Mistake
Using the amount remaining
If a question gives the mass of reactant remaining, do not put that straight into the rate formula. First calculate how much reactant was used up.
Example
Calculating rate from reactant used up
A solid reactant has a mass of 3.00 g at the start. After 75 s, 1.80 g remains. Calculate the mean rate at which the reactant is used up.
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Calculate the mass used up:
3.00 g−1.80 g=1.20 g3.00\ \text{g} - 1.80\ \text{g} = 1.20\ \text{g}3.00 g−1.80 g=1.20 g -
Divide the mass used by the time taken:
mean rate=1.20 g75 s\text{mean rate} = \frac{1.20\ \text{g}}{75\ \text{s}}mean rate=75 s1.20 g -
Give the answer with units:
mean rate=0.016 g/s\text{mean rate} = 0.016\ \text{g/s}mean rate=0.016 g/s
Tip
Let the units guide you
If your answer needs to be in cm³/s, your numerator must be a volume in cm³ and your denominator must be a time in seconds.
Higher Tier: using moles
For Higher Tier, the quantity may be given in moles. A mole is a unit chemists use for an amount of substance.
Definition
Mole
A mole, symbol mol, is a unit for amount of substance. In rate calculations, moles can be used as the quantity of reactant used or product formed.
The calculation method is exactly the same:
mean rate=amount in moltime in s\text{mean rate} = \frac{\text{amount in mol}}{\text{time in s}}mean rate=time in samount in molExample
Calculating rate in moles per second
In a reaction, 0.012 mol of product forms in 45 s. Calculate the mean rate in mol/s.
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The quantity is already in moles, so use moles divided by seconds:
mean rate=amount of product formedtime taken\text{mean rate} = \frac{\text{amount of product formed}}{\text{time taken}}mean rate=time takenamount of product formed -
Substitute the values:
mean rate=0.012 mol45 s\text{mean rate} = \frac{0.012\ \text{mol}}{45\ \text{s}}mean rate=45 s0.012 mol -
Calculate and write the answer in standard form:
mean rate=2.7×10−4 mol/s\text{mean rate} = 2.7 \times 10^{-4}\ \text{mol/s}mean rate=2.7×10−4 mol/s
Reaction rate graphs
A reaction rate graph usually has:
- time on the x-axis
- quantity of product formed or quantity of reactant used up on the y-axis
For a product-formed graph, the curve often rises quickly at first, then becomes less steep, then levels off. The reaction is fastest at the start and stops changing when the reaction has finished.
Key Idea
Steeper means faster
On a reaction rate graph, a steeper line or curve means a faster rate. A horizontal line means the rate is zero because the quantity is no longer changing.
Mean rate from a graph
To calculate a mean rate from a graph, use the change in the y-value divided by the change in the x-value.
mean rate over an interval=ΔquantityΔtime\text{mean rate over an interval} = \frac{\Delta \text{quantity}}{\Delta \text{time}}mean rate over an interval=ΔtimeΔquantityThe symbol Δ\DeltaΔ means “change in”.
Example
Calculating mean rate from graph readings
A graph of gas volume against time shows 20 cm³ at 10 s and 68 cm³ at 70 s. Calculate the mean rate between 10 s and 70 s.
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Find the change in volume:
68 cm3−20 cm3=48 cm368\ \text{cm}^3 - 20\ \text{cm}^3 = 48\ \text{cm}^368 cm3−20 cm3=48 cm3 -
Find the change in time:
70 s−10 s=60 s70\ \text{s} - 10\ \text{s} = 60\ \text{s}70 s−10 s=60 s -
Divide change in volume by change in time:
mean rate=48 cm360 s=0.80 cm3/s\text{mean rate} = \frac{48\ \text{cm}^3}{60\ \text{s}} = 0.80\ \text{cm}^3\text{/s}mean rate=60 s48 cm3=0.80 cm3/s
Rate at a specific time: tangents
A mean rate covers a whole interval. Sometimes you need the rate at one particular moment on a curve. To do this, you use a tangent.
Definition
Tangent
A tangent is a straight line drawn so that it just touches a curve at one chosen point and has the same direction as the curve at that point.
Definition
Gradient
The gradient of a graph is its slope. It is calculated using change in ychange in x\frac{\text{change in y}}{\text{change in x}}change in xchange in y.
For reaction graphs, the gradient of the tangent gives the rate at that specific time. For Higher Tier, you may be asked to calculate this gradient.
How to calculate a tangent gradient
- Draw a tangent at the time you are interested in.
- Choose two clear points on the tangent line, far apart if possible.
- Calculate:
Example
Calculating a tangent gradient
A tangent drawn at 30 s passes through two convenient points: 10 s, 18 cm³ and 50 s, 54 cm³. Calculate the rate at 30 s.
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Use the two points on the tangent, not necessarily points on the curve, to find the change in volume:
54 cm3−18 cm3=36 cm354\ \text{cm}^3 - 18\ \text{cm}^3 = 36\ \text{cm}^354 cm3−18 cm3=36 cm3 -
Find the change in time:
50 s−10 s=40 s50\ \text{s} - 10\ \text{s} = 40\ \text{s}50 s−10 s=40 s -
Calculate the gradient:
rate at 30 s=36 cm340 s=0.90 cm3/s\text{rate at 30 s} = \frac{36\ \text{cm}^3}{40\ \text{s}} = 0.90\ \text{cm}^3\text{/s}rate at 30 s=40 s36 cm3=0.90 cm3/s
Common Mistake
Using the curve instead of the tangent
When finding the rate at a specific time, calculate the gradient of the tangent line, not the gradient between two random points on the curve.
Common Mistake
Falling graphs
If a graph shows the amount of reactant remaining, the gradient is negative because the amount is decreasing. Reaction rate is normally given as a positive value, so use the size of the decrease per second.
Quick method summary
For any rate calculation, ask yourself:
- What quantity is changing: mass, volume, or moles?
- Is the question asking for a mean rate or a rate at a specific time?
- Are the units consistent, especially the time units?
- If using a graph, am I using the correct gradient?
Exam technique
In the exam
- Check whether the graph or data shows product formed, reactant used, or reactant remaining.
- For mean rate, use the overall change divided by the time taken.
- For rate at a specific time, draw a tangent and calculate its gradient using two well-spaced points on the tangent.
- Always include units such as g/s, cm³/s or, for Higher Tier, mol/s.
Self review
Check yourself
- A reaction produces 36 cm³ of gas in 90 s. What is its mean rate?
- Why does a product-formed graph usually become less steep as the reaction continues?
- How is finding a mean rate different from finding the rate at one specific time?
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