The rate of a reaction is how much product forms, or reactant is used, per unit time. From a graph, you measure it as a gradient: a chord gives an average rate and a tangent gives the rate at one instant.
This lesson belongs to SPM Chemistry rate of reaction. Once you can read gradients, move on to explaining factors using collision theory.
How do you find an average rate?
Divide the change in the measured quantity by the time taken. Use the two readings at the ends of the interval and nothing in between.
Average rate = (final reading − starting reading) ÷ (final time − starting time).
Worked example: gas collected from magnesium and acid
An original experiment collects hydrogen in a gas syringe. The readings are:
| Time (s) | 0 | 30 | 60 | 90 | 120 | 150 |
|---|---|---|---|---|---|---|
| Volume (cm³) | 0 | 18 | 31 | 41 | 47 | 50 |
Average rate for the first 60 s: (31 − 0) ÷ 60 = 0.52 cm³/s.
Average rate from 60 s to 120 s: (47 − 31) ÷ 60 = 16 ÷ 60 = 0.27 cm³/s.
The second answer is smaller, which matches the curve flattening. The acid is being used up, so fewer collisions happen each second.
How do you find the rate at exactly 60 s?
Draw a tangent: a straight line that touches the curve at t = 60 s and does not cross it there. Then find the gradient of that line, not of the curve.
Suppose your tangent passes through (0, 8) and (100, 46). Choose two points far apart on the tangent, because a long line gives a more reliable gradient.
Rate at 60 s = (46 − 8) ÷ (100 − 0) = 38 ÷ 100 = 0.38 cm³/s.
A quick reasonableness check: the readings at 30 s and 90 s give (41 − 18) ÷ 60 = 0.38 cm³/s as well. A tangent at 60 s should sit close to that.
The slip that costs marks
The common mistake is to join (0, 0) to the point (60, 31) and call the gradient the rate at 60 s. That gives 0.52 cm³/s, which is the average rate over the first minute.
| Step | Wrong | Right |
|---|---|---|
| Line drawn | Chord from the origin to the point | Tangent touching the curve at 60 s |
| Points used | (0, 0) and (60, 31) | Two far-apart points on the tangent |
| Answer | 0.52 cm³/s | 0.38 cm³/s |
Another frequent slip is leaving out the unit. Always write cm³/s, g/min or whatever the axes give.
Check yourself
A student measures the mass lost by a flask during a reaction. The mass falls from 120.00 g at 0 s to 119.40 g at 50 s. Find the average rate for the first 50 s in g/s and in g/min.
Answer
Mass lost = 120.00 − 119.40 = 0.60 g.
Average rate = 0.60 ÷ 50 = 0.012 g/s.
Multiply by 60 to convert to minutes: 0.012 × 60 = 0.72 g/min.
Check: 0.72 g/min over 50 s (5/6 of a minute) gives 0.72 × 5/6 = 0.60 g. It matches.
What to study next
Gradients explain why a curve flattens, but not why a factor such as temperature changes the gradient. Continue with explaining factors using collision theory, then test yourself with the rate of reaction practice set.
The graph evidence and fair-comparison lab lets you practise reading rates from curves. If you want a teacher to go through your graph working with you, see online one-to-one Chemistry tuition.