The chemistry
A gas syringe can measure the volume of gas collected as a reaction proceeds. Plot gas volume on the vertical axis and time on the horizontal axis. Check the units before calculating a gradient.
A mean rate over an interval is the change in volume divided by the time interval. For example, a rise of 42 cm³ over 30 s gives 1.4 cm³/s. The volume already in the syringe is not a rate.
At any point on a curved volume–time graph, the gradient of a tangent shows how quickly the volume is changing at that instant. Use two widely separated points on the drawn tangent; they need not be observed data points on the curve.
On the invented gas-collection curves, the graph rises steeply at first and then levels off. The falling gradient means less gas is produced per second as the run progresses. A flat line means the measured volume is no longer increasing.
AQA Foundation interprets tangents but does not require the numerical gradient of a tangent. AQA Higher does. Pearson Edexcel includes graph gradients in its rates requirements without a Higher-only restriction.
Worked example
If the syringe reading changes from 15 cm³ at 20 s to 43 cm³ at 40 s, the mean rate over that interval is (43 − 15) ÷ (40 − 20) = 1.4 cm³/s.
Suppose two points on a tangent are (10 s, 20 cm³) and (30 s, 52 cm³). The gradient is (52 − 20) ÷ (30 − 10) = 1.6 cm³/s. This is the instantaneous rate at the time where that tangent touches the original curve.
Specification references
AQA GCSE Chemistry 8462 4.6.1.1–4.6.1.3 and required practical 5; Pearson Edexcel 1CH0 Issue 4 7.1–7.5. Select your course to see which questions apply.