How to interpret rate of reaction graphs

Rate of reaction is a graph-heavy topic, and the questions are very predictable once you know what a curve is telling you. The examiner is usually testing three things: can you read the gradient, can you explain the shape using collision theory, and can you compare two curves. This guide walks through all three, using the rate of reaction syllabus so you can turn these into easy marks.

What is usually on the axes

Most SPM rate graphs plot a quantity of product against time, commonly the volume of gas collected (cm³) on the y-axis and time (s) on the x-axis. Sometimes it is the mass of the flask (falling as gas escapes) or the volume of gas from marble chips and acid. Whatever the quantity, the shape is the same: a curve that is steep at the start, gradually flattens, and finally becomes horizontal.

The gradient is the rate

The single most important idea: the gradient (steepness) of the curve at any point is the rate of reaction at that moment. A steep part means a fast reaction; a shallow part means a slow one; a flat part means the reaction has effectively stopped.

That is why the curve is steepest at the very start. At the beginning the reactant concentration is highest, so particles collide most frequently and successfully, and the reaction is fastest. As reactants are used up, collisions become less frequent, the gradient falls, and the reaction slows. When a reactant is completely used up, no more product forms and the curve plateaus (goes flat).

Average rate versus instantaneous rate

Two different rates come out of the same graph, so keep them separate.

• Average rate over a period = total change in quantity divided by total time. If 48 cm³ of gas is collected in 40 s, the average rate over those 40 s is 48 ÷ 40 = 1.2 cm³ s⁻¹. This is the method on our average rate of reaction page.
• Instantaneous rate at a single moment = the gradient of the tangent drawn to the curve at that point. Draw the tangent, pick two clear points on it, and work out (change in y) ÷ (change in x). Full method with a worked example is on rate from a graph.

A common exam instruction is “find the rate at the 20th second”, that means draw a tangent at t = 20 s and find its gradient, not divide the total by 20.

Worked example: reading one curve

Suppose marble chips react with dilute hydrochloric acid, giving off carbon dioxide, and you collect the gas. The curve rises steeply, then bends over and levels at 60 cm³ after about 50 s.

• Average rate for the whole reaction: 60 cm³ ÷ 50 s = 1.2 cm³ s⁻¹.
• Where is the reaction fastest? At the start, where the gradient is steepest.
• Why does it slow down? The acid concentration falls as it is used up, so collisions between acid particles and the marble are less frequent.
• Why does it go flat at 60 cm³? One reactant (here the limiting reactant) is completely used up, so no more CO₂ is produced.

Comparing two curves

This is where marks are won or lost. When two curves are drawn on the same axes, say a higher concentration versus a lower one, from effect of concentration on rate, read them like this:

• The curve with the steeper initial gradient has the faster reaction. Higher concentration, higher temperature, smaller particle size, or a catalyst all make the curve steeper at the start.
• The curve that reaches its plateau sooner finished faster.
• If both curves level off at the same height, the same amount of product formed, which means the same amount of limiting reactant was used in both.
• If one curve levels off higher, more product formed, so there was more reactant in that experiment.

So a faster experiment with the same quantities gives a steeper curve that plateaus at the same height, just earlier. A larger quantity gives a higher plateau.

Explaining the shapes with collision theory

Whenever a question asks you to explain a curve, reach for collision theory in these words: a reaction happens when particles collide with energy equal to or greater than the activation energy. Anything that makes effective collisions more frequent speeds the reaction up, a higher concentration or pressure packs particles closer, a higher temperature makes them move faster and gives more of them enough energy, a smaller particle size gives more surface area, and a catalyst provides an alternative path with lower activation energy. Tie your explanation of the graph to one of these and you will hit the marking points.

Common mistakes to avoid

• Confusing average and instantaneous rate. “At the 30th second” means a tangent, not a division.
• Saying the reaction stops because it “runs out of time”. It stops because a reactant is used up.
• Reading a higher plateau as a faster reaction. Height is amount of product; steepness is speed. They are different.
• Forgetting units, usually cm³ s⁻¹ for gas volume against time.

Practise on real curves

Print a few past-paper rate graphs and, for each, label where it is fastest, calculate an average rate, draw one tangent, and write a one-line collision-theory reason for the shape. The same four moves answer almost every rate question. If tangents or the compare-two-curves questions keep costing you marks, that is quick to fix with a teacher, our online one-to-one lessons run in English from RM50 an hour, with a paid one-hour trial. See how it works if you would like these drilled against real Paper 2 graphs.