IB Chemistry SLTopic 5 — The Rate of ReactionPaper 1 & 2Core skill~11 min read
The Rate of Reaction
Stoichiometry tells you what a reaction produces, but not whether you will be waiting a microsecond or a century for it. Rate is the missing dimension, and it is measured the same way as any speed: how much changes, divided by how long it took.
📚 What you need to know
Rate of reaction is the change in concentration of a reactant or product per unit time.
Standard units are mol dm–3 s–1, though lab measurements are often in cm3 s–1 or g s–1.
Rate is always quoted as a positive value, even though a reactant graph has a negative gradient.
On a concentration–time graph, the rate is the gradient.
Rate is greatest at the start and falls as reactants are used up; the graph levels off when the reaction stops.
For the rate at a particular instant, draw a tangent and find its gradient.
What rate means
Rate of reaction
rate = change in concentration ÷ time
mol dm–3 s–1
You can follow either side of the equation. Reactant concentration falls, product concentration rises, and because every particle lost from one side appears on the other, the two graphs are mirror images.
Both curves flatten at the same moment. That is the reaction finishing, not the graph running out of paper.
Why does the curve flatten? Because rate depends on reactant particles colliding, and there are fewer of them left as time goes on. The reaction is fastest at t = 0, when reactant concentration is at its highest, and slows continuously from there.
The gradient of a reactant graph is negative — concentration is falling. A rate of –0.004 mol dm–3 s–1 is not a thing. Take the magnitude and quote 0.004.
Average rate and rate at an instant
These are two different questions and they have two different answers.
Average rate over an interval: total change divided by total time. Easy, but it hides everything interesting.
Instantaneous rate at one moment: the gradient of the curve at that point, found by drawing a tangent.
The tangent touches the curve at one point and matches its slope there. Its gradient is the rate at that instant.
🧩 Getting a rate from a tangent
Find the point on the curve at the time you were asked about.
Draw a straight line that touches the curve there without crossing it, extending well in both directions.
Build a large triangle on the tangent, ideally with corners on gridlines.
Read off Δy and Δx from the axes, not by counting squares.
Gradient = Δy / Δx, and quote it with the correct units.
Make the triangle big. A small triangle magnifies every reading error, and a badly drawn tangent is the most common way to lose these marks. Using at least half the width of the graph is a good habit.
WORKED EXAMPLE
From the graph above, the reaction produces 59 cm3 of hydrogen and is complete after 140 s. Calculate the average rate over the whole reaction, and compare it with the rate at 20 s.
Step 1 — average rate59 ÷ 140 = 0.42 cm³ s⁻¹Step 2 — instantaneous rate at 20 s, from the tangentΔV = 40 cm³, Δt = 40 s40 ÷ 40 = 1.0 cm³ s⁻¹1.0 vs 0.42 cm³ s⁻¹Early on the reaction runs more than twice as fast as the overall average. The average is a summary of a rate that was never actually constant.
WORKED EXAMPLE
The concentration of a reactant falls from 0.100 mol dm–3 to 0.064 mol dm–3 in 30 s. Calculate the average rate of reaction.
Step 1 — the change0.100 − 0.064 = 0.036 mol dm⁻³Step 2 — divide by time0.036 ÷ 30 = 0.0012rate = 1.2 × 10⁻³ mol dm⁻³ s⁻¹Positive, even though the concentration went down. The reaction proceeds forwards at that rate.
WORKED EXAMPLE
Two students run the same reaction. Student A’s gas-volume curve is steeper at the start but levels off at the same volume as student B’s. What can you conclude?
The gradientA steeper initial gradient means a FASTER rate for student A.The plateauThe same final volume means the same AMOUNT of product, so both used the same amount of limiting reactant.same quantities, faster conditionsStudent A perhaps used a higher temperature, a more concentrated acid or a powder. Rate and yield are independent — a graph can change shape without changing where it ends.
💡 Exam tip
Quote rates as positive numbers and always attach units.
Asked for the rate “at 30 s”? That means a tangent. Asked for the rate “over the first 30 s”? That is an average.
The initial rate is the steepest part of the curve, at t = 0, and is often the fairest way to compare experiments.
When comparing two curves, look at steepness (rate) and final height (amount) as two separate pieces of information.
Read values off the axis scales, not by counting grid squares whose value you have assumed.
⚠️ Common mix-up
Giving a negative rate from a reactant graph.
Confusing a faster reaction with a bigger yield. A steeper curve that plateaus at the same height gives the same amount, sooner.
Using the chord instead of the tangent when the instantaneous rate was asked for.
Drawing a tiny triangle and magnifying reading errors.
Forgetting units. cm3 s–1 and mol dm–3 s–1 are not interchangeable.
Up next: Measuring Reaction Rates — the graph has to come from somewhere, and choosing the right way to collect the data is itself an exam skill.
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