IB Chemistry SL & HLTopic 5 — The Rate of Chemical ChangePaper 1 & 2Core idea~10 min read
The Rate of Reaction
Some reactions are over before you can blink. Others take years. “Rate” is just the word chemists use for how quickly a reaction gets on with it — and the neat thing is that you can measure it, draw it, and read it straight off a graph.
📘 What you need to know
Rate of reaction is how much the concentration of a reactant or product changes in a given time.
The usual units are mol dm−3 s−1, but you can measure rate in any “amount per time” units (cm3 s−1, g s−1).
On a concentration–time graph, the gradient is the rate. Steeper line, faster reaction.
To get the rate at one particular moment, draw a tangent to the curve and find its gradient.
Reactions are fastest at the start and slow down as the reactants get used up.
Rate is always quoted as a positive number, even though reactant concentration is falling.
What “rate” actually means
Think about a bath filling up. You would not describe how fast it is filling by saying “40 litres”. You would say “40 litres per minute”. Rate always needs two things: an amount and a time.
Reactions work the same way. As a reaction runs, reactants are used up and products build up. So we pick one substance, measure how much its concentration changes, and divide by the time that took.
Rate of reaction
rate = change in concentration ÷ time taken
Concentration is measured in mol dm−3 and time in seconds, so dividing one by the other gives units of mol dm−3 s−1. That is the standard answer if a question just says “state the units of rate”.
You do not have to use concentration. If a reaction gives off a gas, you can measure the volume instead and quote the rate in cm3 s−1. If it loses mass, use g s−1. As long as the thing you measure is proportional to how far the reaction has gone, it works as a measure of rate.
What the graphs look like
Whichever substance you follow, the shape is predictable. Reactants start high and fall. Products start at zero and climb. Both curves are steep at the beginning and flatten out at the end.
Notice the two curves are not just similar shapes — they are the same reaction. If you flip one upside down you get the other.
Students often ask why the curve flattens. It is not because the particles get tired. There are simply fewer reactant particles left in the same volume, so they bump into each other less often.
Reading the rate off the graph
Because rate is “change in amount ÷ change in time”, it is exactly the gradient of the graph. That gives you two different questions an examiner can ask.
1. Average rate over a period
Pick the start and end of the period, and divide the total change by the total time. Straightforward, but it hides the fact that the reaction was much faster at the beginning than at the end.
2. Rate at one exact moment
This is called the instantaneous rate, and it is the one that needs a tangent. A tangent is a straight line that just touches the curve at your chosen point and has the same steepness as the curve there.
🧩 Finding the rate at a given time
Find your time on the x-axis and go up to the curve.
Lay a ruler so it touches the curve at that one point only, matching the slope of the curve.
Draw the tangent long — right across the graph if you can. A short tangent gives a sloppy gradient.
Build a big triangle on the tangent, ideally starting and ending on gridlines.
Divide the vertical change by the horizontal change. Include units.
The tangent only touches at 20 s, but you read the triangle far away from that point. That is deliberate — a long triangle is much easier to read accurately.
Why rate is always positive. If you follow a reactant, its concentration is dropping, so the gradient comes out negative. Chemists just drop the sign. A gradient of −0.25 mol dm−3 s−1 is quoted as a rate of 0.25 mol dm−3 s−1. Follow a product instead and the gradient is already positive.
One reaction, several rates
Here is something the textbooks often skate past. In a reaction like this one, the substances are not used up and made at the same speed:
Watch the coefficients
2N2O5 → 4NO2 + O2
For every 2 molecules of N2O5 that break apart, 4 molecules of NO2 appear and only 1 molecule of O2. So NO2 appears twice as fast as N2O5 disappears, and O2 appears at half that rate.
This matters because a question can hand you the rate for one substance and ask for another. Use the ratio from the balanced equation.
If a question ever says “the rate of reaction” without naming a substance, and the coefficients are not all 1, say which substance your answer refers to. It shows the examiner you know the rates differ.
Worked examples
WORKED EXAMPLE
Reading a rate from a tangent
Using the graph above, a tangent drawn at 20 s passes through the points (0 s, 6 cm3) and (60 s, 54 cm3). Calculate the rate of gas production at 20 s.
Step 1: find the rise54 − 6 = 48 cm³Step 2: find the run60 − 0 = 60 sStep 3: dividerate = 48 ÷ 60 = 0.80rate = 0.80 cm³ s⁻¹units come straight from the axes — cm³ on top, s on the bottom
WORKED EXAMPLE
Average rate from concentrations
In a reaction, the concentration of a reactant falls from 0.480 mol dm−3 to 0.360 mol dm−3 in 40 s. Calculate the average rate of reaction over this period.
Step 1: change in concentration0.480 − 0.360 = 0.120 mol dm⁻³Step 2: divide by the time0.120 ÷ 40 = 3.0 × 10⁻³rate = 3.0 × 10⁻³ mol dm⁻³ s⁻¹this is the average over 40 s — at t = 0 it was faster than this
WORKED EXAMPLE
Linking rates using the equation
For 2N2O5 → 4NO2 + O2, N2O5 is used up at 8.0 × 10−4 mol dm−3 s−1. Find the rate of formation of NO2 and of O2.
Step 1: read the ratio off the equation
2 N₂O₅ : 4 NO₂ : 1 O₂
Step 2: NO₂ is made twice as fast8.0 × 10⁻⁴ × (4 ÷ 2) = 1.6 × 10⁻³Step 3: O₂ is made half as fast8.0 × 10⁻⁴ × (1 ÷ 2) = 4.0 × 10⁻⁴NO₂: 1.6 × 10⁻³ and O₂: 4.0 × 10⁻⁴ mol dm⁻³ s⁻¹divide by the coefficient of the substance you know, then multiply by the one you want
💡 Exam tip
Always give units. A bare number gets no mark. Take the units from the axes or from the quantities in the question.
Make your tangent triangle huge. Examiners allow a tolerance on the gradient, and a big triangle keeps you inside it.
If a graph question says “explain why the graph levels off”, the answer is that a reactant has run out, not that the reaction “got slower on its own”.
When you calculate a gradient from a falling curve, quote the rate as positive and say which substance you followed.
Check the axes before you start. A graph of mass, volume or concentration all give a valid rate, but the units are different each time.
Watch the powers of ten. Rates are often around 10−3 or 10−4, and dropping a factor of ten is the most common slip in this topic.
⚠ Common mix-up
Average rate is not the same as rate at a moment. If a question names a specific time, you need a tangent.
A steeper line means faster, not “more product”. Two reactions can end up with the same amount of product but very different rates.
Drawing the tangent through the origin. The tangent must touch the curve at the time asked for, wherever that is.
Reading the triangle off the curve instead of the tangent. Once the tangent is drawn, the curve is ignored.
Forgetting the coefficients. In 2A → B, A disappears twice as fast as B appears.
Saying the reaction stops when the graph flattens. For a reaction that goes to completion it does stop — but for a reversible reaction the line flattens at equilibrium while both directions carry on.
Up next: Measuring Reaction Rates — the actual lab kit. Gas syringes, balances, colorimeters, and how to pick the right one for a given reaction.
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