GCSE · Chemistry · AQA · Spec 8462

Calculating rates of reactions

A reaction fizzes wildly, then calms down, then stops. 'Fast' and 'slow' are fine words, but a chemist wants a number — and a graph hands you one.

Drag along the curve. Watch the red line tip over.

015304560015304560Time (s)Volume of gas made (cm³)1.80 cm³/sRate at your point (tangent gradient)
Time 10 s

Time: 10 s. Rate at your point (tangent gradient): 1.80 cm³/s

The red line is the tangent. It touches the curve at your point and runs at exactly the same steepness. Its gradient — how many cm³ the volume would rise per second — is the rate of reaction at that moment.

An example reaction that gives off a gas. Drag the point from 0 s towards 40 s: the tangent tips over and the rate falls. The fixed dot marks 40 s, where the curve goes flat — the rate is zero and the reaction has stopped.

Watch out: The height of the curve is not the rate. At 20 s the curve is at 36 cm³ — that's how much gas has been made so far — but the tangent there rises at only 1.2 cm³/s.

Two ways to follow the same reaction

Follow a reactantvsFollow a product

Watch something get used up, or watch something get made. Either one tells you how fast the reaction is going.

Focus

Which way the graph goes

Follow a reactant

Plot the reactant left: the line slopes down, then levels off.

Follow a product

Plot the product made: the line slopes up, then levels off.

The insight

A line going down does not mean a negative rate. The rate is how fast the reactant is being used up — still a positive number, read from how steeply the line falls.

What you measure

Follow a reactant

The mass of reactant in g, or its volume in cm³

Follow a product

The mass of product in g, or its volume in cm³

The quantity that counts

Follow a reactant

Reactant USED = amount at the start − amount left

Follow a product

Product FORMED = amount made since the start

When the reaction stops

Follow a reactant

No more reactant is used up, so the line goes flat

Follow a product

No more product is made, so the line goes flat

Putting a number on it

mean rate of reaction = quantity used or formed ÷ time taken

Measure how much reactant was used up, or how much product was made, then divide by how long it took. What you get is an average for that stretch of time — a mean rate.

The unit comes straight from what you measured, then 'per second': grams give g/s, cm³ give cm³/s. Say g/s out loud as 'grams per second'. Higher: when the quantity is in moles, the rate is in mol/s.

Your turn

Finish the calculation

A reaction starts with 2.50 g of a solid reactant. After 40 s, 0.60 g of it has been used up. Calculate the mean rate of reaction over those 40 s.

  1. mean rate = quantity of reactant used ÷ time takenWe're following a reactant, so start from the reactant version.
  2. missing step
Which line is step 2?

Predict, then check

Back to the gas curve at the top: 21 cm³ after 10 s, and 48 cm³ by 40 s, when it stops.

Which mean rate is bigger — over the first 10 s, or over the whole reaction from 0 to 40 s?

Higher

The rate at one moment

Problem

Using the gas curve at the top of the page, calculate the rate of reaction at 30 s.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

How fast is a reaction going? The answer is in how steep its graph is.

What you need to know

  • You can follow a reaction's rate by measuring how much reactant is used up, or how much product is formed, as time goes on.
  • Mean rate of reaction = quantity of reactant used ÷ time taken, or quantity of product formed ÷ time taken.
  • Quantities are measured as a mass in g or a volume in cm³, so the rate is in g/s or cm³/s.
  • Higher: with quantities in moles, the rate is in mol/s.
  • On a graph of quantity against time, the slope of a tangent measures the rate at that time.
  • Higher: calculate the gradient of a tangent as change in quantity ÷ change in time.

The big picture

The rate of a reaction is how fast a reactant is used up or a product is made. A mean rate is the quantity used or formed divided by the time taken, in g/s or cm³/s (mol/s for moles, at Higher). On a quantity–time graph, the rate at any moment is the gradient of the tangent there: steep means fast, flat means stopped.

Key points

1Rate is how fast a quantity changes — not how much of it there is.
2A mean rate is an average over a stretch of time; a tangent's gradient is the rate at one moment.
3Steep curve: fast. Gentler: slower. Flat: stopped.
4A graph of reactant left falls and a graph of product formed rises, but both give a positive rate.
5The unit follows what you measured: g/s, cm³/s, or mol/s at Higher.

Worked example

Problem

Gas is collected from a reaction. After 10 s there are 16 cm³ of gas; after 30 s there are 46 cm³. Calculate the mean rate of reaction between 10 s and 30 s.

⚠ Watch out

Dividing the quantity at one point by its time and calling it the rate at that moment. That gives the mean rate from the start. The rate at a moment is the gradient of the tangent at that time.

🧠

Memory hook

Height = how much. Steepness = how fast.

✓

Check yourself

A reactant's mass drops from 8.0 g to 5.0 g in 60 s. Find the mean rate, with units. Why isn't it the rate at 60 s? (0.05 g/s — an average, not a tangent.)

Flashcards

(11)
What is the rate of a reaction?
How fast a reactant is used up or a product is formed.
Write the word equation for mean rate of reaction.
Mean rate = quantity of reactant used ÷ time taken (or quantity of product formed ÷ time taken).
You measured a mass in grams, or a volume in cm³. What unit is the rate in?
Mass in g gives g/s. Volume in cm³ gives cm³/s.
Higher: what unit is the rate in when the quantity is in moles?
mol/s — moles per second.
On a quantity–time graph, how do you show the rate at one moment?
Draw a tangent to the curve at that time. The slope of the tangent is the rate.
What does a steep part of a quantity–time curve tell you?
The reaction is fast there. A gentler slope means it is going more slowly.
What does it mean when a quantity–time curve goes flat?
The rate is zero — the reaction has stopped.
Mean rate vs rate at a moment: what's the difference?
A mean rate is an average over a stretch of time. The rate at a moment is the gradient of the tangent at that time.
Higher: how do you calculate the gradient of a tangent?
Read two points far apart on the tangent, then divide the change in quantity by the change in time.
A graph of reactant left slopes downwards. Is the rate negative?
No. The rate is how fast the reactant is being used up, which is a positive number.
Why use the quantity of reactant USED, not the amount left?
The rate is about how much has changed. What's still left is not what reacted.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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