The rate of reaction formula

The rate of reaction formula is mean rate = quantity of reactant used ÷ time taken, or mean rate = quantity of product formed ÷ time taken. The quantity can be a mass in grams, a gas volume in cm³ or, at GCSE Higher and A-level, an amount in moles, giving rates in g/s, cm³/s or mol/s. For example, if a reaction gives off 48 cm³ of gas in 30 seconds, its mean rate is 48 ÷ 30 = 1.6 cm³/s. The rate at one particular moment is the gradient of a tangent to the graph of quantity against time.

The rate of reaction formula

AQA's GCSE Chemistry specification gives both forms, and says the quantity can be measured as a mass in grams or a volume in cm³. Higher tier students also use amounts in moles. You can follow whichever substance is easiest to measure: a gas given off, a solid used up, or a change in mass as gas escapes.

Rate of reaction units

If time is in minutes, the unit becomes g/min or cm³/min. Always give the unit: a rate of "1.6" means nothing on its own.

How to calculate rate of reaction

Example 1: from a gas volume

Magnesium ribbon reacts with hydrochloric acid and 48 cm³ of hydrogen is collected in 30 s. Find the mean rate.

Example 2: from a mass change

Some marble chips fizz in acid while a balance records the total mass. It drops by 2.4 g in 2 minutes as carbon dioxide escapes. Find the mean rate in g/s.

Convert the time: 2 minutes = 120 s.

Example 3: in moles (Higher)

A reaction produces 0.060 mol of product in 40 s. Find the mean rate.

Now try one in the course. Work out the mean rate, then press Mark to check it there.

Rate of reaction graphs

A graph of the quantity of product against time shows the whole reaction at once. The graph below shows the volume of gas from a reaction. Here x is the time in seconds and y is the total volume of gas in cm³.

• The steeper the curve, the faster the reaction.
• The reaction is fastest at the start, when there are the most reactant particles to collide.
• The curve flattens as the reactants are used up, and goes level when the reaction stops. The final height shows the total amount of product.

Mean rate over a time interval

The mean rate between two times is the change in quantity divided by the change in time. On this graph, the volume is 23.6 cm³ at 10 s and 46.6 cm³ at 30 s:

Rate at a particular time: drawing a tangent

To find the rate at one instant, draw a tangent: a straight line that just touches the curve at that time, with the same slope as the curve there. Its gradient is the rate at that moment. AQA asks all students to draw tangents and use their slope as a measure of rate, and Higher tier students to calculate the gradient.

Example 4: rate at 20 s from a tangent

The tangent to this curve at t = 20 s goes through (0, 15.9) and (40, 60.0). Find the rate at 20 s.

Choose two points far apart on your tangent line, not on the curve, to keep the reading error small. The rate at 20 s, 1.10 cm³/s, is lower than the starting rate, because some reactants have already been used up.

Rate from a reaction time: 1/t

In some experiments you do not measure a quantity; you time how long something takes, such as a cross under a flask disappearing as a precipitate forms. A faster reaction takes less time, so the rate goes up as the time comes down, in proportion to 1 ÷ time:

If the cross disappears after 50 s in one experiment and 80 s in another, the relative rates are 1 ÷ 50 = 0.020 s⁻¹ and 1 ÷ 80 = 0.0125 s⁻¹. The first is 1.6 times faster. AQA's required practical on rates asks students to investigate how changing concentration affects the rate, using one method that measures the volume of gas produced and one that involves a change in colour or turbidity.

What changes the rate

Collision theory explains it: a collision only leads to a reaction if it has at least the activation energy. The rate increases if you raise:

• concentration of a solution, or pressure of a gas, so collisions are more frequent;
• surface area of a solid, by breaking it into smaller pieces, so more particles are exposed;
• temperature, so collisions are more frequent and more of them have enough energy;
• or by adding a catalyst, which gives a route with a lower activation energy.

The Reaction Rate Simulator lets you heat, concentrate and catalyse particles and watch the collision rate change, and the Reaction Kinetics course builds up from measuring rate to rate equations. At A-level, the rate is linked to concentrations by a rate equation, rate = k[A]ᵐ[B]ⁿ, and the rate constant k depends on temperature through the Arrhenius equation.

Try it

Reaction Rate Simulator

Heat, concentrate and catalyse particles to see collision theory

Open the simulatorGo to its page

Common mistakes

• Time in minutes. If the question wants g/s or cm³/s, convert minutes to seconds first.
• Using the total volume at the end for a mean rate over part of the reaction. Use the change in volume over the interval you are asked about.
• Gradient from points on the curve instead of the tangent. Read the two points from your straight tangent line.
• A tangent that crosses the curve. It should touch the curve at one point only, with the curve on one side.
• Forgetting units, or writing cm³ instead of cm³/s.

Practise chemistry in a short timed paper

GCSE Chemistry Higher and A-level Chemistry: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so rates of reaction turn up regularly but not in every paper.

Read next

Chemistry · Rates and equilibriumRate of reaction graphs: how to read and compare themHow to read a rate of reaction graph: what the shape means, how temperature, concentration and catalysts change the curve, and how to sketch new curves.