Measuring and Calculating Rates

Knowing what changes the rate of a reaction is one thing; measuring the rate in the laboratory is another. Topic C5 of your OCR Gateway Combined Science course includes a required practical that follows a reaction over time, and you must be able to calculate a rate and read a rate–time graph. There are three standard ways to measure a rate, chosen to match what the reaction produces. This lesson sets out those methods, shows how to calculate a mean rate with the right units, explains the shape of the graph you get, and — for Higher tier — shows how to find the rate at an instant from a tangent.

By the end of this lesson you should be able to describe methods for measuring a rate, calculate a mean rate using $\text{mean rate} = \dfrac{\text{quantity changed}}{\text{time}}$mean rate=timequantity changed​, interpret a quantity-versus-time graph, and (Higher tier) find the rate at a point from the gradient of a tangent.

This lesson spans AO2 (the mean-rate calculation and the practical methods for measuring rate) and AO3 (interpreting the shape of a rate–time graph and finding a rate from the gradient).

Measuring a rate always comes down to the same idea: pick one thing that changes as the reaction proceeds, and measure how much it changes in a given time. The skill is choosing the right quantity to follow for a particular reaction, and then reading the resulting graph correctly.

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Three Methods for Measuring Rate

To measure a rate you follow one measurable quantity as it changes over time. The three standard methods are:

Method	What you measure	Best used when…
Gas volume (gas syringe)	Volume of gas given off at set times	A gas is produced (e.g. magnesium + acid)
Mass loss (balance)	The fall in mass as gas escapes	A gas escapes from an open flask
Turbidity ("disappearing cross")	Time for a mark to disappear	The mixture turns cloudy (a precipitate forms)

Measuring the volume of gas

If a reaction gives off a gas, you can collect it in a gas syringe and record the volume at regular time intervals. For example, magnesium reacting with hydrochloric acid produces hydrogen, which pushes the syringe plunger out. Reading the volume every few seconds lets you plot a graph of gas volume against time and see how the rate changes.

Measuring the loss in mass

If the gas produced is allowed to escape from an open conical flask, you can stand the flask on a balance and record the decreasing mass over time. A loose plug of cotton wool in the neck stops any spray escaping while still letting the gas out. The mass falls as gas leaves. This works well when the gas is dense, such as carbon dioxide from a carbonate reacting with acid.

The turbidity / "disappearing cross" method

When sodium thiosulfate reacts with hydrochloric acid, a fine precipitate of sulfur forms and gradually makes the solution cloudy:

$\text{Na}_2\text{S}_2\text{O}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{S} + \text{SO}_2 + \text{H}_2\text{O}$Na2​S2​O3​+2HCl→2NaCl+S+SO2​+H2​O

A cross is drawn on paper and placed under the flask, and you time how long it takes for the cross to disappear from view as the sulfur clouds the mixture. A shorter time means a faster rate. This method effectively measures the rate as $\dfrac{1}{\text{time}}$time1​ for the cross to vanish.

Exam Tip: Match the method to the reaction: a gas given off → a gas syringe (volume) or a balance (mass loss); a precipitate that clouds the mixture → the disappearing-cross method. For the cross method, remember that a shorter time means a faster rate — a common misconception is to read a longer time as faster.

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Calculating the Mean Rate

The mean (average) rate of a reaction over a period of time is found from:

$\text{mean rate} = \dfrac{\text{quantity of reactant used or product formed}}{\text{time}}$mean rate=timequantity of reactant used or product formed​

The units depend on what you measured: a gas volume gives cm³/s, a mass change gives g/s, and an amount in moles gives mol/s.

Worked Example 1 — Mean rate from a gas volume

A reaction produces $48 \text{ cm}^3$48 cm3 of hydrogen in $60 \text{ s}$60 s. Calculate the mean rate of reaction.

Step 1 — write the equation: $\text{mean rate} = \dfrac{\text{volume of gas}}{\text{time}}$mean rate=timevolume of gas​.

Step 2 — substitute the values: $\text{mean rate} = \dfrac{48}{60}$mean rate=6048​.

Step 3 — calculate: $\text{mean rate} = 0.8 \text{ cm}^3/\text{s}$mean rate=0.8 cm3/s.

Answer: $0.8 \text{ cm}^3/\text{s}$0.8 cm3/s.

Worked Example 2 — Mean rate from a mass loss

In a reaction giving off carbon dioxide, the flask loses $1.2 \text{ g}$1.2 g of mass in $30 \text{ s}$30 s. Calculate the mean rate.

Step 1 — write the equation: $\text{mean rate} = \dfrac{\text{mass lost}}{\text{time}}$mean rate=timemass lost​.

Step 2 — substitute: $\text{mean rate} = \dfrac{1.2}{30}$mean rate=301.2​.

Step 3 — calculate: $\text{mean rate} = 0.04 \text{ g/s}$mean rate=0.04 g/s.

Answer: $0.04 \text{ g/s}$0.04 g/s.

Worked Example 3 — Mean rate over part of a reaction

A reaction gives off $60 \text{ cm}^3$60 cm3 of gas in the first $20 \text{ s}$20 s, and a total of $90 \text{ cm}^3$90 cm3 after $60 \text{ s}$60 s. Calculate the mean rate over the first $20 \text{ s}$20 s and over the whole $60 \text{ s}$60 s.

Over the first $20 \text{ s}$20 s: $\text{mean rate} = \dfrac{60}{20} = 3 \text{ cm}^3/\text{s}$mean rate=2060​=3 cm3/s.

Over the whole $60 \text{ s}$60 s: $\text{mean rate} = \dfrac{90}{60} = 1.5 \text{ cm}^3/\text{s}$mean rate=6090​=1.5 cm3/s.

Answer: the mean rate over the first $20 \text{ s}$20 s is $3 \text{ cm}^3/\text{s}$3 cm3/s; over the whole reaction it is $1.5 \text{ cm}^3/\text{s}$1.5 cm3/s. The rate over the first part is higher because the reaction is fastest at the start, which drags the overall average down.

Exam Tip: Always give the rate's unit — cm³/s for a gas volume, g/s for a mass change, mol/s for moles. Divide the quantity changed by the time; a bare number with no unit will not score the final mark.

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Interpreting a Rate–Time Graph

A graph of quantity (gas volume or mass) against time has a characteristic shape that you must be able to describe and explain:

• it is steepest at the start, because the concentration of the reactants is highest then, so collisions are most frequent and the reaction is fastest;
• it gradually becomes less steep as the reactants are used up and the rate falls;
• it levels off (becomes horizontal) when the reaction stops — usually because a reactant has run out.

The gradient (steepness) of the line at any point tells you the rate at that moment: a steeper line means a faster rate.

Notice that the two curves level off at the same final volume: changing the temperature changes how fast the gas is produced, but not the total amount of gas, which depends only on how much reactant there was. The hotter reaction is steeper at the start (faster) and finishes sooner.