Measuring rates of reaction

Defining and measuring reaction rate, average and instantaneous rates from gas-volume and mass-loss graphs, drawing tangents, and the practical investigation of how temperature, concentration, surface area and catalysts change the rate.

Concrete sets over days, a firework explodes in milliseconds, and the iron in a shipwreck takes centuries to rust away. Chemists need to put numbers on "fast" and "slow", because a reaction that is too slow is useless in a factory and one that is too fast can be dangerous. The tool for that is a graph of how much product forms over time.

What a rate is

The rate of reaction is the change in the amount (or concentration) of a reactant or product per unit time:

$$\text{rate} = \frac{\Delta(\text{quantity})}{\Delta t}$$

The units follow from what you measure: mL s⁻¹ for a gas volume, g s⁻¹ for a mass, mol L⁻¹ s⁻¹ for a concentration. In Year 10 (Science lesson 4D) you saw that reactions go faster when they are hotter or more concentrated. At Stage 6 the job is to measure those effects properly and explain them.

Ways to follow a reaction

Pick a property that changes as the reaction goes and that you can measure without stopping it.

Method	Example reaction	What you record
Gas volume (gas syringe or inverted measuring cylinder)	Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)	volume of H₂ every 10–30 s
Mass loss (open flask on a balance, cotton wool plug)	CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)	mass every 30 s; the loss is CO₂
Time for a precipitate to hide a mark	Na₂S₂O₃(aq) + 2HCl(aq) → 2NaCl(aq) + S(s) + SO₂(g) + H₂O(l)	time for a cross under the flask to disappear; rate ∝ 1/time
Colour (colorimeter)	MnO₄⁻ reduced by oxalate; purple fades	absorbance over time

Gas volume against time for magnesium and hydrochloric acid. A faster reaction rises more steeply but finishes at the same volume if the amount of limiting reagent is the same.

Average and instantaneous rate

A product–time curve is steepest at the start and flattens as the reactants are used up. The rate therefore falls during the reaction.

The average rate over an interval is the change in quantity divided by the time taken: the gradient of the straight line (chord) joining two points on the curve.
The instantaneous rate at one moment is the gradient of the tangent to the curve at that point.
The initial rate is the gradient of the tangent at t = 0. It is the fairest way to compare experiments, because the starting conditions are exactly the ones you set.

Finding the instantaneous rate at 40 s: draw the tangent, then pick a large rise and run on it.

Average and instantaneous rate from a gas curve

0.050 g of magnesium ribbon reacts with excess 1.0 mol L⁻¹ HCl. The volume of hydrogen is 32.2 mL at 40 s and 51.0 mL at the end. A tangent drawn at 40 s passes through (10 s, 18.2 mL) and (90 s, 55.7 mL). Find (a) the average rate over the first 40 s, (b) the instantaneous rate at 40 s and (c) the instantaneous rate in mol s⁻¹ (molar volume 24.79 L mol⁻¹ at 25 °C and 100 kPa).

(a) average rate = 32.2 mL ÷ 40 s = 0.81 mL s⁻¹

(b) gradient of tangent = (55.7 − 18.2) ÷ (90 − 10) = 37.5 ÷ 80 = 0.47 mL s⁻¹

Check the final volume: n(Mg) = 0.050 ÷ 24.31 = 2.06 × 10⁻³ mol, which gives 2.06 × 10⁻³ mol of H₂ = 2.06 × 10⁻³ × 24.79 = 0.0510 L = 51.0 mL.

Draw a tangent so that it touches the curve at one point and the curve sits evenly on one side of it. Make the line long and choose two points far apart on it, not on the curve; a short triangle makes small reading errors large.

InteractiveRate tangents: magnesium and acid

Try this

With the defaults (1.0 mol L⁻¹, 25 °C, ribbon), move the tangent to 60 s. The readouts show 39.6 mL, an instantaneous rate of 0.28 mL s⁻¹ and an average rate of 0.66 mL s⁻¹. Why is the average larger than the instantaneous rate?
Set the time to 0 s to read the initial rate (1.28 mL s⁻¹). Now choose 2.0 mol L⁻¹. What happens to the initial rate?
Return to 1.0 mol L⁻¹ and raise the temperature to 35 °C. Compare the initial rate with the 2.0 mol L⁻¹ run.
Choose Powder. Why does every curve still end at 51.0 mL?

Factors that change the rate

Change	Effect on rate	Effect on the amount of product
Higher temperature	increases, often roughly doubling for a 10 °C rise near room temperature	none (if the limiting reagent is unchanged)
Higher concentration (or gas pressure)	increases	none, unless the reagent you changed is the limiting one
Larger surface area (smaller pieces, powder)	increases, for reactions involving a solid	none
Catalyst	increases	none; the catalyst is not used up

Lesson 3G explains each of these with collision theory.

Depth investigation: factors affecting the rate of reaction

Aim: to measure how one factor (temperature, concentration, surface area or a catalyst) changes the initial rate of a reaction.

Example design (concentration): react 0.050 g pieces of magnesium ribbon with 50 mL of HCl at 0.25, 0.50, 1.0, 1.5 and 2.0 mol L⁻¹, collecting hydrogen in a gas syringe and recording the volume every 10 s for 2 minutes.

Variables: independent: acid concentration. Dependent: initial rate (mL s⁻¹) from the tangent at t = 0, or the time to collect 20 mL. Controlled: mass and length of ribbon (cut from the same roll and cleaned), acid volume, temperature (water bath), swirling.

Other designs: temperature: sodium thiosulfate and HCl in water baths at 20, 30, 40, 50 °C, timing the disappearing cross. Surface area: equal masses of large marble chips, small chips and powder with excess HCl, recording mass loss. Catalyst: hydrogen peroxide with and without 0.1 g MnO₂ (filter and dry the MnO₂ afterwards to show its mass is unchanged).

Typical results: doubling the HCl concentration roughly doubles the initial rate of hydrogen production; in the thiosulfate design the time halves for about each 10 °C rise; powdered marble loses mass several times faster than large chips, but the final mass loss is the same.

Processing: plot volume (or mass loss) against time for every run on one set of axes; draw tangents at t = 0; graph initial rate against the independent variable and describe the trend. For the thiosulfate design, plot 1/time against temperature.

Validity, reliability, accuracy: change one variable at a time; keep the other reagent in excess so the final volume is constant; repeat each run three times and average, discarding outliers with a reason; start timing at the moment of mixing (a reaction that starts before the bung is in loses gas). A gas syringe is more accurate than bubbles collected over water, which partly dissolve.

Safety: safety glasses; HCl is corrosive; the thiosulfate reaction releases SO₂, so work in a ventilated room and pour the mixture into a sodium carbonate solution afterwards; hydrogen is flammable.

Test yourself

In a mass-loss experiment a flask of marble chips and acid loses 0.88 g in the first 120 s. What is the average rate of CO₂ production in mol s⁻¹?
Why does the gradient of a gas volume–time curve decrease as the reaction proceeds?
The same mass of zinc is reacted with excess acid as (I) granules and (II) powder. Which statement is correct?
A tangent to a volume–time curve at 30 s passes through (0 s, 12 mL) and (60 s, 48 mL). What is the instantaneous rate at 30 s?

Label the tangent construction.

Put the steps for finding an instantaneous rate in order.

The instantaneous rate is the gradient of a to the curve. The rate at t = 0 is called the rate. Increasing the surface area of a solid reactant the rate but does not change the final amount of . Running each trial three times improves .

6 marks

Design an investigation to determine how temperature affects the rate of reaction between sodium thiosulfate solution and hydrochloric acid. Include the variables, a method, how you would process the results and one safety precaution.

Your answer