Measuring Rates of Reaction

Before we can write rate equations or determine reaction orders, we need to be able to measure how fast a reaction proceeds. The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. In practice, we measure a physical quantity that is proportional to concentration and track how it changes.

Defining Rate

The rate of reaction can be expressed as:

Rate = change in concentration / change in time

For a reactant: Rate = −Δ[A] / Δt (negative because concentration decreases)

For a product: Rate = +Δ[B] / Δt (positive because concentration increases)

Units of rate are typically mol dm⁻³ s⁻¹, though mol dm⁻³ min⁻¹ is also used for slower reactions.

Stoichiometric Rates

For the reaction: 2A → B, the rate of disappearance of A is twice the rate of appearance of B.

If Δ[A]/Δt = −0.040 mol dm⁻³ s⁻¹, then Δ[B]/Δt = +0.020 mol dm⁻³ s⁻¹.

The general rate for aA → bB is:

Rate = −(1/a)(Δ[A]/Δt) = +(1/b)(Δ[B]/Δt)

Methods for Measuring Rate

Summary Table of Experimental Methods

Method	What is measured	Suitable when	Continuous or discrete?
Gas syringe	Volume of gas	Gas is produced	Continuous
Mass loss	Mass of flask	Gas escapes	Continuous
Colorimetry	Absorbance	Reactant/product is coloured	Continuous
Clock reaction	Time to fixed change	Visible endpoint exists	Discrete (initial rate)
Titration (quenching)	Concentration by titration	Accurate [X] needed at specific times	Discrete
Conductimetry	Electrical conductivity	Ions formed or consumed	Continuous
Pressure change	Total pressure	Gas-phase reaction, Δn ≠ 0	Continuous

1. Gas Collection

If a reaction produces a gas, you can collect it using a gas syringe or by collecting it over water using an inverted measuring cylinder. Measuring the volume of gas produced at regular time intervals gives a volume-time graph, which can be converted to a concentration-time graph if the total volume is known.

Example: The reaction of magnesium with hydrochloric acid:

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

The volume of H₂ collected over time allows you to track the rate.

Worked Example: Converting volume to moles

At 25 °C and 1 atm, the molar volume of a gas is approximately 24.0 dm³ mol⁻¹.

If 48 cm³ of H₂ is collected in the first 30 seconds:

Moles of H₂ = 48 / 24000 = 0.0020 mol

Average rate of H₂ production = 0.0020 / 30 = 6.7 × 10⁻⁵ mol s⁻¹

2. Mass Loss

If a gas escapes from the reaction vessel, the total mass decreases. Placing the reaction flask on a balance and recording mass at regular intervals gives a mass-time curve. The rate of mass loss is proportional to the rate of reaction.

Example: The reaction of calcium carbonate with acid:

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)

As CO₂ escapes, the mass falls. Note: the flask must be open (no bung) for gas to escape, which means this method is not suitable if the gas is toxic.

3. Colorimetry (Spectrophotometry)

If a reactant or product is coloured, you can use a colorimeter to measure absorbance or transmittance of light through the solution. Absorbance is proportional to concentration (Beer-Lambert law: A = εcl), so tracking absorbance over time gives a concentration-time profile.

Example: The reaction of bromine with an alkene -- bromine is orange/brown, and the solution decolourises as bromine reacts. Monitoring absorbance at an appropriate wavelength tracks the decrease in [Br₂].

4. Clock Reactions

In a clock reaction, you measure the time taken for a fixed, visible change to occur. The classic example is the iodine clock:

H₂O₂(aq) + 2I⁻(aq) + 2H⁺(aq) → I₂(aq) + 2H₂O(l)

Starch indicator is added. The solution remains colourless until enough I₂ is produced to turn the starch blue-black. You measure the time (t) to this colour change. Since the amount of I₂ produced at the endpoint is constant, rate ∝ 1/t.

Clock reactions are particularly useful for the initial rate method because they effectively measure the average rate over a fixed, short period at the start of the reaction.

Worked Example: Processing clock reaction data

Experiment	[H₂O₂] / mol dm⁻³	[I⁻] / mol dm⁻³	Time / s	1/t / s⁻¹
1	0.10	0.10	60	0.0167
2	0.20	0.10	30	0.0333
3	0.10	0.20	30	0.0333

From Experiments 1 and 2: [H₂O₂] doubles, 1/t doubles → first order in H₂O₂. From Experiments 1 and 3: [I⁻] doubles, 1/t doubles → first order in I⁻.

5. Titration (Quenching)

Samples are withdrawn from the reaction mixture at regular intervals and quenched (the reaction is stopped -- for example, by adding the sample to ice-cold water or to excess sodium hydrogencarbonate to neutralise acid). The quenched sample is then titrated to determine the concentration of a reactant or product at that moment.

This method is accurate but labour-intensive and gives discrete data points rather than a continuous curve.

Continuous Monitoring vs Initial Rate Method

Continuous Monitoring

In continuous monitoring, you track the reaction from start to finish, recording data at regular intervals. This produces a complete concentration-time graph.

The rate at any point is the gradient of the tangent to the curve at that point.
The initial rate is the gradient of the tangent at t = 0.

For a first-order reaction, the concentration-time graph is an exponential decay curve. For a zero-order reaction, it is a straight line.

The Initial Rate Method

The initial rate method involves running the experiment multiple times with different starting concentrations and measuring the initial rate each time. By comparing how the initial rate changes when concentrations change, you can determine the order with respect to each reactant.

For clock reactions, the initial rate is proportional to 1/t, where t is the time to the fixed endpoint.

flowchart TD
    A["Choose experimental method"] --> B{"Is the reaction<br/>fast or slow?"}
    B -->|"Fast (seconds)"| C["Clock reaction<br/>or rapid colorimetry"]
    B -->|"Moderate (minutes)"| D["Gas syringe, mass loss,<br/>or colorimetry"]
    B -->|"Slow (hours)"| E["Titration with<br/>quenching"]
    C --> F["Measure initial rates<br/>at different concentrations"]
    D --> G{"Continuous monitoring<br/>or initial rate?"}
    E --> F
    G -->|Continuous| H["Plot [X] vs time<br/>Draw tangents for rates"]
    G -->|Initial rate| F
    F --> I["Compare rate changes<br/>to find orders"]
    H --> J["Test straight-line plots<br/>to confirm order"]

Interpreting Concentration-Time Graphs

Reading Rate from a Curve

To find the rate at a particular time on a concentration-time graph:

Draw a tangent to the curve at the desired time.
Calculate the gradient of the tangent: gradient = Δ[concentration] / Δt.
The magnitude of the gradient is the rate at that moment.

At t = 0, the tangent gives the initial rate. As the reaction progresses, the tangent becomes less steep (the rate decreases) because reactant concentration falls.

Worked Example: Initial Rate from a Tangent

A student measures the concentration of H₂O₂ during its decomposition and plots a concentration-time graph. At t = 0, the tangent to the curve passes through the points (0 s, 0.50 mol dm⁻³) and (200 s, 0.10 mol dm⁻³).

Initial rate = (0.50 − 0.10) / (0 − 200) = 0.40 / (−200) = −0.0020 mol dm⁻³ s⁻¹

The rate is 0.0020 mol dm⁻³ s⁻¹ (the negative sign indicates the concentration is decreasing, which is expected for a reactant).

Worked Example: Rate at a Later Time

The same student draws a tangent at t = 100 s, passing through (60 s, 0.28 mol dm⁻³) and (140 s, 0.12 mol dm⁻³).

Rate at t = 100 s = |(−0.28 − (−0.12))| / (140 − 60) = (0.28 − 0.12) / 80 = 0.16 / 80 = 0.0020 mol dm⁻³ s⁻¹

Wait -- the rate appears the same. Let us re-read the tangent: (60, 0.28) and (140, 0.12):

Rate = (0.12 − 0.28)/(140 − 60) = −0.16/80 = −0.0020 mol dm⁻³ s⁻¹

Actually, if this is the same rate as the initial rate, it may indicate zero-order kinetics. In practice, the tangent gradient typically decreases for first-order reactions.

Rate-Time Graphs

A rate-time graph shows how the rate changes over the course of a reaction. For most reactions, the rate starts high and decreases as reactants are consumed. The shape depends on the order:

Zero order: rate is constant (horizontal line) until the reactant is used up, then drops to zero.
First order: rate decreases exponentially (the curve mirrors the concentration-time curve because rate = k[A]).
Second order: rate decreases more steeply than first order.

Identifying Order from Graph Shapes

Graph type	Zero order	First order	Second order
[A] vs t	Straight line (negative gradient)	Exponential decay	Steeper curve than 1st order
Rate vs [A]	Horizontal line	Straight line through origin	Upward curve (parabola)
ln[A] vs t	Curve	Straight line (gradient = −k)	Curve
1/[A] vs t	Curve	Curve	Straight line (gradient = k)

Common Mistakes to Avoid

Confusing rate with extent. A reaction that produces 100 cm³ of gas is not necessarily faster than one that produces 50 cm³. Rate is about how quickly the change happens, not how much change occurs.
Reading the gradient incorrectly. The gradient of a tangent requires two well-separated points on the tangent line itself, not on the curve.
Forgetting the sign convention. Rate is always quoted as a positive number. The gradient of [reactant] vs t is negative; take the magnitude.
Assuming 1/t IS the rate. In clock reactions, 1/t is PROPORTIONAL to the initial rate, not equal to it. You can use it to compare relative rates but not to quote an absolute rate without a calibration constant.
Using the wrong time intervals. In the mass loss method, the rate over an interval is the mass change divided by the time interval -- not the cumulative mass divided by the total time.

Summary

Measuring rates accurately is the experimental foundation for determining rate equations. Gas collection, mass loss, colorimetry, clock reactions, and titration each have their place depending on the reaction. The initial rate method and continuous monitoring are the two main experimental approaches. Concentration-time graphs are interpreted using tangents, and rate-time graphs show how the rate changes as the reaction proceeds.

A-Level Deep Dive: Measuring Rates of Reaction

Spec mapping

Edexcel 9CH0 specification, Topic 9 — Kinetics I requires candidates to be able to determine the rate of a reaction from a concentration–time graph by drawing a tangent at a chosen time, and to describe experimental methods for following the rate, including gas collection, mass loss, colorimetry, conductivity and titrimetric quenching (refer to the official specification document for exact wording). The skill of initial-rate determination is the bridge to Topic 16 (Kinetics II), where multiple initial rates at different starting concentrations are used to deduce orders. The graphical work also draws on mathematical skill 0c (using ratios, fractions and percentages) and 3a (interpreting graphs) as listed in Appendix 6 of the specification. Examined principally on Paper 2 (Section A — Topics 11–19) and Paper 3 (synoptic, including Core Practicals). Half-life arguments rely on this graphical foundation.

Worked example with full mark scheme

Question (8 marks):

A student investigates the reaction $\text{H}_2\text{O}_2(\text{aq}) + 2\,\text{HI}(\text{aq}) \rightarrow 2\,\text{H}_2\text{O}(\text{l}) + \text{I}_2(\text{aq})$ by withdrawing 10.0 cm³ samples at intervals, quenching them, and titrating against thiosulfate. The data give the following concentrations of H₂O₂ at the times shown.

t / s	0	60	120	240	480	720
[H₂O₂] / mol dm⁻³	0.500	0.354	0.250	0.125	0.063	0.031

(a) State why the samples must be quenched before titration. (2)

(b) Draw a tangent to the curve at $t = 0$ and use it to estimate the initial rate of disappearance of H₂O₂. (Assume tangent through (0, 0.500) and (200, 0.150) on the candidate's graph.) (3)

Solution with mark scheme:

(a) M1 — quenching arrests the reaction so that the concentration measured corresponds to the time of sampling. A1 — without quenching, reaction continues during titration, giving a systematically lower [H₂O₂]. Quenching is typically achieved by adding excess cold water to dilute, or by adding a sharp pH change to deactivate any catalyst.

(b) M1 — drawing the tangent to the smooth curve at $t = 0$ (not chord through (0, 0.500) and (60, 0.354), which under-estimates the initial gradient by ~30%). M1 — calculating gradient: $\Delta y / \Delta x = (0.500 - 0.150) / (0 - 200) = -0.00175$ mol dm⁻³ s⁻¹. A1 — initial rate of disappearance of H₂O₂ is $|-0.00175|$ = 1.75 × 10⁻³ mol dm⁻³ s⁻¹ (units explicit). Common error: chord-not-tangent is the single most common mark loss; examiners reward "tangent at $t = 0$ " explicitly.

(c) M1 — examining successive half-lives: from 0.500 to 0.250 takes ~120 s; from 0.250 to 0.125 takes ~120 s (240 → 360 visually); from 0.125 to ~0.063 takes ~120 s. M1 — half-life is constant (≈ 120 s). A1 — constant half-life is the diagnostic of first order; therefore the reaction is first order with respect to H₂O₂.

Total: 8 marks (M5 A3, split as shown).

Specimen question modelled on the Edexcel 9CH0 Paper 2 format

Question (6 marks): The reaction $\text{Mg}(\text{s}) + 2\,\text{HCl}(\text{aq}) \rightarrow \text{MgCl}_2(\text{aq}) + \text{H}_2(\text{g})$ can be followed in three ways: (i) by collecting H₂ gas in a syringe, (ii) by mass loss on a balance with a cotton-wool plug, (iii) by titrating samples of the acid against alkali at intervals.

(a) For each method, state one practical advantage and one practical limitation. (3)