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Chemistry (IAL)

Kinetics

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Edexcel IAL Chemistry · Unit 4

Kinetics

The big idea: a reaction's rate depends on the concentration of certain reactants — and the way it depends on them (the "order") reveals exactly which molecules are colliding in the slow, bottleneck step of the mechanism.

Summary — What This Chapter Covers

  • Rate of reaction = how fast reactants disappear or products appear, measured in mol dm⁻³ s⁻¹.
  • Rate equations & orders — rate = k[A]ᵐ[B]ⁿ, and orders can only be found by experiment, never from the balanced equation.
  • Graphs — concentration-time and rate-concentration graphs have distinct shapes for zero, first, and second order.
  • Obtaining rate data — titration, colorimetry, mass loss, gas volume: matching the method to the reaction.
  • Initial rate method & clock reactions — measuring the very start of a reaction, using tangents or 1/t.
  • Continuous monitoring — tracking concentration throughout the whole reaction (e.g. iodination of propanone by colorimetry).
  • Rate-determining step — the slowest step controls the rate; only species in this step appear in the rate equation.
  • Reaction mechanisms — deducing plausible step-by-step mechanisms, including SN1 and SN2 nucleophilic substitution.
  • Activation energy & the Arrhenius equation — linking rate constant, temperature, and activation energy; using ln k vs 1/T plots.

1. Kinetic Rates — The Basics

The rate of reaction is simply how quickly a reactant is used up, or a product is formed, per unit time. Its units are always mol dm⁻³ s⁻¹ — concentration divided by time.

Think of it like: filling (or draining) a bathtub. The "rate" is how many litres change per second. It doesn't matter whether you're watching the tap (product forming) or the plug (reactant disappearing) — both tell you the same story about how fast the process is happening.
Core Definition
Rate = Δ(amount of reactant or product) / time
Change in concentration (mol dm⁻³) divided by the time taken (s).

You can measure rate by watching almost any property that changes during a reaction:

  • Mass lost over time (e.g. gas escaping from an open flask)
  • Volume of gas produced over time
  • Colour changes (using a colorimeter)
  • pH changes over time
  • Changes in electrical conductivity

Here's the key insight this chapter builds on: if you plot rate against concentration of a reactant and get a straight line through the origin, that tells you rate is directly proportional to concentration — i.e. Rate ∝ [reactant], or Rate = k[reactant]. Doubling the concentration doubles the rate; halving it halves the rate. This one relationship is the seed of everything else in the chapter.

Practice Question

A reaction has the rate expression Rate = k[X]. If [X] is tripled, what happens to the rate? What if [X] is reduced to a quarter of its original value?

2. Rate Equations & Orders

For a general reaction A(aq) + B(aq) → C(aq) + D(g), the rate equation is written:

General Rate Equation
Rate = k [A]ᵐ [B]ⁿ
k = rate constant · m = order with respect to A · n = order with respect to B
⚠ Critical Rule Rate equations can only be found by doing experiments and analysing data. You can never read them off the balanced stoichiometric equation. This trips up almost every student at some point — the coefficients in the equation (like the "2" in 2NO₂) tell you nothing about the order unless you're told the rate-determining step matches it exactly.

What "Order" Actually Means

The order with respect to a reactant is the power that reactant's concentration is raised to in the rate equation. It tells you how sensitive the rate is to changes in that reactant's concentration.

OrderWhat happens to rateIn rate equation?
Zero (0)Changing concentration has no effect on rateNot included at all
First (1)Rate is directly proportional — double concentration, double rateIncluded as [X]¹ = [X]
Second (2)Rate proportional to the square — double concentration, rate ×4Included as [X]²

The overall order of a reaction is just the sum of all the individual orders (m + n + ...).

Think of it like: a dimmer switch vs. an on/off switch. Zero order is like a light on a separate circuit — turning your dimmer (concentration) does nothing to it. First order is a normal dimmer — twist it twice as far, it's twice as bright. Second order is a dimmer wired to itself twice over — twist it twice as far, and it's four times as bright because the effect compounds.

Determining Orders from Experimental Data

The standard technique: find two experiments where only one reactant's concentration changes while all others stay constant. Compare how the rate changes.

Experiment[(CH₃)₃CBr] / mol dm⁻³[OH⁻] / mol dm⁻³Initial rate / mol dm⁻³ s⁻¹
11.0×10⁻³2.0×10⁻³3.0×10⁻³
22.0×10⁻³2.0×10⁻³6.0×10⁻³
31.0×10⁻³4.0×10⁻³1.2×10⁻²

Comparing 1 and 2: [(CH₃)₃CBr] doubles, [OH⁻] constant → rate doubles → order 1 with respect to (CH₃)₃CBr.

Comparing 1 and 3: [OH⁻] doubles, [(CH₃)₃CBr] constant → rate increases ×4 (2²) → order 2 with respect to OH⁻.

Resulting Rate Equation
Rate = k [(CH₃)₃CBr] [OH⁻]²

Calculating the Rate Constant, k

Once you have the rate equation, rearrange it to find k using any one experiment's data — then check your answer against another experiment; they should agree.

Example
k = Rate ÷ ([Na₂CO₃][Cl⁻])
= 4.38×10⁻⁶ ÷ (0.0250 × 0.0125) = 1.40×10⁻² mol⁻¹ dm³ s⁻¹
💡 Finding Units of k Substitute the actual units into the rearranged equation and cancel. For a 2nd-order overall reaction: units of k = (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³ × mol dm⁻³) = mol⁻¹ dm³ s⁻¹. Always double-check by cancelling step by step — don't just memorise "the answer" for a given overall order, because the individual orders can combine differently.
Practice Question

The rate equation for a reaction is Rate = k[A][B]². Deduce the overall order of reaction, and state what happens to the rate if [A] is doubled while [B] is halved.

3. Reaction Orders — Reading the Graphs

You need to recognise order from two different types of graph: concentration vs. time, and rate vs. concentration. Exams love mixing these up, so let's be really precise about each shape.

Concentration–Time Graphs

ZERO ORDER FIRST ORDER SECOND ORDER [X] [X] [X] |\ |\ |\ | \ | \ | \ | \ | \___ | \____ | \ | \___ | \______ | \ | \____ | \_______ |_____\____ t |______________ t |________________________ t Straight line down Curve, decreasing Steeper curve, decreasing (constant gradient gradient (slower even faster — the = constant rate) decay over time) "cliff" then "plateau"
📌 Key point For a zero-order reactant, the gradient of the concentration-time graph is the rate — and it's constant throughout, which is why the graph is a perfectly straight line. Rate = k here.

Order From Half-Life

The half-life (t½) is the time taken for a reactant's concentration to fall to half its value. This gives you a fast way to spot the order without doing a full rate calculation:

  • Zero order — successive half-lives decrease with time (it gets quicker to halve as concentration drops)
  • First order — half-life stays constant throughout the entire reaction (this is the classic radioactive-decay-style pattern)
  • Second order — successive half-lives increase with time (it gets slower and slower to halve)
💡 Exam Tip A constant half-life is one of the fastest ways to prove a reaction is first order without doing any calculations — examiners love giving you a table of time vs. concentration and asking you to spot this pattern by eye.

Rate–Concentration Graphs

This is a completely different graph — now the y-axis is rate itself, not concentration. Don't confuse the shapes with the ones above!

ZERO ORDER FIRST ORDER SECOND ORDER Rate Rate Rate |______________ | / | / | | / | | | | / | / | | / | / | | / | / |_______________ [X] |__/________ [X] |__/________ [X] Flat horizontal line Straight line Curve bending Rate = k through origin upward Rate = k[X] Rate = k[X]²
⚠ Common Mix-up Students often confuse a zero-order concentration-time graph (straight line going DOWN) with a first-order rate-concentration graph (straight line going UP through the origin). Both are straight lines — but they mean completely different things! Always check which quantity is on each axis before deciding the order.
Practice Question

A student plots concentration of a reactant against time and gets a curve. When they measure the half-life at different points, they find it takes 20s, then 20s, then 20s again for the concentration to keep halving. What is the order of reaction with respect to this reactant?

4. Obtaining Rate Data

To measure a rate, you need to track some property that changes proportionally with concentration. The trick in exams is picking the right method for the right reaction — you need to know the pros, cons, and when each one fails.

Colorimetry (Colour Changes)

A colorimeter shines light through a solution and measures how much passes through (or is absorbed). Works brilliantly when a coloured species is a reactant or product — e.g. the browny-orange of iodine fading as it reacts.

⚠ Limitation Colorimetry cannot be used to monitor a reaction forming a coloured precipitate — the solid scatters and blocks the light in an unpredictable way, so the readings don't relate cleanly to concentration.

Mass Loss

If a gas escapes the reaction vessel, the mass measured on a balance decreases over time — this mass loss is proportional to the amount of gas (and therefore reactant used).

💡 Watch the numbers This only works well if the gas is dense enough to register a measurable mass change on a typical 2–3 decimal place balance. Carbon dioxide (Mr = 44) works fine; hydrogen (Mr = 2) is far too light — the mass change would be too small to detect reliably.

Gas Volume

Using a gas syringe (or an inverted, water-filled measuring cylinder for gases that aren't water-soluble), you can measure the volume of gas produced over time — this gives a graph that mirrors the amount of product formed.

Titration & Quenching

You can take samples during a reaction and titrate them to find concentration — but the very act of titrating takes time, during which the reaction keeps going and messes up your result. The fix is quenching: rapidly stopping (or drastically slowing) the reaction in the sample the instant it's removed, so you get a "frozen" snapshot to titrate accurately.

The Disappearing Cross Experiment

A classic example: sodium thiosulfate + hydrochloric acid produces a cloudy yellow sulfur precipitate that gradually obscures a cross drawn beneath the flask.

Reaction
Na₂S₂O₃(aq) + 2HCl(aq) → 2NaCl(aq) + SO₂(g) + H₂O(l) + S(s)
⚠ Limitation This method generates only one data point per run (the time for the cross to disappear) — it can't build a full concentration-time graph the way continuous monitoring can.

5. The Initial-Rate Method

The initial rate is the rate at the very start of the reaction, at t = 0 — before any reactant has had time to be significantly used up, so concentrations are still at their known starting values.

Method 1: Tangent at t = 0

  1. Run the reaction and record a property (e.g. gas volume) over time
  2. Plot a concentration/volume-time graph
  3. Draw a tangent to the curve exactly at t = 0
  4. Calculate the gradient of that tangent — this gradient is the initial rate
Worked Example
Gradient = Δy/Δx = 42/38 = 1.10 mol dm⁻³ s⁻¹
Initial rate of CaCO₃ + 2.0 mol dm⁻³ HCl reaction, found from the tangent drawn at t = 0.

Method 2: Clock Reactions

A far more convenient approach for many reactions — instead of plotting a whole graph, you just time how long it takes for one specific visible change to happen (a colour change, or a precipitate obscuring a mark). This single measurement, t, gives you an estimate of the initial rate:

Clock Reaction Relationship
Initial rate ∝ 1/t
The shorter the time to the visible change, the faster the initial rate.
Think of it like: timing a sprinter's first 10 metres instead of watching their whole race. It's a quick, useful snapshot of how fast they started — but it assumes their speed didn't change much in that short window. That's exactly the assumption clock reactions rely on: that the rate doesn't change significantly during the short time being measured.
⚠ The Big Assumption (and its limitation) Clock reactions assume the rate of reaction stays roughly constant between t = 0 and the moment you stop the clock. In reality, concentration is always falling, so rate is always falling too (for orders > 0). The shorter the measured time, the more accurate your estimate of the true initial rate — as reaction time increases, the estimate becomes progressively less accurate. The initial rate from a clock reaction is always an estimate, never an exact value.
[KI] / mol dm⁻³ ×10⁻²Time for blue colour / sRate = 1/t (s⁻¹)
1.515400.025
3.030200.050
6.060100.100

Notice: concentration doubles (1.515→3.030) and rate doubles (0.025→0.050) — confirming first order with respect to iodide.

Practice Question

In an iodine clock experiment, doubling the concentration of one reactant causes the time for the colour change to be exactly halved. What order is the reaction with respect to that reactant?

6. Continuous Monitoring Method

Unlike the initial-rate method (a single snapshot), continuous monitoring tracks the reaction the whole way through, giving you a complete concentration-time graph you can analyse at any point — not just t = 0.

Case Study: Iodination of Propanone

This is the flagship example for this technique. Propanone reacts with iodine, catalysed by dilute sulfuric acid:

Reaction
CH₃COCH₃ + I₂ → CH₃COCH₂I + HI

Because the iodine is coloured (and the products aren't), a colorimeter can track its concentration decreasing continuously as the reaction proceeds. Before starting, you first build a calibration curve — measuring absorbance for solutions of known iodine concentration — so you can convert future absorbance readings back into concentrations.

The result is a smooth concentration-time curve. To find the rate at any chosen moment (not just t = 0), you draw a tangent at that point and calculate its gradient — exactly the same tangent technique as the initial-rate method, just applied anywhere along the curve.

Worked Example — Rate at 300 seconds
Gradient = Δy/Δx = 0.0069/590 = 1.17×10⁻⁵ mol dm⁻³ s⁻¹
✓ Why this matters Continuous monitoring is more powerful than the initial-rate method because a single experiment gives you rate data across the entire concentration range — letting you plot a full rate-concentration graph and directly see whether the shape is a straight line (first order) or a curve (second order), rather than needing multiple separate experiments.

7. Rate-Determining Steps From Equations

Think of it like: a motorway with three lanes merging into one narrow tollbooth. No matter how fast cars travel on the open motorway, the overall journey time is controlled entirely by how quickly cars pass through that one tollbooth. The tollbooth is the "rate-determining step" — the bottleneck that sets the pace for everything.

A chemical reaction can only go as fast as its slowest elementary step — this is the rate-determining step (RDS). Crucially:

🔑 The Golden Rule Only species that appear in the rate-determining step show up in the overall rate equation. Species that only appear in fast steps after the RDS are invisible to the rate equation — changing their concentration won't affect the overall rate at all (this is why they get order zero, or don't appear in the equation).

Predicting a Mechanism From the Rate Equation

Take the reaction of nitrogen dioxide with carbon monoxide:

Overall Equation
NO₂(g) + CO(g) → NO(g) + CO₂(g)
Experimentally Found Rate Equation
Rate = k[NO₂]²

This rate equation tells us the reaction is zero order with respect to CO (it doesn't appear at all) and second order with respect to NO₂. That means two molecules of NO₂ — and zero molecules of CO — must be involved in the slow step.

Step 1 (SLOW — rate-determining): 2NO₂(g) → NO(g) + NO₃(g) Step 2 (FAST): NO₃(g) + CO(g) → NO₂(g) + CO₂(g) ───────────────────────────────── Overall (steps combined, cancel NO₃ and one NO₂): NO₂(g) + CO(g) → NO(g) + CO₂(g) ✓ matches!
💡 Sanity Check Always verify your proposed elementary steps add up exactly to the given overall stoichiometric equation, with any intermediates (like NO₃ above) cancelling out cleanly. If they don't cancel to match, your mechanism is wrong — examiners specifically check this.
Practice Question

For the reaction CH₃CH₂CH₃ + Br₂ + OH⁻ → CH₃CH₂CH₂Br + H₂O + Br⁻, the experimental rate equation is Rate = k[CH₃CH₂CH₃][OH⁻]. What does this tell you about the role of Br₂ in the mechanism?

8. Reaction Mechanisms — Deduction, SN1 & SN2

⚠ Important Nuance Kinetics can only ever suggest a mechanism consistent with the data — it can never prove one is correct. What kinetic data can do is disprove a proposed mechanism if the predicted rate equation doesn't match experiment.

SN1 Mechanism (Tertiary Halogenoalkanes)

In tertiary halogenoalkanes, the carbon attached to the halogen is also bonded to three alkyl groups. These react via a two-step mechanism:

  1. Slow, rate-determining step: the C–X bond breaks heterolytically, the halogen leaves as X⁻, forming a tertiary carbocation intermediate
  2. Fast step: the nucleophile then attacks the carbocation
SN1 Rate Equation
Rate = k[halogenoalkane]
"1" = unimolecular — only ONE species (the halogenoalkane) is involved in the rate-determining step. The nucleophile's concentration doesn't matter because it only reacts in the fast second step.

SN2 Mechanism (Primary Halogenoalkanes)

In primary halogenoalkanes, the carbon attached to the halogen is bonded to just one alkyl group. These react via a single-step mechanism:

The nucleophile attacks the δ+ carbon at the same time as the C–X bond breaks and the halogen leaves — one smooth, simultaneous step (through a transition state), with no separate carbocation ever forming.

SN2 Rate Equation
Rate = k[halogenoalkane][nucleophile]
"2" = bimolecular — TWO species collide in the one and only (rate-determining) step, so both appear in the rate equation.
📌 Quick Reference
  • Primary halogenoalkanes → only SN2
  • Secondary halogenoalkanes → a mix of both SN1 and SN2
  • Tertiary halogenoalkanes → only SN1
Think of it like: SN1 is like a nightclub with one bouncer checking IDs one at a time (slow, only depends on how many people are already in the queue). SN2 is like a doorway where two people have to squeeze through together at the exact same instant — the "rate" of people getting through depends on how many are on both sides of the door at once.
Practice Question

A tertiary halogenoalkane reacts with hydroxide ions. If you double the concentration of hydroxide ions but keep the halogenoalkane concentration the same, what happens to the rate? Explain why in terms of the mechanism.

9. Activation Energy & the Arrhenius Equation

The rate constant k isn't actually constant in the way its name suggests — it only stays fixed if temperature and the presence of a catalyst stay the same. Change either of those, and k changes too. The Arrhenius equation tells us exactly how.

The Arrhenius Equation
k = A e^(−Eₐ/RT)
k = rate constant · A = Arrhenius constant (related to collision frequency & orientation) · Eₐ = activation energy (J mol⁻¹) · R = gas constant (8.31 J K⁻¹ mol⁻¹) · T = temperature (Kelvin)

The intuition: at higher temperatures, a greater fraction of molecules have energy exceeding the activation energy Eₐ. Since rate (and k) is directly proportional to that fraction of "successful" molecules, higher T → higher k → faster rate. Similarly, a higher Eₐ means fewer molecules clear the bar, so k decreases.

The Linearised (Logarithmic) Form

Because the exponential form is awkward to use directly with real data, we take natural logs of both sides to get a straight-line equation:

Linearised Arrhenius Equation
ln k = −Eₐ/R × (1/T) + ln A
This is exactly y = mx + c, where y = ln k, x = 1/T, gradient m = −Eₐ/R, and y-intercept c = ln A.

Calculating Eₐ Directly From k and T

Rearranging ln k = ln A − Eₐ/RT for Eₐ gives:

Rearranged for Eₐ
Eₐ = (ln A − ln k) × RT
Worked Example

Calculate the activation energy of a reaction at 400 K, where k = 6.25×10⁻⁴ s⁻¹, A = 4.6×10¹³, and R = 8.31 J mol⁻¹ K⁻¹.

Using an Arrhenius Plot (Graph Method)

If you have several k values at different temperatures, plot ln k (y-axis) against 1/T (x-axis). This gives a straight, downward-sloping line.

ln k | |• | • | • | • | • |_________________ 1/T (K⁻¹) Gradient = −Eₐ/R → Eₐ = −gradient × R Y-intercept = ln A → A = e^(intercept)
  1. Calculate 1/T and ln k for every data point
  2. Plot ln k against 1/T and draw a line of best fit
  3. Find the gradient of the line — this equals −Eₐ/R, so Eₐ = −gradient × R
  4. Read off (or extrapolate to) the y-intercept — this equals ln A, so A = e^(intercept)
💡 Exam Tip When reading the gradient off a graph, pick two points that are far apart on the best-fit line (not two of your original data points if they're close together) to minimise reading error. Always double check whether the gradient is negative — since Eₐ and R are both positive, the gradient of ln k vs 1/T is always negative. If you calculate a positive Eₐ from a graph with a positive gradient, you've made a sign error somewhere.
Practice Question

An Arrhenius plot has a gradient of −4200 K. Calculate the activation energy in kJ mol⁻¹ (R = 8.31 J K⁻¹ mol⁻¹).

What to Memorise

Rate of reaction Change in concentration of reactant/product per unit time. Units: mol dm⁻³ s⁻¹.
Order of reaction (with respect to a reactant) The power that reactant's concentration is raised to in the rate equation. Found only by experiment — never from the stoichiometric equation.
Overall order The sum of all individual orders in the rate equation.
Rate equation Rate = k[A]ᵐ[B]ⁿ — links rate to reactant concentrations and the rate constant, k.
Rate constant, k Stays fixed only if temperature and catalyst are unchanged. Its units depend on the overall order — always work them out by cancelling, don't memorise a fixed answer.
Half-life (t½) Time for concentration to halve. Constant for first order; decreasing for zero order; increasing for second order.
Initial rate The rate at t = 0, found from the tangent to a concentration-time graph at the origin, or estimated via clock reactions (rate ∝ 1/t).
Continuous monitoring Tracking a reaction throughout its entire course (e.g. via colorimetry), allowing rate to be found at any point via tangents.
Rate-determining step (RDS) The slowest elementary step in a mechanism. Only species involved in this step appear in the rate equation.
SN1 mechanism Two-step; tertiary halogenoalkanes; slow carbocation formation is rate-determining; Rate = k[halogenoalkane] only.
SN2 mechanism One-step; primary halogenoalkanes; simultaneous bond breaking/forming; Rate = k[halogenoalkane][nucleophile].
Arrhenius equation k = Ae^(−Eₐ/RT), or linearised: ln k = −Eₐ/R × (1/T) + ln A. Plot ln k vs 1/T: gradient = −Eₐ/R, intercept = ln A.

Concepts Checklist

Exam Tips — Common Mistakes & Mark-Scheme Traps

Never read orders off the balanced equation Stoichiometric coefficients (like the "2" in 2NO₂) have nothing to do with reaction order unless explicitly linked to the rate-determining step. Orders come from experimental data only.
Read standard form carefully Values like 6.0×10⁻³ vs 6.0×10⁻² are easy to misread under exam pressure — always double-check the powers of ten before doing ratio comparisons between experiments.
Don't confuse graph types A straight line could mean zero order (on a concentration-time graph) OR first order (on a rate-concentration graph). Always check which quantities are on each axis before naming the order.
Always check your mechanism adds up When proposing elementary steps for a mechanism, they must sum exactly to the overall stoichiometric equation, with intermediates cancelling cleanly. Examiners specifically check this — a "plausible-looking" mechanism that doesn't balance is marked wrong.
Work out units of k by cancelling, every time Don't memorise "k has units of mol⁻¹ dm³ s⁻¹" for a given overall order — substitute the actual units from the rate equation and cancel step by step, since the individual orders can combine in different ways to give the same overall order.
Watch your J vs kJ conversion in Arrhenius calculations Eₐ calculated from ln k = ln A − Eₐ/RT comes out in joules (since R is in J K⁻¹ mol⁻¹) — a very common slip is forgetting to divide by 1000 to report the final answer in kJ mol⁻¹.
The gradient of an Arrhenius plot is always negative Since Eₐ and R are both positive, ln k vs 1/T always slopes downward. If your calculated gradient comes out positive, you've made an arithmetic or sign error — go back and check.
Match the experimental method to the reaction's properties Colorimetry fails for precipitates (light scattering); mass loss fails for very light gases like H₂; titration requires quenching to avoid the reaction continuing during analysis. Examiners frequently ask you to justify or criticise a chosen method.
Clock reaction results are estimates, not exact values If asked to evaluate the accuracy of a clock reaction method, mention that longer measured times give less accurate initial-rate estimates, since the assumption of "roughly constant rate" holds less well the longer you wait.
Kinetics Revision Guide · Edexcel International A Level Chemistry · Built for active recall
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Also in the full note
  • 2. Rate Equations & Orders
  • 8. Reaction Mechanisms — Deduction, SN1 & SN2
  • 9. Activation Energy & the Arrhenius Equation
  • Exam Tips — Common Mistakes & Mark-Scheme Traps
  • Titration & Quenching
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