Kinetics
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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.
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.
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:
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.
| Order | What happens to rate | In rate equation? |
|---|---|---|
| Zero (0) | Changing concentration has no effect on rate | Not included at all |
| First (1) | Rate is directly proportional — double concentration, double rate | Included as [X]¹ = [X] |
| Second (2) | Rate proportional to the square — double concentration, rate ×4 | Included as [X]² |
The overall order of a reaction is just the sum of all the individual orders (m + n + ...).
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⁻³ | Initial rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|
| 1 | 1.0×10⁻³ | 2.0×10⁻³ | 3.0×10⁻³ |
| 2 | 2.0×10⁻³ | 2.0×10⁻³ | 6.0×10⁻³ |
| 3 | 1.0×10⁻³ | 4.0×10⁻³ | 1.2×10⁻² |
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⁻.
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.
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
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)
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!
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.
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).
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.
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
- Run the reaction and record a property (e.g. gas volume) over time
- Plot a concentration/volume-time graph
- Draw a tangent to the curve exactly at t = 0
- Calculate the gradient of that tangent — this gradient is the initial rate
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:
| [KI] / mol dm⁻³ ×10⁻² | Time for blue colour / s | Rate = 1/t (s⁻¹) |
|---|---|---|
| 1.515 | 40 | 0.025 |
| 3.030 | 20 | 0.050 |
| 6.060 | 10 | 0.100 |
Notice: concentration doubles (1.515→3.030) and rate doubles (0.025→0.050) — confirming first order with respect to iodide.
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:
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.
7. Rate-Determining Steps From Equations
A chemical reaction can only go as fast as its slowest elementary step — this is the rate-determining step (RDS). Crucially:
Predicting a Mechanism From the Rate Equation
Take the reaction of nitrogen dioxide with carbon monoxide:
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.
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
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:
- Slow, rate-determining step: the C–X bond breaks heterolytically, the halogen leaves as X⁻, forming a tertiary carbocation intermediate
- Fast step: the nucleophile then attacks the carbocation
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.
- Primary halogenoalkanes → only SN2
- Secondary halogenoalkanes → a mix of both SN1 and SN2
- Tertiary halogenoalkanes → only SN1
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 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:
Calculating Eₐ Directly From k and T
Rearranging ln k = ln A − Eₐ/RT for Eₐ gives:
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.
- Calculate 1/T and ln k for every data point
- Plot ln k against 1/T and draw a line of best fit
- Find the gradient of the line — this equals −Eₐ/R, so Eₐ = −gradient × R
- Read off (or extrapolate to) the y-intercept — this equals ln A, so A = e^(intercept)
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
Concepts Checklist
Exam Tips — Common Mistakes & Mark-Scheme Traps
- 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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