Overview
- Topic: A-level Chemistry — Rate Equations, Orders, Rate Constant, Mechanisms.
- Covers how to measure rate, determine orders from graphs and tables, calculate k and units, and deduce rate-determining step and mechanism.
- Emphasis: orders must be determined experimentally, not from balanced equations.
Rate And Measurement
- Rate = change in concentration / time; units typically mol dm^-3 s^-1.
- Can measure concentration directly or by proportional observable (gas volume, mass loss, color change).
- Ensure measurements are proportional/inversely proportional to concentration.
Factors Affecting Rate
- Concentration of reactants, temperature, surface area (solids), presence of catalyst, pressure for gases.
- Increasing concentration increases number of particles and collisions (Maxwell–Boltzmann idea), hence rate.
Rate Equation And Orders
- General form: rate = k [A]^m [B]^n where m, n are orders for A and B, k is rate constant.
- Orders (m, n) must be found experimentally; at A-level typically 0, 1, or 2.
- Order with respect to a reactant shows how rate changes when that concentration changes:
- Zero order: rate independent of concentration ([X]^0 = 1).
- First order: rate ∝ [X]^1 (doubling [X] doubles rate).
- Second order: rate ∝ [X]^2 (doubling [X] quadruples rate).
Recognizing Orders From Rate vs Concentration Graphs
- First order: straight line through origin for rate vs [A].
- Second order: upward-curving graph; slope increases with [A].
- Zero order: horizontal line (rate constant regardless of [A]).
Determining Orders From Experimental Series (Initial Rates)
- Vary one reactant while keeping others in large excess (effectively constant).
- Plot concentration vs time for each trial, draw tangent at t = 0 to get initial rate.
- Compare trials where only one concentration changed:
- If rate change ∝ change^1 → first order.
- If rate change ∝ change^2 → second order.
- If rate unchanged → zero order.
Using Log Plots When Graph Shape Is Ambiguous
- Take logs: log(rate) = m log([A]) + log(k) → y = mx + c.
- Plot log(rate) vs log([A]) gives straight line; gradient = order m; intercept = log(k).
Concentration vs Time Graph Shapes (Identifying Order)
- Zero order: linear decline; gradient = -rate; rate = k (k units mol dm^-3 s^-1).
- First order: exponential decay with constant half-life (t1/2 constant).
- Second order: steep initial decline then levels; half-life increases with time.
Rate Constant k
- k links concentrations to rate; larger k → faster reaction.
- k depends on temperature (increases with T; typically exponential increase).
- Calculate k by rearranging rate equation: k = rate / ([A]^m [B]^n).
- Determine units by substituting units into rearranged expression.
Table: Units Of k By Overall Order
| Overall Order | Units |
|---|
| 0 | mol dm^-3 s^-1 |
| 1 | s^-1 |
| 2 | mol^-1 dm^3 s^-1 |
| 3 | mol^-2 dm^6 s^-1 |
Working With Data Tables (Finding Orders And k)
- Compare experiment pairs where only one concentration changes.
- Determine how rate changes relative to concentration change to find order.
- Sum powers for overall order.
- Example approaches:
- If [A] ×3 and rate ×3 → first order in A.
- If [B] ×2 and rate ×4 → second order in B.
- If no pair has one reactant constant, infer by imagining changes and combining effects.
- With known rate equation, use one experiment to calculate k; then fill missing rates/concentrations by substitution.
Rate-Determining Step And Mechanisms
- Multi-step reactions: the slowest step controls overall rate (rate-determining step).
- Reactants appearing in the rate-determining step appear in the rate equation.
- Orders (powers) in rate equation correspond to stoichiometric coefficients of reactants in the rate-determining step.
- Intermediates do not appear in the overall rate equation; replace intermediates by earlier-step reactants that produce them.
- Catalysts appear in the rate equation (they influence rate) but not in the overall chemical equation.
Examples Linking Mechanism And Rate Law
- If rate law = k [A]^2 [H+]^1, the rate-determining step involves 2 A and 1 H+.
- If intermediate Y formed in step 1 (X + Z → Y), and step 2 (slow) uses Y, express Y in terms of X and Z to derive rate law: e.g., rate ∝ [X]^2[Z]^1.
- Catalysts (e.g., H+) used in slow step and regenerated later; they appear in rate law, not overall equation.
SN1 vs SN2 Mechanistic Identification By Rate Law
- SN2: bimolecular slow step; rate ∝ [halogenoalkane]^1 [nucleophile]^1 → second order overall (rate depends on nucleophile concentration).
- SN1: unimolecular slow step (formation of carbocation); rate ∝ [halogenoalkane]^1 and nucleophile is zero order (nucleophile concentration does not affect rate).
- Experimental determination of order for nucleophile distinguishes SN1 vs SN2.
- Typical tendency: primary halogenoalkanes favor SN2; tertiary favor SN1.
Key Terms And Definitions
- Rate of reaction: change in concentration per unit time.
- Initial rate: gradient of tangent at t = 0 on concentration vs time or observable vs time curve.
- Order of reaction: exponent showing dependence of rate on reactant concentration.
- Overall order: sum of individual orders in rate equation.
- Rate constant (k): proportionality constant; temperature-dependent.
- Rate-determining step: slowest step in multi-step mechanism setting overall rate.
- Catalyst: speeds reaction, appears in rate law, regenerated by end.
Action Items / Exam Tips
- Always determine orders experimentally; do not infer from balanced equation.
- When given tables, find experiment pairs where only one concentration changes.
- Use log-log plots if rate vs [A] shape is unclear.
- Calculate k from one complete experiment, then predict missing values.
- Convert units carefully when finding units for k; use overall order to remember common units.
- For mechanism questions, match rate law exponents to coefficients in rate-determining step.