Short on time? This page is the recap. For explanations, the graphs and worked examples, use the full study guide.
Recap
- Reactions are followed over time by spectrophotometry (absorbance ∝ concentration), gas pressure or volume, conductivity or pH, or sampling and titration.
- The initial rate is the slope of the concentration–time curve at t = 0, when the concentrations are known exactly.
- A rate law gives the rate as k multiplied by each reactant concentration raised to a power: rate = k[A]ᵐ[B]ⁿ.
- Each power is the order with respect to that reactant. Their sum is the overall order.
- Orders are found by experiment. They are not read from the coefficients of an overall equation.
- The rate constant k is the same for every experiment at one temperature. It changes when the temperature changes.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| rate = k[A]ᵐ[B]ⁿ | rate law | calculate a rate, or k from one experiment |
| rate ratio = (concentration ratio)ᵐ | one concentration changes, all else fixed | find the order in that reactant |
| order = log(rate ratio) ÷ log(conc. ratio) | same idea with awkward factors | find an order from any ratio |
| units of k = M¹⁻ⁿ s⁻¹ | n = overall order | 0: M s⁻¹; 1: s⁻¹; 2: M⁻¹ s⁻¹; 3: M⁻² s⁻¹ |
Assumptions behind the numbers
- All experiments are at the same temperature, so k is the same in each.
- The rates are initial rates, so products have not built up and the starting concentrations apply.
- For spectrophotometry, absorbance is proportional to concentration (same wavelength and path length).
Mistakes to avoid
- Using coefficients as orders.
- Doubling for second order. Second order: × 4 when the concentration doubles.
- Crediting a reactant with a rate change caused by another. Remove known effects first.
- Wrong or missing units for k. Work them out from the overall order.
- Saying k changed because the rate changed with concentration.
- Dropping a zero-order reactant from the reaction as if it were not used up.
Quick self-check
- For rate = k[A][B]², what happens to the rate if [B] triples? If [A] halves and [B] doubles? (× 9; × 2)
- What are the units of k for an overall second-order reaction? (M⁻¹ s⁻¹)
- A first-order reaction has a rate of 8.0 × 10⁻³ M s⁻¹ when [A] = 0.20 M. What is k? (0.040 s⁻¹)
Next: practice questions.