Rate Equations and Rate Constants
Quick Notes
- Rate of reaction: Change in concentration per unit time.
- Order: Power to which a concentration term is raised in the rate equation.
- Overall order: Sum of the individual orders.
- Rate constant, k: A constant in the rate equation that accounts for temperature, activation energy and proportion of collisions with correct orientation. Units depend on the overall order.
- Half-life, t1/2: Time for concentration of a reactant to halve.
- Rate-determining step: Slowest step in a reaction mechanism.
- Orders and Rate Equations:
- Rate equations: rate = k[A]m[B]n, where m and n are orders of reaction with respect to A and B (0, 1, or 2).
Full Notes
Key Terms and Definitions
- Rate of reaction: Describes how fast reactants are used up or products formed, measured in mol dm⁻³ s⁻¹.
- Order of reaction: Shows how the rate depends on concentration of each reactant.
- Overall order: Total of the powers of concentration terms in the rate equation.
- Rate constant (k): Links the concentration of reactants to the reaction rate. Value depends on temperature.
- Half-life (t1/2): The time it takes for the concentration of a reactant to fall to half its initial value.
- Rate-determining step: The slowest step in a multi-step mechanism; it controls the overall rate.
Orders and Rate Equations
Rate equations show how the rate of a reaction depends on reactant concentrations and the rate constant (k).
![OCR (A) A-Level Chemistry rate equation showing rate = k[A]ⁿ[B]ᵐ, where n and m are reaction orders.](images/rateequation.png)
Where:
- k = rate constant
- […] = concentration of reactant
- m and n = orders of reaction with respect to each reactant
Note – the rate equation is found experimentally. m and n must be determined from experimental data, not stoichiometry.
Rate Constant (k)
Temperature, activation energy and the proportion of collisions with correct orientation determine a reaction’s rate.
These are accounted for by the rate constant (k), which varies with temperature.
Calculating the Rate Constant (k)
Rate constants can only be calculated using experimental data.
A reaction with the following rate equation and reactant concentrations has a reaction rate of 0.05 mol dm⁻³ s⁻¹. Calculate the rate constant, k, for the reaction and give its units.
Rate equation: rate = k [A]¹ [B]²
- Rate = 0.05 mol dm⁻³ s⁻¹
- [A] = 0.10 mol dm⁻³, [B] = 0.20 mol dm⁻³
- k = Rate ÷ ([A] × [B]²)
- k = 0.05 ÷ (0.10 × 0.20²)
- k = 0.05 ÷ (0.10 × 0.04) = 12.5 mol⁻² dm⁶ s⁻¹
Answer: k = 12.5 mol⁻² dm⁶ s⁻¹
Units of k depend on the overall order of reaction.
| Order | Rate Equation | Units of k |
|---|---|---|
| Zero | Rate = k | mol dm−3 s−1 |
| First | Rate = k [A] | s−1 |
| Second | Rate = k [A]2 | mol−1 dm3 s−1 |
| Third | Rate = k [A]3 | mol−2 dm6 s−1 |
Summary
- Rate equations show how the rate depends on concentrations of reactants and the rate constant.
- Orders of reaction are determined experimentally and indicate how concentration changes affect rate.
- Rate constant, k, incorporates temperature, activation energy and collision orientation.
- Units of k depend on the overall order of the reaction.