📘 IB Understanding
Rate equations depend on the mechanism of the reaction and can only be determined experimentally. The rate constant, k, is temperature-dependent and its units are determined from the overall order of the reaction.
The Rate Law
For a reaction involving reactants A and B, the rate equation (or rate law) takes the general form:
Where:
- \(k\) is the rate constant (specific to a reaction at a given temperature)
- \([A]\) and \([B]\) are the molar concentrations of the reactants
- \(m\) and \(n\) are the orders of reaction with respect to each reactant
⚠️ Key Point
The exponents \(m\) and \(n\) are not the stoichiometric coefficients from the balanced equation. They can only be found experimentally. This is because the rate law depends on the reaction mechanism, not the overall equation.
The Rate Constant, k
The rate constant \(k\) is a proportionality constant. It reflects collision frequency, orientation requirements, and activation energy. A larger k means a faster reaction at a given temperature.
| Property of k | Detail |
|---|---|
| Temperature dependence | k increases with temperature (more particles overcome Eₐ) |
| Catalyst effect | A catalyst increases k by providing an alternative pathway |
| Concentration effect | k is independent of concentration |
| Units | Depend on overall order of reaction (see below) |
Units of k
The units of k can be derived from the rate equation using the general formula:
| Overall Order | Units of k |
|---|---|
| 0 | mol dm⁻³ s⁻¹ |
| 1 | s⁻¹ |
| 2 | mol⁻¹ dm³ s⁻¹ |
| 3 | mol⁻² dm⁶ s⁻¹ |
Worked Example
Given: Rate = k[A]¹[B]². Find the units of k.
Solution:
Overall order = 1 + 2 = 3
\(k = \frac{\text{Rate}}{[A][B]^2} = \frac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3})(\text{mol dm}^{-3})^2}\)
\(k = \text{mol}^{-2}\text{ dm}^{6}\text{ s}^{-1}\)
📋 Exam Tip
The rate constant k only remains constant if the temperature does not change. If you change the temperature or add a catalyst, the value of k will change.