Experimental Determination of Rate Laws
Rate equations cannot be deduced from overall balanced reaction equations; they depend strictly on reaction mechanisms and must be determined experimentally.
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
Orders Are Independent of Stoichiometric Coefficients
The reaction orders \(m\) and \(n\) in \(\text{Rate} = k[A]^m[B]^n\) are not the stoichiometric coefficients from the balanced equation. They reflect the molecularity of the rate-determining step in a multi-step mechanism.
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
Deducing Units of the Rate Constant
Problem: Given the rate equation \(\text{Rate} = k[A][B]^2\), determine the overall reaction order and deduce the units of the rate constant \(k\).
Step 1: Overall Order
\(\text{Overall order} = 1 + 2 = 3\)
Step 2: Rearrange for \(k\) and substitute units
\(k = \dfrac{\text{Rate}}{[A][B]^2} = \dfrac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3})(\text{mol dm}^{-3})^2} = \mathbf{\text{mol}^{-2}\text{ dm}^{6}\text{ s}^{-1}}\)
Temperature Dependence of the Rate Constant
The rate constant \(k\) is constant at a specific temperature. Increasing temperature increases \(k\) exponentially according to the Arrhenius equation. Always state the temperature when quoting numerical values for \(k\).
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