Rate Equations and Experimental Determination HL Only
Quick Notes:
- Rate equations are expressions showing how the rate of a reaction depends on the concentration of reactants.
- General form: rate = k[A]m[B]n
- k = rate constant
- m, n = orders with respect to A and B (determined from data)
- Rate equations cannot be predicted from the balanced chemical equation.
- Must be determined by experiment, typically using initial rates.
- The overall order of the reaction is the sum of all individual orders.
Full Notes:
What Is a Rate Equation?
A rate equation (or rate law) shows how the reaction rate depends on the concentrations of reactants.
Rate equations can only be determined using experimental data.
General form: rate = k[A]m[B]n
- k = rate constant (depends on temperature)
- [A], [B] = concentrations of reactants
- m, n = reaction orders with respect to A and B
These exponents are not necessarily the same as the stoichiometric coefficients.
Reaction Order
The order of reaction with respect to a reactant is the power to which its concentration is raised in the rate equation and links changes in concentrations of reactants to changes in the rate of a reaction.
The order of a reaction ‘with respect to…’ just means how changing the concentration of a particular reactant affects the rate of the reaction (independent of other reactants).
Zero order – changing the concentration of the reactant doesn’t affect the rate.
First order – changing the concentration of the reactant changes the rate by the same factor (for example, if reactant concentration is doubled (×2), rate also doubles (×2)).
Second order – changing the concentration of the reactant changes the rate by the factor squared (for example, if the reactant concentration is doubled, rate quadruples (22 = 4)).
Orders of reactions can only be determined experimentally and the overall order of a reaction is the sum of all orders for each reactant.
How to Determine Rate Equations Experimentally
By measuring the rate of a reaction at differing concentrations of each reactant, we can determine the orders with respect to each reactant and use these to construct an overall rate equation.
Example: Reaction: A + B → Products
| Experiment | [A] / mol dm⁻³ | [B] / mol dm⁻³ | Rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 0.02 |
| 2 | 0.20 | 0.10 | 0.04 |
| 3 | 0.10 | 0.20 | 0.16 |
[A] has doubled from exp. 1 to exp. 2 and [B] is constant. Rate has doubled (0.02 to 0.04). This means reaction must be first order with respect to A.
[B] has doubled from exp. 1 to exp. 3 and [A] is constant. Rate has quadrupled (×4), gone from 0.04 to 0.16. This means reaction must be second order with respect to B.
Thus, the rate equation is: Rate = k [A]1 [B]2
Summary
- Rate equations express the relationship between rate and reactant concentrations.
- Must be determined by experimental data.
- Exponents (orders) are not from the chemical equation.
- Used to understand and predict reaction mechanisms and kinetics.