📘 IB Understanding
Rate equations can only be determined experimentally. The method of initial rates involves comparing pairs of experiments where only one reactant concentration changes.
The Method of Initial Rates
The key principle is simple:
By keeping all concentrations constant except one, you can isolate the effect of that reactant on the rate.
Worked Example
Experimental Data
| Exp | [A] / mol dm⁻³ | [B] / mol dm⁻³ | Initial Rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 2.0 × 10⁻⁴ |
| 2 | 0.20 | 0.10 | 4.0 × 10⁻⁴ |
| 3 | 0.10 | 0.20 | 8.0 × 10⁻⁴ |
Step-by-Step Solution
Finding order with respect to A (compare Exp 1 and 2):
[A] doubles (0.10 → 0.20), [B] stays constant.
Rate doubles (2.0 → 4.0): \((2)^x = 2\), so \(x = 1\) (first order in A)
Finding order with respect to B (compare Exp 1 and 3):
[B] doubles (0.10 → 0.20), [A] stays constant.
Rate quadruples (2.0 → 8.0): \((2)^y = 4\), so \(y = 2\) (second order in B)
Rate equation: Rate = k[A]¹[B]² (Overall order = 3)
Finding k
Once you know the rate equation, substitute any experiment's data to find k:
\(k = \frac{\text{Rate}}{[A][B]^2} = \frac{2.0 \times 10^{-4}}{(0.10)(0.10)^2} = \frac{2.0 \times 10^{-4}}{1.0 \times 10^{-3}} = 0.20\text{ mol}^{-2}\text{ dm}^{6}\text{ s}^{-1}\)
📋 Exam Tip
Always find two experiments where the concentration of only one reactant changes while all others are held constant. This isolates the effect and makes the maths straightforward.