Chemistry · General chemistry II · Worked example
Find Ea and A from an Arrhenius plot
A first-order reaction has these rate constants at four temperatures. Find the activation energy and the frequency factor.
Transform the data
Arrhenius plots use 1/T in K⁻¹ and ln k, so compute both for every row before fitting.
| T (K) | k (s⁻¹) | 1/T (K⁻¹) | ln k |
|---|---|---|---|
| 300 | 1.92 × 10⁻³ | 3.3333 × 10⁻³ | −6.255 |
| 310 | 4.46 × 10⁻³ | 3.2258 × 10⁻³ | −5.413 |
| 320 | 9.81 × 10⁻³ | 3.1250 × 10⁻³ | −4.624 |
| 330 | 2.06 × 10⁻² | 3.0303 × 10⁻³ | −3.882 |
Fit a straight line
The points lie on a straight line (R² = 0.9999998), so one activation energy describes this range. The least-squares slope and intercept are:
Activation energy from the slope
The slope equals −Ea/R, so Ea = −R × slope.
Frequency factor from the intercept
The intercept is ln A. A has the units of k, and because it is an extrapolation to 1/T = 0, two significant figures are plenty.
Result
Ea = 65.1 kJ/mol and A ≈ 4.2 × 10⁸ s⁻¹.
Your turn
Using Ea = 65.1 kJ/mol and A = 4.2 × 10⁸ s⁻¹ from this example, estimate k at 340 K.
Show the answer and explanation
k ≈ 4.2 × 10⁻² s⁻¹.
k = 4.2 × 10⁸ × e^(−65100/(8.314 × 340)) = 4.2 × 10⁸ × e^(−23.03) ≈ 4.2 × 10⁻² s⁻¹. 340 K is just outside the measured range, so treat this as a short extrapolation.
Keep exploring
Fit the same four points in the Kinetics studio, then add a prediction temperature and see when it warns about extrapolation.
Return to the concept →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
- Tro, Chemistry: A Molecular Approach, 4th ed., §14.5 The Effect of Temperature on Reaction Rate, pp. 642–647 (Arrhenius plots, pp. 644–645; two-point form, p. 646)
- OpenStax Chemistry 2e — Collision theory