Why heat speeds up reactions
Molecules must collide with enough energy to react, at least the activation energy Ea. As temperature rises, a larger share of molecules has that energy, so reactions speed up, often dramatically. In 1889, Svante Arrhenius captured this in an equation that is still used in chemistry, biology, food science and materials testing.
The formulas
- Arrhenius equation: k = A × exp(−Ea ÷ RT)
- Two temperatures: k₂ = k₁ × exp(−Ea/R × (1/T₂ − 1/T₁))
- Activation energy: Ea = R × ln(k₂/k₁) ÷ (1/T₁ − 1/T₂)
- Q10 = (k₂/k₁)^(10 ÷ (T₂ − T₁))
Temperatures are in kelvin and R = 8.314 J/(mol·K). The pre-exponential factor A cancels out when comparing two temperatures, so you only need Ea or two measured rate constants.
Worked example
A reaction has Ea = 50 kJ/mol and a rate constant of 1 (in any unit) at 25 °C. What happens at 35 °C?
- T₁ = 298.15 K, T₂ = 308.15 K.
- 1/T₂ − 1/T₁ = −1.088 × 10⁻⁴ K⁻¹.
- k₂ = exp(50,000 ÷ 8.314 × 1.088 × 10⁻⁴) = exp(0.655) = 1.92.
The reaction runs almost twice as fast after 10 °C of warming, so Q10 = 1.92.
Finding Ea from experiments
Switch the calculator to “Activation energy” and enter rate constants measured at two temperatures. With more data points, plot ln k against 1/T (an Arrhenius plot): the points fall on a line whose slope is −Ea/R.
How Ea changes the temperature effect
| Ea (kJ/mol) | Rate increase from 25 to 35 °C |
|---|---|
| 20 | 1.30 × |
| 50 | 1.92 × |
| 75 | 2.67 × |
| 100 | 3.70 × |
High activation energies make reactions very sensitive to temperature.
Applications
- Food and drug stability: accelerated aging tests store products at 40 °C and use the Arrhenius equation to predict shelf life at room temperature.
- Biology: metabolic and enzyme rates usually have Q10 values between 2 and 3, until the enzyme denatures at high temperature.
- Batteries and electronics: degradation roughly doubles for every 10 °C, which is why heat shortens their life.
- Cooking: a slow cooker and an oven cook the same dish at very different speeds.
Limits
The equation assumes Ea does not change with temperature. It fails for enzyme reactions beyond their optimum temperature, for reactions with several competing steps, and over very wide temperature ranges.