RGT Rule (Q10 Rule)

First determine the temperature change ΔT and divide it by 10 K: that gives the number of doubling steps. Then raise the temperature coefficient Q₁₀ to this power: $v_{2} = v_{1}\cdot{}Q_{10}^{(\frac{\Delta{}T}{10} K)}$. Example with $Q_{10} = 2$: heating from 20 °C to 50 °C means $\Delta{}T = 30 K$, three steps and a factor of $2^{3} = 8$. A reaction that previously took 24 minutes is then finished in about 3 minutes. Non-integer steps work too: for $\Delta{}T = 15 K$ you calculate $2^{1.5} \approx{} 2.8$. On cooling, ΔT becomes negative and the factor smaller than 1, the reaction slows down.

The reason lies in the Arrhenius equation: only particles with enough energy overcome the activation barrier, and their fraction depends exponentially on temperature. Even slight heating shifts the particles' energy distribution so that markedly more collisions succeed. For typical activation energies around $\frac{50 kJ}{mol}$, the Arrhenius calculation near room temperature yields just about a factor of 2 per 10 K; that is exactly where the rule of thumb comes from. It is therefore not a separate law of nature but a special case. Reactions with higher activation energy respond more sensitively to temperature (Q₁₀ closer to 3 or 4), those with a low barrier more weakly (Q₁₀ nearer 1.5 to 2).

The Q10 rule is a deliberately coarse rule of thumb for estimates, not an exact formula. It works best between about 0 and 100 °C and over moderate spans of a few tens of kelvin. Strictly speaking its Q₁₀ is itself temperature dependent, because the exact Arrhenius equation does not deliver a constant factor per 10 K; over wide ranges the two calculations diverge. The rule fails completely for enzymes and microorganisms above the temperature optimum: there the protein denatures and the rate collapses instead of rising further. Diffusion-controlled and explosive reactions do not follow it either. For exams: estimate with the Q10 rule, calculate exactly with Arrhenius.

Q₁₀ is the factor by which the reaction rate increases when the temperature rises by exactly 10 K. For many chemical reactions it lies between 2 and 4, for purely physical processes such as diffusion only around 1.2 to 1.5. You determine it experimentally from two rate measurements: $Q_{10} = (\frac{v_{2}}{v_{1}})^{(\frac{10 K}{\Delta{}T})}$. In biology, Q₁₀ is an important parameter for metabolic rates: the heartbeat and respiration of cold-blooded animals follow it, as does the germination speed of seeds. A high Q₁₀ indicates a high activation energy of the underlying process, because the two quantities are linked through the Arrhenius equation.

Spoilage is chemistry: enzymatic reactions, oxidations and the metabolism of microorganisms run faster the warmer it is. Cooling reverses the RGT rule. From 20 °C room temperature to 5 °C fridge temperature is $\Delta{}T = -15 K$; with $Q_{10} = 3$, as is typical for many biological processes, the factor is $3^{(-1.5)} \approx{} 0.19$. The spoilage reactions therefore run at only about one fifth of the rate, and the shelf life rises correspondingly to roughly five times. In the freezer the effect is even stronger; additionally, freezing the water drastically restricts the mobility of the molecules. Exactly the same logic is used in reverse when cooking and in accelerated ageing tests, where heating deliberately speeds up the processes.