Vol. V · The Molecules of Food Plate 10 of 11reaction rate, Arrhenius, Q10, activation energy, temperature dependence, kineticsMH

Reaction Speed and Temperature.

"Ten degrees doubles the rate" is a rule of thumb. The real rule depends on how much energy a reaction needs to get started.

Molecules react when they collide with enough energy to rearrange. Warmer molecules move faster, so a larger share of collisions have that energy, and reactions speed up. Svante Arrhenius put it in a law: the rate grows exponentially as temperature rises, and how steeply depends on the reaction's activation energy — the energy barrier it must climb. Cooks summarise it as Q10, the factor by which a reaction speeds up for ten more degrees.

Reactions with small activation energies, such as the loss of vitamin C, speed up gently: Q10 about 1.5. Browning, with a large one, more than triples for every ten degrees near 150 °C. Protein unfolding, with a huge one, switches on over a few degrees (V.5). The workshop plots several reactions on one chart.

Below: the rates of four cooking reactions against temperature on a logarithmic axis (course Arrhenius parameters), and Q10 for each at the temperature you choose.

What you will learn
Workshop
Rates (per minute, log scale) of vitamin C loss (45 kJ/mol), chlorophyll loss (55), collagen to gelatin (65) and Maillard browning (125), from course parameters. Q10 = rate(T + 10) ÷ rate(T).

Steep and shallow reactions

At 100 °C, vitamin C loss speeds up by a factor of 1.46 for ten more degrees, while Maillard browning speeds up 2.86 times; near 150 °C browning's Q10 is still 2.27. Over the range a pan covers, from a 120 °C surface to a 170 °C one, browning runs 75 times faster. That steepness is why a hot pan browns in a minute what a warm one cannot brown in ten, and why burning comes on so suddenly (VIII.8).

The rule of thumb that ten degrees doubles a rate is right only for reactions with an activation energy around 55 kJ/mol near room temperature. Use the real numbers where they matter: food spoils about twice as fast at 15 °C as at 5 °C (most spoilage chemistry and growth is in that range), fats go rancid faster in a warm cupboard, and a braise at 95 °C finishes noticeably sooner than at 85 °C.

Svante Arrhenius proposed his equation in 1889 to explain how sugar is broken down in acid at different temperatures — a kitchen reaction, inverting sucrose (VII.9).

Terms

Activation energy
The energy barrier a reaction must climb; larger means more sensitive to temperature.
Arrhenius law
Rate = A · exp(−Ea / RT): rates rise exponentially with temperature.
Q10
The factor by which a rate increases for a 10 °C rise.
Rate constant
A number describing how fast a reaction proceeds at a given temperature.
Reactions speed up exponentially with temperature; the larger the activation energy, the steeper — browning far more than vitamin loss.

Sources

  1. Maillard browning: apparent activation energies of roughly 100–160 kJ/mol are reported for colour formation (M. A. J. S. van Boekel, Kinetic Modeling of Reactions in Foods, CRC Press, 2009). The course uses 125 kJ/mol and a teaching scale of browning.
  2. Chlorophyll to pheophytin in heated green vegetables: first order, activation energy about 50–60 kJ/mol, much faster in acid (S. J. Schwartz and T. V. Lorenzo, Crit. Rev. Food Sci. Nutr. 29, 1990). Teaching values within these ranges.