Week 8 Module: Reaction Kinetics

Research question#

Roasting Peking duck skin (北京烤鸭) a little hotter produces noticeably more browning in the same amount of time — not a proportionally small increase, but a disproportionately large one. Module 3 established that some food transitions have their own timescale, separate from temperature; this module asks how that timescale actually depends on temperature, using duck-skin Maillard browning as the case and pork-belly collagen conversion (from Module 3) as a comparison.

Specimen Peking duck skin (北京烤鸭), Maillard browning at oven temperature

Where this sits#

Second module of Stage 3, Transport, Kinetics and Transformation. Module 7 covered how heat and moisture physically move through food; this module covers what happens once they arrive — how fast a chemical or structural change proceeds at a given temperature. Module 9 uses the same rate-law idea implicitly when discussing how quickly a crust dries during frying.

The model: the Arrhenius equation#

The rate constant of most food-relevant thermally-driven reactions, including Maillard browning and collagen hydrolysis, follows an Arrhenius temperature dependence:

k(T) (rate constant, units depend on reaction order)

how fast the reaction proceeds at absolute temperature T.

A (pre-exponential factor)

a reaction-specific constant related to how often molecules collide in the right orientation to react.

E_a (activation energy, J·mol⁻¹)

the energy barrier the reaction must overcome; a larger E_a makes the rate more sensitive to temperature, not less likely to happen eventually.

R (gas constant, 8.314 J·mol⁻¹·K⁻¹)

fixed.

T (absolute temperature, K)

note this is Kelvin, not °C — the exponential's sensitivity comes from T appearing in a denominator on an absolute scale.

Because k depends exponentially on 1/T, reactions with a large E_a are far more temperature-sensitive than reactions with a small one. Maillard browning reactions are reported with comparatively high activation energies, which is consistent with duck skin’s browning rate jumping sharply for a modest oven-temperature increase. Collagen-to-gelatin hydrolysis (Module 3) proceeds over a narrower practical temperature window in a braise, but its rate is still governed by the same functional form — the two reactions differ in A and E_a, not in which equation applies.

Model

k(T) = A·exp(−E_a/RT)

Linearised as

ln k vs 1/T

Steeper slope

larger E_a

What you measure and analyse#

Given a supplied table of browning-rate measurements at three oven temperatures, you linearise the Arrhenius equation (plotting ln k against 1/T) to extract an apparent activation energy from the slope, and use it to predict the browning rate at a fourth, untested temperature.

Activity#

A recipe says “roast at 220 °C for 45 minutes, or 200 °C for 65 minutes” for equivalent browning. Using an activation energy from the literature range for Maillard browning (cite your source — do not invent a number), check whether the two temperature/time pairs given by the recipe are roughly consistent with a single Arrhenius rate law, or whether the recipe appears to be relying on more than temperature alone (for example, surface drying, covered in Module 9).

References#

• Damodaran, S. & Parkin, K.L. (Eds.) (2017). Fennema’s Food Chemistry, 5th ed. CRC Press.
• Walstra, P. (2003). Physical Chemistry of Foods. Marcel Dekker.