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Rate of Reaction

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Consider the reaction:

$\displaystyle \alpha A +\ \beta B \rightarrow \gamma C +\ \delta D$

involving the molecules A, B, C & D with stoichiometric coefficients α, β, γ & δ respectively. How do we define the rate of reaction?

There are several options:

Average time for A or B to react from mixing
Time taken from A and B making contact to C and D being formed? (~10^-14 s)
Rate of change of particular species’ concentration

Definition

Rate of reaction is defined in terms of the rate of change of a particular species’ concentration

For example, we can define the rate in terms of the rate of change of the concentration of reactant A or product C:

$\displaystyle rate = -\frac{1}{\alpha} \frac{d[A]}{dt} = \frac{1}{\gamma} \frac{d[C]}{dt}$

Note how the derivative is divided by the species’ stoichiometric coefficient and a minus sign is introduced if the species is a reactant since its concentration will decrease while the rate is always positive by convention.

Units

Thus the reaction rate has units of concentration per unit time. The most common units are as mol dm^-3 s^-1 for reactions happening in a liquid or aqueous phase and molecules cm^-3 s^-1 for reactions occuring in the gas phase.