Rate equations and orders · Grade 12
A rate equation shows how the rate of a reaction depends on the concentration of each reactant: rate = k[A]ᵐ[B]ⁿ. The powers are the orders of reaction, and they can only be found by experiment. The rate constant, k, changes with temperature, as the Arrhenius equation describes.
Key facts
- Order 0: the rate does not depend on that concentration. Order 1: doubling the concentration doubles the rate. Order 2: doubling it makes the rate four times as fast.
- The overall order is the sum of the orders. The units of k depend on it: mol dm⁻³ s⁻¹ for zero order, s⁻¹ for first order, dm³ mol⁻¹ s⁻¹ for second order.
- Orders come from initial-rates experiments (change one concentration at a time) or from concentration–time graphs: a straight line for zero order, a constant half-life for first order.
- For a first-order reaction the half-life is constant and k = ln 2 ÷ t½.
- The rate-determining step is the slowest step in the mechanism. The species in the rate equation take part in it, or in a step before it.
- The Arrhenius equation: k = Ae^(−Ea/RT). A graph of ln k against 1/T is a straight line with gradient −Ea/R.