first order

Meaning: A reaction is first order in a reactant when its rate depends on that concentration to the first power. As the reactant is used up, the rate falls in proportion, so [A] decays exponentially. Radioactive decay follows the same pattern.

Equation: rate = k[A], and ln[A] = ln[A]₀ − kt, with t½ = 0.693/k. Here [A] is the concentration at time t (mol/L), [A]₀ is the starting concentration (mol/L), k is the rate constant (s⁻¹), t is time (s), and t½ is the half-life (s). The number 0.693 is ln 2.

On the MCAT: You may get a table of initial rates from several trials. If doubling one concentration doubles the rate, the reaction is first order in that reactant. You may instead get concentration-versus-time data or a graph. A straight line on a plot of ln[A] versus t, with slope −k, signals first order. A concentration that halves in each equal time interval also signals first order. Calculations often use the half-life: after n half-lives, the fraction remaining is (1/2)ⁿ.

Common confusion: Students read the order from the coefficients of the balanced equation. The order must be found from experiment. Only for an elementary step does it match the molecularity. Also, a constant half-life belongs to first-order reactions only. For zero-order and second-order reactions, the half-life depends on the starting concentration.