second order
Summary
A second-order reaction has a rate law whose concentration exponents add to 2, such as rate = k[A]² or rate = k[A][B]. Most testable: for rate = k[A]², a plot of 1/[A] versus time is a straight line with slope k, and k has units M⁻¹s⁻¹.
Detail
Meaning: A second-order reaction has an overall order of 2: the exponents on the concentration terms in the experimentally determined rate law add to 2. It may be rate = k[A]² or rate = k[A][B]. For rate = k[A]², doubling [A] quadruples the rate.
Equation: 1/[A] = 1/[A]₀ + kt, for rate = k[A]². [A] is concentration at time t (M), [A]₀ is initial concentration (M), k is the rate constant (M⁻¹s⁻¹), and t is time (s). Half-life: t½ = 1/(k[A]₀), in s.
On the MCAT: Initial-rate tables: compare trials to find each exponent. Graphs: a straight line of 1/[A] versus t signals second order, with slope k (ln[A] versus t is linear for first order, and [A] versus t for zero order). The units of k, M⁻¹s⁻¹, also reveal the order.
Common confusion: Order comes from experiment, not from the coefficients in the balanced equation (except for a single elementary step). Also, the half-life of a second-order reaction is not constant: it lengthens as [A] falls, unlike first order.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.