rate constants
Summary
A rate constant, k, is the proportionality constant in a rate law, linking reaction rate to reactant concentrations. It does not change as concentrations change, but it increases with temperature or with a catalyst that lowers activation energy.
Detail
Meaning: The rate constant k is the proportionality constant in a rate law, rate = k[A]ᵐ[B]ⁿ. It is fixed for a given reaction at a given temperature, and a larger k means a faster reaction at the same concentrations. k rises with temperature and falls as activation energy rises; a catalyst raises k by lowering activation energy. Units depend on overall order: M/s (zero), s⁻¹ (first), M⁻¹s⁻¹ (second).
Equation: k = Ae^(−Ea/RT), where A is the frequency factor (same units as k), Ea is activation energy (J/mol), R is 8.314 J/(mol·K), and T is temperature (K).
On the MCAT: Passages give initial rates for several trials. Compare trials to find the orders, then solve for k and its units. Units alone reveal the overall order. Other questions ask how k changes with temperature or a catalyst, or use t½ = 0.693/k for first-order reactions.
Common confusion: Students think k falls as reactant is used up. The rate falls because concentrations fall, but k stays constant unless conditions such as temperature or a catalyst change. Also, a catalyst raises the forward and reverse constants alike, so Keq = kf/kr (for an elementary step) is unchanged.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- General Chemistry (Petrucci)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.