Arrhenius equation
Summary
The Arrhenius equation, k = Ae^(−Ea/RT), gives a reaction's rate constant in terms of temperature and activation energy. Raising T or lowering Ea increases k, and k depends exponentially on T, not linearly.
Detail
Meaning: The equation links the rate constant k to the fraction of collisions that have at least the activation energy. A higher temperature puts more molecules above Ea, so k rises. A lower Ea, as with a catalyst, also raises k. A, the frequency (pre-exponential) factor, reflects collision frequency and proper orientation.
Equation: k = Ae^(−Ea/RT), where k is the rate constant (units depend on reaction order), A is the frequency factor (same units as k), Ea is the activation energy (J/mol), R is the gas constant (8.314 J/(mol·K)), and T is the absolute temperature (K). Linear form: ln k = ln A − Ea/(RT).
On the MCAT: Passages give rate constants at two temperatures and ask you to compare them, or ask how a catalyst or a temperature change affects k. A plot of ln k versus 1/T is a straight line with slope −Ea/R and intercept ln A. A steeper negative slope means a larger Ea, so the rate is more sensitive to temperature. Changing reactant concentration does not change k.
Common confusion: Students often assume that doubling T doubles k, or they put T in °C. T must be in kelvin, and the dependence is exponential. Raising T increases k for both endothermic and exothermic reactions. Ea controls how fast equilibrium is reached, not where it lies.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- Physical Chemistry (Atkins)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.