The Arrhenius equation primarily relates activation energy to what quantity?

The Arrhenius equation primarily relates activation energy to what quantity?

• A. Temperature
• B. Rate constant
• C. Collision frequency
• D. Equilibrium constant

Answer: (B)

Activation energy sets how big the rate constant will be for a given temperature. The Arrhenius equation, k = A e^{-Ea/(R T)}, shows this directly: the rate constant k depends on Ea through the exponential term. A higher activation energy makes the exponent more negative, reducing k and slowing the reaction at the same temperature; raising the temperature makes the exponent less negative, increasing k. This direct relationship is also seen when you take the natural log: ln k = ln A - Ea/(R T). Here, Ea appears as the slope when you plot ln k against 1/T, illustrating how Ea governs how sensitive the rate is to temperature. Temperature affects k as well, but Ea’s primary link is to the rate constant. Equilibrium constants are determined by thermodynamics and do not reflect this direct Ea–rate constant relationship.

Activation energy sets how big the rate constant will be for a given temperature. The Arrhenius equation, k = A e^{-Ea/(R T)}, shows this directly: the rate constant k depends on Ea through the exponential term. A higher activation energy makes the exponent more negative, reducing k and slowing the reaction at the same temperature; raising the temperature makes the exponent less negative, increasing k. This direct relationship is also seen when you take the natural log: ln k = ln A - Ea/(R T). Here, Ea appears as the slope when you plot ln k against 1/T, illustrating how Ea governs how sensitive the rate is to temperature. Temperature affects k as well, but Ea’s primary link is to the rate constant. Equilibrium constants are determined by thermodynamics and do not reflect this direct Ea–rate constant relationship.