According to the Arrhenius equation, if the activation energy Ea is lowered at the same temperature, what happens to the rate constant k?

• A. k decreases
• B. k increases
• C. k stays the same
• D. Cannot determine

Answer: (B)

At a fixed temperature, the rate constant depends on the activation energy through k = A exp(-Ea/RT). Lowering Ea makes the exponent -Ea/RT less negative, so the exponential term increases and k grows (assuming the pre-exponential factor A stays the same). Intuitively, a smaller energy barrier means more molecules have enough energy to react, speeding up the reaction. The math also shows this: d(ln k)/dEa = -1/(RT) < 0, so decreasing Ea increases k. Hence the rate constant increases.