According to the Arrhenius equation, what happens to the rate constant k as the activation energy (E_a) increases, assuming temperature remains constant?

• A. The rate constant increases.
• B. The rate constant first increases, then decreases.
• C. The rate constant decreases.
• D. The rate constant remains unchanged.

Answer: (C)

Verified step by step guidance

1. Recall the Arrhenius equation, which relates the rate constant \(k\) to the activation energy \(E_a\) and temperature \(T\): \[k = A \times e^{-\frac{E_a}{RT}}\] where \(A\) is the frequency factor, \(R\) is the gas constant, and \(T\) is the absolute temperature.
2. Understand that the exponential term \(e^{-\frac{E_a}{RT}}\) controls how \(k\) changes with \(E_a\). Since \(E_a\) is in the numerator of the exponent with a negative sign, increasing \(E_a\) makes the exponent more negative.
3. Because the exponent becomes more negative as \(E_a\) increases, the value of \(e^{-\frac{E_a}{RT}}\) decreases, which means the rate constant \(k\) decreases.
4. Note that temperature \(T\) is held constant in this problem, so the only variable affecting \(k\) in the exponential term is \(E_a\).
5. Therefore, as the activation energy \(E_a\) increases at constant temperature, the rate constant \(k\) decreases, meaning the reaction rate slows down.