Considering the Arrhenius equation, which of the following changes will increase the rate constant k for a chemical reaction?

• A. Decreasing the frequency factor A
• B. Decreasing the temperature
• C. Increasing the activation energy
• D. Increasing the temperature

Answer: (D)

Verified step by step guidance

1. Recall the Arrhenius equation, which relates the rate constant \(k\) to temperature \(T\), activation energy \(E_a\), and frequency factor \(A\): \[k = A \times e^{-\frac{E_a}{RT}}\] where \(R\) is the gas constant.
2. Understand the role of each parameter: - \(A\) (frequency factor) represents the frequency of collisions with proper orientation. - \(E_a\) (activation energy) is the minimum energy required for the reaction to proceed. - \(T\) (temperature) affects the exponential term, influencing how many molecules have enough energy to overcome \(E_a\).
3. Analyze the effect of decreasing the frequency factor \(A\): Since \(k\) is directly proportional to \(A\), decreasing \(A\) will decrease \(k\), so this change will not increase the rate constant.
4. Analyze the effect of decreasing the temperature \(T\): Since \(T\) appears in the denominator of the exponent, decreasing \(T\) makes the exponent more negative, thus decreasing \(k\). So, decreasing temperature lowers the rate constant.
5. Analyze the effect of increasing the activation energy \(E_a\): Increasing \(E_a\) makes the exponent more negative, which decreases \(k\). Therefore, increasing \(E_a\) lowers the rate constant. Conversely, increasing temperature \(T\) reduces the magnitude of the negative exponent, increasing \(k\).