Question

The Activation energy for the reaction A $\rightarrow$ B + C, at a temperature $T_K$ was 0.04606 RT J/mol. What is the ratio of Arrhenius factor to the Rate constant for this reaction?

• A. 1.585
• B. 3.2 \times 10^{-2}
• C. 1.047 \times 10^{-2}
• D. 1.047

Hint:

When dealing with the Arrhenius equation, you can find the ratio of the Arrhenius factor to the rate constant by using the exponential relationship involving activation energy.

Answer 1

The Correct Option is D

The Arrhenius equation is given by: \[ k = A \exp \left( - \frac{E_a}{RT} \right) \] where \( k \) is the rate constant, \( A \) is the Arrhenius factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. To find the ratio of the Arrhenius factor to the rate constant, we can use the given activation energy expression: \[ E_a = 0.04606 RT \quad \text{(where \( R = 8.314 \, \text{J/mol·K} \))} \] The rate constant at temperature \( T_K \) is: \[ k = A \exp \left( - \frac{0.04606 RT}{RT} \right) = A \exp (-0.04606) \] The ratio of the Arrhenius factor to the rate constant is: \[ \frac{A}{k} = \frac{A}{A \exp (-0.04606)} = \exp (0.04606) \approx 1.047 \]
Thus, the ratio of the Arrhenius factor to the rate constant is approximately 1.047.