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Multiple Choice
The rate constant for a reaction is 1 × 10⁻³ M sec⁻¹ at 27°C and the Arrhenius frequency factor is 3500 sec⁻¹. What is the activation energy?
A
37.33 kJ
B
0.0141 J
C
3.13 kJ
D
21.17 kJ
Verified step by step guidance
1
Identify the Arrhenius equation: \( k = A e^{-\frac{E_a}{RT}} \), where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = 27 + 273.15 \).
Rearrange the Arrhenius equation to solve for the activation energy \( E_a \): \( E_a = -RT \ln\left(\frac{k}{A}\right) \).
Substitute the known values into the equation: \( R = 8.314 \text{ J/mol K} \), \( k = 1 \times 10^{-3} \text{ M sec}^{-1} \), \( A = 3500 \text{ sec}^{-1} \), and the calculated \( T \) in Kelvin.
Calculate the natural logarithm \( \ln\left(\frac{k}{A}\right) \), then multiply by \(-RT\) to find the activation energy \( E_a \) in Joules, and convert it to kilojoules if necessary.