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Multiple Choice
If an increase in temperature from 25°C to 35°C doubles the reaction rate constant, what is the activation energy of the reaction? Assume the Arrhenius equation applies.
A
Approximately 104 kJ/mol
B
Approximately 13 kJ/mol
C
Approximately 52 kJ/mol
D
Approximately 26 kJ/mol
Verified step by step guidance
1
Start by recalling the Arrhenius equation: \( k = A e^{-\frac{E_a}{RT}} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin.
Since the rate constant doubles when the temperature increases from 25°C to 35°C, set up the ratio of the rate constants: \( \frac{k_2}{k_1} = 2 \).
Convert the temperatures from Celsius to Kelvin: \( T_1 = 25 + 273.15 = 298.15 \) K and \( T_2 = 35 + 273.15 = 308.15 \) K.
Use the Arrhenius equation in the form of \( \ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \) to solve for the activation energy \( E_a \).
Substitute the known values into the equation: \( \ln(2) = \frac{E_a}{8.314} \left( \frac{1}{298.15} - \frac{1}{308.15} \right) \) and solve for \( E_a \).