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Multiple Choice
The activation energy for a first-order reaction is 26.5 kJ/mol. At 10.0°C, the rate constant is 0.020 s⁻¹. Calculate the temperature at which the rate constant is 0.040 s⁻¹ using the Arrhenius Equation.
A
20.0°C
B
25.0°C
C
30.0°C
D
35.0°C
Verified step by step guidance
1
Start by understanding the Arrhenius Equation, which is used to calculate the rate constant of a reaction at different temperatures. The equation is: , where is the rate constant, is the pre-exponential factor, is the activation energy, and is the gas constant.
Use the Arrhenius Equation in its logarithmic form to compare the rate constants at two different temperatures: . For two temperatures, this can be rearranged to: .
Substitute the given values into the equation. You have = 0.020 s⁻¹ at = 10.0°C (convert to Kelvin by adding 273.15), and = 0.040 s⁻¹. The activation energy is 26.5 kJ/mol, which should be converted to J/mol (multiply by 1000).
Calculate the difference in the natural logarithms of the rate constants: . Then, rearrange the equation to solve for the unknown temperature .
Finally, solve for using the rearranged equation. Remember to convert the temperature back to Celsius if needed by subtracting 273.15 from the Kelvin result.