Multiple Choice
Considering the Arrhenius equation, which of the following changes will increase the rate constant k for a chemical reaction?
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15. Chemical Kinetics
Arrhenius Equation
Multiple Choice
A reaction with an activation energy Ea = 55.00 kJ/mol is run at temperature of 30ºC. Determine the temperature required to increase the rate constant 3 times.
A
319 K
B
46 K
C
288.6 K
D
303 K
Verified step by step guidance1
Convert the initial temperature from Celsius to Kelvin by adding 273.15 to the given temperature: T1 = 30 + 273.15 K.
Use the Arrhenius equation in its logarithmic form to relate the rate constants at two different temperatures: ln(k2/k1) = (Ea/R) * (1/T1 - 1/T2), where k2 is the new rate constant, k1 is the initial rate constant, Ea is the activation energy, R is the gas constant (8.314 J/mol·K), T1 is the initial temperature, and T2 is the final temperature.
Since the rate constant is to be increased 3 times, set k2/k1 = 3.
Rearrange the equation to solve for T2: 1/T2 = 1/T1 - (R/Ea) * ln(3).
Substitute the known values into the equation: Ea = 55000 J/mol (since 1 kJ = 1000 J), R = 8.314 J/mol·K, and T1 from step 1. Solve for T2 to find the required temperature in Kelvin.
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