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Multiple Choice
A reaction is found to have an activation energy of 108 kJ/mol. If the rate constant for this reaction is 4.60 × 10⁻⁶ s⁻¹ at 275 K, what is the rate constant at 366 K according to the Arrhenius Equation?
A
7.89 × 10⁻⁵ s⁻¹
B
1.23 × 10⁻⁴ s⁻¹
C
3.45 × 10⁻⁶ s⁻¹
D
9.01 × 10⁻⁷ s⁻¹
Verified step by step guidance
1
Identify the given values: Activation energy (Ea) = 108 kJ/mol, initial rate constant (k1) = 4.60 × 10⁻⁶ s⁻¹, initial temperature (T1) = 275 K, and final temperature (T2) = 366 K.
Convert the activation energy from kJ/mol to J/mol by multiplying by 1000, since the Arrhenius equation requires energy in J/mol.
Use the Arrhenius equation in its two-point form: \( \ln \left( \frac{k_2}{k_1} \right) = \frac{-E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \), where R is the gas constant (8.314 J/mol·K).
Substitute the known values into the equation: \( \ln \left( \frac{k_2}{4.60 \times 10^{-6}} \right) = \frac{-108000}{8.314} \left( \frac{1}{366} - \frac{1}{275} \right) \).
Solve for \( k_2 \) by calculating the right-hand side of the equation, then exponentiating both sides to isolate \( k_2 \).