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Multiple Choice
A reaction is found to have an activation energy of 38.0 kJ/mol. If the rate constant for this reaction is 1.60 x 10^2 M^-1s^-1 at 249 K, what is the rate constant at 436 K according to the Arrhenius Equation?
A
2.00 x 10^2 M^-1s^-1
B
4.50 x 10^3 M^-1s^-1
C
3.20 x 10^3 M^-1s^-1
D
1.60 x 10^2 M^-1s^-1
Verified step by step guidance
1
Identify the given values: activation energy (Ea) = 38.0 kJ/mol, initial rate constant (k1) = 1.60 x 10^2 M^-1s^-1, initial temperature (T1) = 249 K, and final temperature (T2) = 436 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: \( \ln \left( \frac{k_2}{1.60 \times 10^2} \right) = \frac{-38000}{8.314} \left( \frac{1}{436} - \frac{1}{249} \right) \).
Solve for \( k_2 \) by calculating the right side of the equation, then exponentiating both sides to isolate \( k_2 \).