Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
Using the Arrhenius Equation, what is the rate constant at 40°C for the reaction: Fe(phen)3 2+ + 3 H3O+ + 3 H2O → Fe(H2O)6 2+ + 3 phenH+, given that the activation energy, Ea, is 126 kJ/mol and the rate constant at 30°C is 9.8 × 10^-3 s^-1?
A
9.8 × 10^-3 s^-1
B
8.5 × 10^-3 s^-1
C
1.2 × 10^-2 s^-1
D
1.5 × 10^-2 s^-1
Verified step by step guidance
1
Identify 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, and \( T \) is the temperature in Kelvin.
Use the two-point form of the Arrhenius Equation to find the new rate constant: \( \ln \left( \frac{k_2}{k_1} \right) = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \), where \( k_1 \) and \( k_2 \) are the rate constants at temperatures \( T_1 \) and \( T_2 \) respectively.
Convert the temperatures from Celsius to Kelvin: \( T_1 = 30^\circ C + 273.15 = 303.15 \ K \) and \( T_2 = 40^\circ C + 273.15 = 313.15 \ K \).
Substitute the known values into the equation: \( \ln \left( \frac{k_2}{9.8 \times 10^{-3}} \right) = -\frac{126000}{8.314} \left( \frac{1}{313.15} - \frac{1}{303.15} \right) \).
Solve for \( k_2 \) by calculating the right-hand side of the equation and then exponentiating to find \( k_2 \).