Which of the following methods is most appropriate for determining the activation energy of the redox reaction q^{2+} + 2 r^{+} ightarrow q^{0} + 2 r^{2+}?

• A. Determine the enthalpy change using a calorimeter.
• B. Balance the redox equation and count the number of electrons transferred.
• C. Measure the rate constant at different temperatures and use the Arrhenius equation.
• D. Calculate the difference in standard reduction potentials of q and r.

Answer: (C)

Verified step by step guidance

1. Understand that activation energy (Ea) is a kinetic parameter that describes the minimum energy required for a reaction to proceed, and it is not directly related to thermodynamic quantities like enthalpy or standard reduction potentials.
2. Recognize that methods involving calorimetry or standard reduction potentials provide thermodynamic information (enthalpy change or cell potential), but do not give direct information about the activation energy.
3. Recall that the activation energy can be determined experimentally by measuring the rate constant (k) of the reaction at different temperatures.
4. Use the Arrhenius equation, which relates the rate constant to temperature and activation energy: \[k = A \cdot e^{-\frac{E_a}{RT}}\] where \(A\) is the frequency factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.
5. Plotting \(\ln(k)\) versus \(\frac{1}{T}\) gives a straight line whose slope is \(-\frac{E_a}{R}\). From this slope, calculate the activation energy \(E_a\).