The activation energy of a chemical reaction is the minimum amount of energy required for the reactant molecules to undergo a chemical transformation and form products. It is an important parameter that determines the rate at which a reaction occurs.

To determine the activation energy of a chemical reaction, one method is to evaluate the rate constants at two different temperatures. This is the correct answer (option C) because it is based on the Arrhenius equation, which describes the relationship between the rate constant and temperature.

Here is a detailed explanation of why evaluating rate constants at two different temperatures helps determine the activation energy of a chemical reaction:

1. Arrhenius equation:
The Arrhenius equation is given by:
k = A * e^(-Ea/RT)
Where:
- k is the rate constant of the reaction,
- A is the pre-exponential factor or frequency factor,
- Ea is the activation energy,
- R is the gas constant, and
- T is the temperature in Kelvin.

2. Effect of temperature on rate constant:
According to the Arrhenius equation, the rate constant of a reaction is exponentially dependent on the temperature. As the temperature increases, the rate constant also increases.

3. Evaluating rate constants at two different temperatures:
By measuring the rate constants at two different temperatures, we can set up two equations using the Arrhenius equation. Let's assume the rate constants at temperature T1 and T2 are k1 and k2, respectively.

Using the Arrhenius equation for k1:
k1 = A * e^(-Ea/RT1)

Using the Arrhenius equation for k2:
k2 = A * e^(-Ea/RT2)

4. Taking the ratio:
Dividing the equation for k1 by the equation for k2 gives:
k1/k2 = (A * e^(-Ea/RT1)) / (A * e^(-Ea/RT2))
k1/k2 = e^((Ea/R)*((1/T2) - (1/T1)))

5. Simplifying the equation:
Taking the natural logarithm of both sides of the equation, we get:
ln(k1/k2) = (Ea/R)*((1/T2) - (1/T1))

6. Determining the activation energy:
By rearranging the equation, we can solve for Ea:
Ea = R * ((1/T2) - (1/T1)) * ln(k1/k2)

7. Conclusion:
By evaluating the rate constants at two different temperatures and using the Arrhenius equation, we can determine the activation energy of a chemical reaction. This method allows us to calculate the activation energy without directly measuring the reaction rate at different temperatures.