Final answer:
To determine the activation energy for a reaction, we can use the Arrhenius equation. By using two sets of temperature and their corresponding rate constants, we can calculate the activation energy using logarithmic equations.
Step-by-step explanation:
In order to determine the activation energy for a reaction, we need to use the Arrhenius equation which relates the rate constant (k) to the temperature (T). The equation is given as: k = Ae^(-Ea/RT), where A is the frequency factor, Ea is the activation energy, R is the gas constant (8.314 J/Kmol), and T is the temperature in Kelvin.
Using the given data, let's assume we have two sets of temperature (T1 and T2) and their corresponding rate constants (k1 and k2). We can set up two equations using the Arrhenius equation:
(1) k1 = A * e^(-Ea/(R * T1))
(2) k2 = A * e^(-Ea/(R * T2))
By taking the natural logarithm of both equations and solving for Ea, we can find the value of the activation energy. Let's do the calculations using the given data:
ln(k1) = ln(A * e^(-Ea/(R * T1))) = ln(A) - Ea/(R * T1)
ln(k2) = ln(A * e^(-Ea/(R * T2))) = ln(A) - Ea/(R * T2)
Let's substitute the values of ln(k1), ln(k2), and the corresponding temperatures into the equations and solve for Ea.