The temperature dependence of the rate constant ( k ) for a chemical reaction is given by the empirical equation: k = 10 - 5000 T where T is the temperature in Kelvin. Based on the Arrhenius equation, the pre-exponential factor ( A ) and the activation energy ( E_a ) for this reaction are respectively:

Step-by-step solution

The standard logarithmic form of the Arrhenius equation is: k = A - E_a RT The given empirical equation is: k = 10 - 5000 T Comparing the two equations term by term: 1) Intercept: A = 10 A = e¹⁰ 2) Slope term: E_a RT = 5000 T E_a R = 5000 E_a = 5000 R Thus, the pre-exponential factor is e¹⁰ and the activation energy is 5000 R . Answer: A = e¹⁰ , E_a = 5000 R