Question

The temperature dependence of the acid-catalysed hydrolysis of penicillin is investigated. This is a first order reaction that only depends on the concentration of the penicillin. The dependence of the rate constant, k, as a function of temperature is given in the following table:

Temperature (K)	k(s-1)
290	2.9e-5
320	2.61e-4

Determine the activation energy of this reaction. Express your answer in kJ mol-1 to the first decimal place (XX.X).

Determine the Arrhenius pre-factor, A for this reaction. Express your answer in s-1 to three significant figures (X.XXEX).

Answer 1

Initi al temperature, T 290 K Rate constant of the reaction at T,k = 2.9x10-5 s- Final temperature, T= 320 K Rate constant of the reacti on at T,,k, = 2.6x 104 s-1 Gas constant, R = 8.314 JKm ol1 1 1 According to Arhenius theory, In. RT T 2.6x10 2.9x10 1 1 S 8.314 JKmol290K 320K (3.233x10 K1 2.19 2. 8.314 JKmol- J 5.63x10 1 kJ Activation energy -X mol 103 J - 56.3 kJ/mol Initi al temperature, T 290 K Rate constant of the reaction at T,k = 2.9x10- s-1 Gas constant, R = 8.314x103 kJK-mol1 Activatati on of the reacti on, E = 56.3 kJ/mol -a Rate constant, k = Ae ke Arrhenius factor, A = 563 kJmol (8314*10* ык"то"\20 к) = (2.9x10 (2.9x103.3 -(29x10)1.38x10") = 4.0x 105 s- S