35.38 The activation energy for a reaction is 50. J mol^-1. Determine the effect

Question

35.38

The activation energy for a reaction is 50. J mol^-1. Determine the effect on the rate constant for this reaction with a change in temperature from 273 K to 298 K. The rate constant for the reaction of hydrogen with iodine is 2.45 times 10^-4 M^-1 s^-1 at 302 degree C and 0.950 M^-1 s^-1 at 508 degree C. a. Calculate the activation energy and Arrhenius preexponential factor for this reaction. b. What is the value of the rate constant at 400. degree C? Consider the gas phase thermal decomposition of 1.0 atm of(CH_3)_3COOC(CH_3)_3 (g) to acetone (CH_3)_2CO(g) and ethane (C_2H_6)(g). Which occurs with a rate constant of 0.0019 s^-1. After initiation of the reaction, at what time would you expect the pressure to be 1.8 atm?

Explanation / Answer

k1 = 2.5x10-4 Ms-1 at T1 =302C = 575 K

k2 = 0.950 Ms-1 at T2 = 508 C = 781 K

From Arrhenius equatoion

log (k2/k1) = [Ea/2.303R ] [1/T1 -1/T2]

log 0.95/2.45x10-4 = Ea/8.314J [1/575 -1/781]

thus Ea = 149787 J

= 149.787 kJ

From Arrhenius equation

log k1 = logA -Ea/RT1

log 2.45x10-4 = log A - (149787/8.314 x575)

   A= 5.23 x1027

Arrhenius factor = 5.23 x1027 at 575 K

b) k at 400K

log 0.95/K1 = [149787/2.303 x 8.314] [1/673 -1/781]

k1 =0.03=2347Ms-1

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