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a) If a first-order reaction has an activation energy of 104.6 kJ/mol and, in th

ID: 916255 • Letter: A

Question

a) If a first-order reaction has an activation energy of 104.6 kJ/mol and, in the equation k = k0 exp (-Ea/RT), k0 has a value of 5×1013/s, at what temperature will the reaction have a half-life of (i) 1 h; (ii) 1 day? [Note: the value of R is 8.314 kJ/kmol·K.] (b) If the sterilization of a biomaterial was heating at 121°C for 5 min, it could only be heated at 111°C due to the failure of the heating system. How long should the biomaterial be heated at this lower temperature assuming the Ea/R of this first order sterilization process is 35,751 K.

Explanation / Answer

t1/2 = 1 h = 3600 sec

k = 0.693 / t1/2

    = 0.693 / 3600

     = 1.925 x 10^-4 s-1

k = k0 exp (-Ea/RT)

1.925 x 10^-4 = 5×10^13 x exp (- 104.6 / (8.314 x 10^-3) x T)

T = 313.76 K

Temperature = 313.76 K

2)

t1/2 = 1 day = 86400 sec

k = 0.693 / t1/2

    = 0.693 / 86400

     = 8.021 x 10^-6 s-1

k = k0 exp (-Ea/RT)

8.021 x 10^-6 = 5×10^13 x exp (- 104.6 / (8.314 x 10^-3) x T)

T = 290.7 K

Temperature = 290.7 K