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.

Answer 1

k = k0 exp (-Ea/RT),

activation energy,Ea is of 104.6 kJ/mol.

k0 = 5×1013/s,

R = 8.314 kJ/kmol·K.]

Using Arrhenius Equation,

Use the equation

ln(k₁/k₂)=-Ea/R(1/T₁-1/T₂)

To find the new temperature if the rate constant at that temperature is 15M^-1s^-1 while at temperature 389K the rate constant is 7M^-1s^1,

Substitute the values in the equation to find the temperature,

ln(15/7)=-[(104.6 X 1000)/8.314](1/T₁ - 1/389)

T₁ = 390.6K