Calculate the rate of some reaction that obeys Avrami kineti

Calculate the rate of some reaction that obeys Avrami kinetics, assuming that the constants n and k have values of 2.0 and 0.009, respectively, for time expressed in seconds.

Solution

The rate of reaction is computed using

rate =1/t_0.5

Therefore it is first necessary to determine t_0.5, or the time necessary for the reaction to reach y = 0.5.

Using- exp(-ktⁿ) = 1 - y

taking log on both sides

-ktⁿ = 1 - y

t ⁿ = -ln (1 - y)/k

   t   = (-ln (1 - y)/k) ^1/n

   t _0.5 =(-ln (1 - 0.5)/k) ^1/n

Using k= 0.009, n=2.0

t _0.5 =(-ln (1 - 0.5)/0.009) ^1/2 = 8.776 seconds

   rate of reaction =1/t_0.5 = 1/8.776 = 0.114 s^-1