Question

For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter n is known to have a value of 2.1. If, after 146 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 86% completion?

Answer 1

Answer:

t = 25.10 sec

Explanation:

we know that Avrami equation

$Y = 1 - e^{-kt^n}$

here Y is percentage of completion  of reaction = 50%

t  is duration of reaction = 146 sec

so,

$0.50 = 1 - e^{-k^146^2.1}$

$0.50 = e^{-k306.6}$

taking natural log on both side

ln(0.5) = -k(306.6)

$k = 2.26\times 10^{-3}$

for 86 % completion

$0.86 = 1 - e^{-2.26\times 10^{-3} \times t^{2.1}}$

$e^{-2.26\times 10^{-3} \times t^{2.1}} = 0.14$

$-2.26\times 10^{-3} \times t^{2.1} = ln(0.14)$

$t^{2.1} = 869.96$

t = 25.10 sec