Question

For some transformation having kinetics that obey the Avrami equation , the parameter n is known to have a value of 1.1. If, after 114 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 87% completion
y = 1 - exp(-kt^n)

Answer 1

Answer:

total time  = 304.21 s

Explanation:

given data

y = 50% = 0.5

n = 1.1

t = 114 s

y = 1 - exp(-kt^n)

solution

first we get here k value by given equation

y = 1 - $e^{(-kt^n)}$   ...........1    

put here value and we get

0.5 = 1 - e^{(-k(114)^{1.1})}    

solve it we get

k = 0.003786  = 37.86 × $10^{4}$

so here

y = 1 - $e^{(-kt^n)}$

1 - y  =  $e^{(-kt^n)}$

take ln both side

ln(1-y) = -k × $t^n$  

so

t = $\sqrt[n]{-\frac{ln(1-y)}{k}}$    .............2

now we will put the value of y = 87% in equation  with k and find out t

t = $\sqrt[1.1]{-\frac{ln(1-0.87)}{37.86*10^{-4}}}$

total time  = 304.21 s