This question is incomplete, the complete question is;
For some transformation having kinetics that obey the Avrami equation, the parameter n is known to have a value of 2. If, after 100 s, the reaction is 40% complete, how long (total time in seconds) will it take the transformation to go to 95% completion
y = 1 - exp( -ktⁿ )
Answer: the time required for 95% transformation is 242.17 s
Explanation:
First, we calculate the value of k which is the dependent variable in Avrami equation
y = 1 - exp( -ktⁿ )
exp( -ktⁿ ) = 1 - y
-ktⁿ = In( 1 - y )
k = - In( 1 - y ) / tⁿ
now given that; n = 2, y = 40% = 0.40, and t = 100 s
we substitute
k = - In( 1 - 0.40 ) / 100²
k = - In(0.60) / 10000
k = 0.5108 / 10000
k = 0.00005108 ≈ 5.108 × 10⁻⁵
Now calculate the time required for 95% transformation
tⁿ = - In( 1 - y ) / k
t = [- In( 1 - y ) / k ]^1/n
n = 2, y = 95% = 0.95 and k = 5.108 × 10⁻⁵
we substitute our values
t = [- In( 1 - 0.95 ) / 5.108 × 10⁻⁵ ]^1/2
t = [2.9957 / 5.108 × 10⁻⁵]^1/2
t = [ 58647.22 ]^1/2
t = 242.17 s
Therefore the time required for 95% transformation is 242.17 s
