Respuesta :
Answer:
t = 259.04 sec
Explanation:
from Avrami equation we have
Y= 1 - e^{-Kt^n}
here
Y = 50%
T Time of reaction completion = 148 sec
n = 1.8
putting all value to get constant K
0.5=1- e^{-K*148^1.8}
e^{-K*148^1.8} = 0.5
Taking log on both side
-K*148^{1.8} = -0.693
K=8.59 * 10^{-5}
NOW GIVEN
0.85= 1 - e^{- 8.59 * 10^{-5} *t^1.8}
e^{- 8.59 * 10^{-5} *t^1.8} = 0.15
Taking log on both side
- 8.59 * 10^{-5} *t^1.8 = -1.897
t = 259.04 sec
The total amount of time it will take the transformation to go to 85% completion is equal to 267.34 seconds.
Given the following data:
- n = 1.8.
- Time = 148 seconds.
- y = 50% = 0.5.
What is Avrami equation?
The Avrami equation was derived by Johnson Mehl Avrami and it is used to describe how crystallized solids are transformed from one phase to another at constant temperature.
How to calculate the constant (k).
Mathematically, the Avrami equation is given by:
[tex]y=1 - e^{-Kt^n} \\\\e^{-Kt^n}=1-y\\\\-kt^n=ln(1-y)\\\\kt^n=-ln(1-y)\\\\k=\frac{-ln(1-y)}{t^n}[/tex]
Substituting the given parameters into the formula, we have;
[tex]k=\frac{-ln(1-0.5)}{148^{1.8}} \\\\k=\frac{-ln(0.5)}{8062.53}\\\\k=\frac{-(-0.6932)}{8062.53}\\\\k=\frac{0.6932}{8062.53}\\\\k=8.60 \times 10^{-5}[/tex]
At 85% completion, the total time is given by:
[tex]y=1 - e^{-Kt^n} \\\\t=n\sqrt{\frac{-ln(1-y)}{k} } \\\\t=1.8\sqrt{\frac{-ln(1-0.85)}{8.6 \times 10^{-5}} } \\\\t=1.8\sqrt{\frac{-ln(0.15)}{8.6 \times 10^{-5}} }\\\\t=1.8\sqrt{\frac{-(-1.8971)}{8.6 \times 10^{-5}} }\\\\t=1.8\sqrt{22059.53}\\\\t=1.8 \times 148.53[/tex]
Time, t = 267.34 seconds.
Read more on Avrami equation here: https://brainly.com/question/15567509
