For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter n is known to have a value of 1.8. If, after 148 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 85% completion?

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