For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter n is known to have a value of 1.7. If, after 100 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 99% completion

Given Information:

constant = n = 1.7

transformation time 50% completion = t₅₀ = 100 s

Required Information:

transformation time 99% completion = t₉₀ = ?

transformation time 99% completion =

Step-by-step explanation:

The Avrami equation is used to model the transformation of solids that is from one phase to another provided that temperature is constant.

The equation is given by

Where t is the transformation time in seconds and n, k are constants.

Let us first find the constant k, since after 100 s transformation is 50% complete,

Take ln on both sides,

Now we can find out the time when the transformation is 99% complete.

Take ln on both sides,

Again take ln on both sides

Take exponential on both sides

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step-by-step explanation: