Question

For some transformation having kinetics that obey the Avrami equation y = 1 - e⁻ᵏᵗⁿ 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?

Answer 1

To solve for the total time for a transformation to reach 99% completion with n=1.7, we use the given 50% completion time at 100 seconds to find the rate constant k and then solve for t when the reaction is 99% complete using the Avrami equation.

Step-by-step explanation:

To determine the total time for a transformation that follows the Avrami equation (y = 1 - e-ktn) when n is 1.7, we need to solve for the time when the reaction is 99% complete. Given that at 100 seconds the reaction is 50% complete, we can set up the equation for the 50% completion point: 0.5 = 1 - e-k(100)1.7. Solving for k, we get:

k = -(ln(1 - 0.5)/(1001.7))

We then use this k value to find the time when the reaction is 99% complete by setting up the equation: 0.99 = 1 - e-kt1.7. Substituting our value for k and solving for t, we get the total time for 99% completion.

The necessary steps involve using natural logarithms (ln) and algebraic manipulations to solve for t. This process employs mathematical operations within the field of physical chemistry, specifically involving reaction kinetics.