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15.35

Posted: Tue Feb 21, 2017 1:17 am
by Christina_F_3F
"The half-life for the second order reaction of a substance A is 50.5 s when [A]naught=0.84 M. Calculate the time needed for concentration of A to decrease to a) one sixteenth, b) one-fourth, c) one-fifth it's original value."
For this question, after looking at the solutions manual, I could pretty easily see the pattern of what you're supposed to do. For example, for a) you would write:
T= (16/[A]naught - 1/[A]naught) / k
What I don't understand, however, is why this equation works, and why you would write the equation this way.
If anyone could explain this I would much appreciate it.
Thank you!

Re: 15.35

Posted: Tue Feb 21, 2017 10:42 pm
by Anna_Kim_2E
For second order, -d[A]/dt = k[A]^2 . Integration of both sides results in an equation 1/[A] = kt + 1/[A]0. Hence, in order to find out for the half life, we use this equation when it is in second order.