When given t_1/2

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Casey Collet 1I
Posts: 23
Joined: Fri Sep 26, 2014 2:02 pm

When given t_1/2

Postby Casey Collet 1I » Sun Feb 22, 2015 5:59 pm

If on a test we were given the half life of a first order reaction and asked to find the time needed for the concentration to decrease and the time given is not a multiple of one half in terms of integers, could we use (1/2)^n=time given and find n using natural logs? For example, problem 14.27 part c asks how long it would take the initial concentration to reach 15% and using (1/2)^n=.15 gives the same answer as the solution manual.

Neil DSilva 1L
Posts: 70
Joined: Fri Sep 26, 2014 2:02 pm

Re: When given t_1/2

Postby Neil DSilva 1L » Sun Feb 22, 2015 6:59 pm

Since the logic for your method is the same as the logic used in parts a and b, I believe you could use your method to solve a problem like that. But I believe you mixed up the equation in your description. (so the ratio of final concentration to initial concentration or the percent of initial concentration after time has passed) and not the time given. But then yes, you would solve for n using ln and multiply that by the half-life to get the time.

Also, just as a sidenote: this would only work for first-order half-life equations.

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