## When given t_1/2

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

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

### When given t_1/2

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

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. $(\frac{1}{2})^{n} = \frac{[A]}{[A]_{0}}$ (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.

### Who is online

Users browsing this forum: No registered users and 1 guest