## half life calculations

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

Sarah Blake-2I
Posts: 153
Joined: Fri Aug 30, 2019 12:16 am

### half life calculations

How do half life calculations differ between zero order, first order, and second order reactions? Also, how would you find the quarter life of a reaction?

VPatankar_2L
Posts: 104
Joined: Thu Jul 25, 2019 12:17 am
Been upvoted: 1 time

### Re: half life calculations

The integrated rate law for the zero order reaction is [A] = - k t + [A]0. When t=t1/2, we can substitute this value into the equation to get [A] at t1/2 = -k(t1/2) + [A]o. So t1/2 = [A]o / 2 k. The integrated rate law for first order reaction is ln [A] = -k t + ln [A]o. When t = t1/2 we can substitute this value into the equation to get ln [A at t1/2] = -kt1/2 + ln [Ao] where the ratio of [A at t1/2] to [Ao] is 1/2. So t1/2 = 0.693/k. The integrated rate law for a second order reaction is (1/[A]) = k t + (1/[A]o). when t=t1/2 is subsituted fot t, we get (1/[A at t1/2]) = k t1/2 + (1/[A]o). So t1/2 = 1/k [A]o. to find the quarter life of a reaction, depending on the order of the reaction, you would plug in the inital concentrtaion for Ao and the concentration at t=t1/4 for A.

smurphy1D
Posts: 51
Joined: Mon Nov 18, 2019 12:18 am

### Re: half life calculations

Quarter life of a reaction would be essentially the same as a half life, but anywhere you would put 1/2 in the equation would be replaced with 1/4

Miriam Villarreal 1J
Posts: 105
Joined: Sat Aug 17, 2019 12:16 am

### Re: half life calculations

the half-life of zero order reaction decrease as the concentration decrease
the half life of a first order reaction is independent of its initial concentration.
the half-life of a second order reaction only depends on the initial concentration and the rate constant.