## Half-life Clarification

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

Rogelio Bazan 1D
Posts: 64
Joined: Tue Nov 14, 2017 3:01 am

### Half-life Clarification

To clarify my notes from the lecture, there is a different half-life equation based on which Reaction Order that we are dealing with? For example, zero order has its own half-life equation so on and so forth? Thank you.

Emma Scholes 1L
Posts: 62
Joined: Fri Sep 28, 2018 12:18 am

### Re: Half-life Clarification

Yes. The half life equation depends on the reaction order.

Brian Hom 2F
Posts: 60
Joined: Fri Sep 28, 2018 12:24 am

### Re: Half-life Clarification

Yes, each order has its own half life equation, because each order has different rates. However, in all the types of orders for reactions, the higher the k, the faster the rate.

Melody P 2B
Posts: 35
Joined: Fri Sep 29, 2017 7:06 am

### Re: Half-life Clarification

Yes, because the half life equations are derived from the integrated rate laws. And the integrated rate laws differ in terms of reaction order.

This should help!
Last edited by Melody P 2B on Mon Mar 11, 2019 2:53 pm, edited 2 times in total.

Rachel-Weisz3C
Posts: 66
Joined: Fri Sep 28, 2018 12:23 am

### Re: Half-life Clarification

Yes. Each rate law has its own equation for 1/2 life. For example, the half-life for the 1st order is $t\frac{1}{2}=\frac{0.693}{k}$ and the half-life for 2nd order is $t\frac{1}{2} = \frac{1}{k[A]}$.

Posts: 59
Joined: Fri Apr 06, 2018 11:04 am

### Re: Half-life Clarification

Yes, and these are the equations I found:
For a zero order reaction A products , rate = k:
t½ = [Ao] / 2k
For a first order reaction A products , rate = k[A]:
t½ = 0.693 / k
For a second order reaction 2A products or A + B products (when [A] = [B]), rate = k[A]2:
t½ = 1 / k [Ao]