## Half-life

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

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

### Half-life

As I am going through Kinetics in the textbook I am still having trouble understanding Half-life. If someone can help me clarify the concepts to Half-life and the equation(s) involved it would be of great help. Thank you.

aisteles1G
Posts: 117
Joined: Fri Sep 28, 2018 12:15 am

### Re: Half-life

Half life is referring the time it takes for half of the current sample to die, so its not a set amount of substance that will die since 1/2 of 200 is different than 1/2 of 300 but the time for the half of the material to 'die' is the same regardless of the initial amount so t1/2 (half life) is a constant for a specific substance. Therefore we can use it to figure out the initial or final concentrations.
Use t1/2=Ln(2)/kr for zero order reactions so either find the half life or Kr, then you can plug the kr or t1/2, in for time, into the other equations to get [A], hope this helps!

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

### Re: Half-life

These are the equations I found for Half Lives:
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]

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

### Re: Half-life

Thank you so much, this is really helpful. So just to clarify, according to which order reaction we are dealing with we use the corresponding equation.
For example) zero order; rate = k: t½ = [Ao] / 2k, first order; rate = k[A]: t½ = 0.693 / k, second order; rate = k[A]2: t½ = 1 / k [Ao]

JT Wechsler 2B
Posts: 62
Joined: Fri Sep 28, 2018 12:16 am

### Re: Half-life

The half life is the amount of time that it takes for half of a sample to die off. This can be taken with respect to radioactive isotopes or even (like in our case) the amount of time for a certain reactant to decrease by half.