## Half life

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

Dakota_Campbell_1C
Posts: 51
Joined: Fri Sep 28, 2018 12:15 am

### Half life

Where does the 0.693 come from in the half life equation for first order reactions. Will that value ever change? I just want to know where it comes from and why we use it.

Samantha Silva 1F
Posts: 37
Joined: Tue Feb 13, 2018 3:00 am

### Re: Half life

It is the natural logarithm of 2.

Brandon Mo 4K
Posts: 70
Joined: Fri Sep 28, 2018 12:15 am

### Re: Half life

Using the integrated rate law of the first order reactions: ln [A] = -k t + ln [A]o, you can solve for the half-life (t1/2) by setting [A]= (1/2)[A]o.

Eventually you get, t1/2 = ln(2)/k or 0.693/k.

Posts: 63
Joined: Fri Sep 28, 2018 12:19 am

### Re: Half life

After deriving the equation you are left with ln(2)/k.

Ricky Ma DIS 4E
Posts: 72
Joined: Fri Sep 28, 2018 12:27 am

### Re: Half life

What are the different kinds of answers that the half life equation can give us?