### Half life

Posted:

**Fri Mar 15, 2019 1:55 am**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.

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=148&t=44664

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Posted: **Fri Mar 15, 2019 1:55 am**

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.

Posted: **Fri Mar 15, 2019 2:08 am**

It is the natural logarithm of 2.

Posted: **Fri Mar 15, 2019 3:08 am**

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.

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

Posted: **Fri Mar 15, 2019 4:13 am**

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

Posted: **Fri Mar 15, 2019 12:01 pm**

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