Posted by Help on .
Problem:
In a first order decomposition reaction, 50% of a compound decomposes in 10.5 minutes. What is the rate constant of the reaction?
The solution my professor gave says:
k = .693 / 10.5min
Where did the .693 come from?
Thanks

Chemistry 
DrBob222,
That is the natural logarithm of 2. You can do it this way.
Let's start with 100 atoms of something.
No = 100. Since it is 50% decomposed in 10.5 min, then 10.5 is the halflife and N at the end of that time will be 50.
So ln(No/N) = kt
ln(100/50) = k*t_{1/2}
ln(2) = k*t_{1/2}
0.693 = k*t_{1/2} and
k = 0.693/t_{1/2}