Chemistry
posted by Help .
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

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}