Question
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
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
Answers
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 half-life and N at the end of that time will be 50.
So ln(No/N) = kt
ln(100/50) = k*t<sub>1/2</sub>
ln(2) = k*t<sub>1/2</sub>
0.693 = k*t<sub>1/2</sub> and
k = 0.693/t<sub>1/2</sub>
Let's start with 100 atoms of something.
No = 100. Since it is 50% decomposed in 10.5 min, then 10.5 is the half-life and N at the end of that time will be 50.
So ln(No/N) = kt
ln(100/50) = k*t<sub>1/2</sub>
ln(2) = k*t<sub>1/2</sub>
0.693 = k*t<sub>1/2</sub> and
k = 0.693/t<sub>1/2</sub>
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