A. Logs were designed
to simplify calculations before calculators. They convert from
multiplication and division to addition and sutraction, respectively.
We have to deal with them in Kinetics because they naturally
occur as a result of our integration of the rate laws and becuase
ln is the inverse (anti-log) of 
.
You'll get far if you remember these important rules about natural
logs (ln):
equation
#1: 
equation
#2: 
equation
#3: 
Similar relationships
work for log base 10 too, the only difference is that the inverse
of log is 
.
If a first order
reaction is found to have a rate constant, k = 0.050 /s at 70°C.
If the initial concentration of reactant, [reactant]o = 1.3 M,
what concentration is expected at time, t = 12 s?
A. We begin by writing down the integrated rate law for a first
order reaction:
According to equation
#1 above, the left-hand side of the integrated rate law can be
rewritted as:
If we plug in our
numbers, we have:
or:
Now, to solve for
[A]t, we need to undo the ln.
Taking the
of both sides and using equation #3, we get:
|
The last part involves
solving for  . I've shown the
steps on my calculator (yours might be different).
The final answer
is:
|
 |