The first order reaction is defined by the rate law:
rate = k[A]
where k is the rate constant and [A] is the concentration of the reactant.
If we integrate this rate law, we get:
ln([A]_t/[A]_0) = -kt
where [A]_t is the concentration of A at time t, [A]_0 is the initial concentration of A, k is the rate constant, and t is time.
We can use this equation to solve for k given the initial and final concentrations of A and the time interval.
In this case, we have:
[A]_t = 0.632 M
[A]_0 = 0.816 M
t = 16.0 min
Substituting these values into the equation above, we get:
ln(0.632/0.816) = -k(16.0)
Solving for k, we get:
k = (1/16.0) * ln(0.816/0.632) = 0.0316 min^-1
Therefore, the value of the rate constant k for this first order reaction is 0.0316 min^-1.
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