The rate constant, k, for the decomposition reaction : k = 0.0124 / days
Given
The half-life of 56 days
Required
The rate constant, k
Solution
For first-order, rate law : ln[A]=−kt+ln[A]o
The half-life : the time required to reduce to half of its initial value.
The half life :
t1/2 = (ln 2) / k
k = (ln 2) / t1/2
k = 0.693 / 56 days
k = 0.0124 / days
The rate constant for the decomposition reaction has been 0.0124/days.
The rate constant has been given by;
log [Final concentration] = kt + log [Initial concentration]
k has been the rate constant, and t has been the time.
The initial concentration has been 1, after the half life period the concentration has been half i.e. 0.5 .
The given half life has been 56 days.
The rate constant can be calculated as:
log 1 = k(56) + log 0.5
k(56) = 0.693
k = 0.0124/days.
The rate constant for the decomposition reaction has been 0.0124/days.
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