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Chemical Kinetics I 121
-kt = ln[A] - ln[Ao] and kt = In[&] - ln[A] = ln([Ao]/[A]), since
log(A/B) = log A - log B.
+ t = ln(53/23)/(5.18 x = 161 1.58 s = 26.9 min.

Example No. 2: Given that the initial concentration of a compound
A, being consumed in a reaction obeying first-order kinetics, is 13.7
mM, determine how long it would take the reaction to be 80%
complete, given that k, the specific rate constant, is 8.3 x s-l.
What is the half-life of the reaction?

First-order kinetics: ln[A] = -kt + ln[Ao]
Given: k = 8.3 x s-', [&I = 13.7 mM.
Since the reaction is 80% complete, this means only 20% of the initial
concentration of A remains at this stage of the reaction.
+ [A] = (20/100)[&] = 0.2[&] =+ unknown = t

-kt = ln[A] - ln[Ao] and kt = In[&] - ln[A] = ln{[&]/[A]), since
log(A/B) = log A - log B. Therefore, kt = ln([Ao]/(0.2[Ao])) = In 5.
+t = (In 5)/(8.3 x = 1939.1 s = 32.3 min.
t1/2 = (In 2)/k = (In 2)/(8.3 x = 835.12 s = 13.9 min.

DETERMINATION OF THE ORDER OF A REACTION

The order of a reaction may be determined by a number of different
methods. Two of the most common methods are:

Integrated Rate Equations
In this method, a reaction order is assumed, and a graph is plotted for
the corresponding rate equation. This is repeated until the order
yielding the best fit line is obtained.

Advantage:
1. Needs only a single kinetics experiment.

Disadvantages:
1. Assumes form of rate law and tests the assumption.
2. Depends on the accuracy of the measurement.
3. Can be sensitive to side-reactions, impurities or products.