Question

The 1st order reaction is 60% complete in 20 minutes. How long will the reaction take to be 84% complete?
A. 54
B. 68
C. 40
D. 76

Answer 1

Hint: In this question we will use the 1st order reaction equation to establish a relationship between the two different stages of reaction i.e. at 60% and 84%. We know that in 1st order reaction
$k = \dfrac{{2.303}}{t}\log \dfrac{a}{{a - x}}$, where
a = initial stage of reaction
x= final stage of reaction
t = total time

Complete step by step answer:
Let a = 100
Therefore according to the given question the reaction is 60% complete in 20 minutes.
\[ \Rightarrow k = \dfrac{{2.303}}{{20}}\log \dfrac{{100}}{{100 - 60}}\]​ ..... (i)
Now as per the question we need to find out that how long it will take to complete 84% of reaction
Therefore,
\[\; \Rightarrow k = \dfrac{{2.303}}{t}\log \dfrac{{100}}{{100 - 84}}\]​..... (ii)
But as we all know $k$remains same throughout the reaction, therefore (i) = (ii),
\[ \Rightarrow \dfrac{{2.303}}{{20}}\log \dfrac{{100}}{{100 - 60}} = \;\dfrac{{2.303}}{t}\log \dfrac{{100}}{{100 - 84}}\]
\[ \Rightarrow t = 20 \times \dfrac{{0.795}}{{0.397}}\]
$ \Rightarrow t = 40{\text{ mins}}$

Therefore, the correct option is C.

Additional information:
Reaction lifetime is defined as the time taken by the reaction to proceed to 98% of completion. The shorter the life time, the faster the reaction. Reaction life times are used to compare the various reactions. Reactions are also compared with half life periods. The half life period is defined as the time during which the concentration of a reactant is reduced to one-half of its initial value or the time in which half of the reaction is completed.

Note: There are several factors which affect the rate of reaction and time period, few of them are listed below:
1.Concentration of reactants
2.Effect of temperature
3.Presence of a positive catalyst
4.Presence of a negative catalyst
5.Physical state of reactants
These need to be taken care while solving such problems.