For the first-order reaction half-life is 14 s. The time required for the initial concentration

step 1 Dear students, in the given problem, Problem 62 of Chapter 4, Chemical Kinetics, we have asked t

For the first-order reaction half-life is 14 s. The time...

For the first-order reaction half-life is $14 \mathrm{~s}$. The time required for the initial concentration to reduce to $1 / 8$ th of its value is:
(a) $21 \mathrm{~s}$
(b) $32 \mathrm{~s}$
(c) $42 \mathrm{~s}$
(d) $142 \mathrm{~s}$

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Key Concepts

First-Order Reactions

A first-order reaction is one in which the reaction rate is directly proportional to the concentration of a single reactant. The integrated rate law for first-order kinetics shows how the concentration decreases exponentially over time, making such reactions predictable in terms of timing and concentration changes.

Half-Life

The half-life of a reaction is the time it takes for the concentration of a reactant to decrease to half its original value. In first-order reactions, the half-life remains constant regardless of the starting concentration, providing a useful measure for predicting the time required for concentration changes.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. In the context of first-order kinetics, the reactant concentration decreases exponentially over time, enabling calculations for various fractions of the initial concentration using logarithmic relationships and the concept of half-life.

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