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# Determining the Half-Life of a First-Order ReactionThe

ISBN: 9780321696724 27

## Solution for problem 9PE Chapter 14

Chemistry: The Central Science | 12th Edition

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Problem 9PE

Problem  9PE

Determining the Half-Life of a First-Order Reaction

The reaction of C4H9Cl with water is a first-order reaction. (a) Use Figure to estimate the halflife for this reaction. (b) Use the half-life from (a) to calculate the rate constant.

Figure Concentration of butyl chloride (C4H9Cl) as a function of time.

How does the instantaneous rate of reaction change as the reaction proceeds?

(a) Using Equation calculate t½ for the decomposition of the insecticide described in Sample Exercise.

Sample Exercise

Using the Integrated First-Order Rate Law

The decomposition of a certain insecticide in water at 12 °C follows first-order kinetics with a rate constant of 1.45 yr-1. A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0 × 10-7 g/cm3. Assume that the temperature of the lake is constant (so that there are no effects of temperature variation on the rate). (a) What is the concentration of the insecticide on June 1 of the following year? (b) How long will it take for the insecticide concentration to decrease to 3.0 × 10-7 g/cm3?

(b) How long does it take for the concentration of the insecticide to reach one-quarter of the initial value?

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