   # For the reaction A → products, successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A] 0 = 0.10 M . Calculate the concentration of A at the following times. a. 80.0 min b. 30.0min ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 55E
Textbook Problem
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## For the reaction A → products, successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A]0 = 0.10 M. Calculate the concentration of A at the following times.a. 80.0 minb. 30.0min

(a)

Interpretation Introduction

Interpretation: The successive half-lives and the initial concentration of a reaction is given. By using these values, the concentration of A is to be calculated for each given time.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

To determine: The concentration of A at 80.0min .

### Explanation of Solution

Given

The initial concentration of A is 0.10M .

The time is 80.0min .

The successive half lives are 10.0min,20.0min and 30.0min . It is clear from the value that each half life is double the preceding value. But this trend of increase in value of half life is found in second order reaction. Hence, the given reaction is second order reaction.

Formula

The half-life of second order reaction is calculated using the formula,

t12=1k[A]0

Where,

• t12 ishalf life.
• k is rate constant.
• [A]0 isinitial concentration.

Substitute the values of t12 and [A]0 in the above equation.

t12=1k[A]010.0min=1k[0.10M]k=1.0M1min1

The integral rate law equation of second order reaction is,

1[A]=kt+1[A]0

Where,

• k is rate constant

(b)

Interpretation Introduction

Interpretation: The successive half-lives and the initial concentration of a reaction is given. By using these values, the concentration of A is to be calculated for each given time.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

To determine: The concentration of A at 30.0min .

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