   # A first-order reaction is 75.0% complete in 320. s. a. What are the first and second half-lives for this reaction? b. How long does it take for 90.0% completion? ### 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 50E
Textbook Problem
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## A first-order reaction is 75.0% complete in 320. s.a. What are the first and second half-lives for this reaction?b. How long does it take for 90.0% completion?

(a)

Interpretation Introduction

Interpretation: The time of 75% completion of first order reaction is given. The first two half-lives are to be calculated for this reaction. Also, the time for the completion of 90% reaction is to be calculated.

Concept introduction: All chemical reactions follow rate law. This law shows that how the rate of a chemical reaction depends on the concentration of reactants.

The half-life is defined as the time required for the concentration of reactant to be reduced to one-half of its initial value.

To determine: The first and second half lives of the given reaction.

### Explanation of Solution

Given

The time elapsed is 320s .

It is assumed that initially 100% of reactant is present. It is given that 75% reaction is completed. It means that 25% of reactant is left. Hence,

[A0]=100[A]=25

Where,

• [A]0 is initial concentration.
• [A] is concentration of reactant left.

Formula

The integral rate law equation of first order reaction is,

kt=ln([A]0[A]) (1)

Where,

• k is rate constant.
• [A]0 is initial concentration.
• [A] is concentration at time t .
• t is time.

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

kt=ln([A]0[A])k×320s=ln(10025)k=0.00433s1

For first half life,

[A]=[A]02t=t12

Where,

• t12 is half life

(b)

Interpretation Introduction

Interpretation: The time of 75% completion of first order reaction is given. The first two half-lives are to be calculated for this reaction. Also, the time for the completion of 90% reaction is to be calculated.

Concept introduction: All chemical reactions follow rate law. This law shows that how the rate of a chemical reaction depends on the concentration of reactants.

The half-life is defined as the time required for the concentration of reactant to be reduced to one-half of its initial value.

To determine: The time required for completion of 90% reaction.

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