BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

Americium is used in smoke detectors and in medicine for the treatment of certain malignancies. One isotope of americium, 241Am, has a rate constant, k, for radioactive decay of 0.0016 y‒1. In contrast, radioactive iodine-125, which is used for studies of thyroid functioning, has a rate constant for decay of 0.011 d‒1.

  1. (a) What are the half-lives of these isotopes?
  2. (b) Which isotope decays faster?
  3. (c) If you are given a dose of iodine-125 containing 1.6 × 1015 atoms, how many atoms remain after 2.0 days?

(a)

Interpretation Introduction

Interpretation:

The half-lives of 241Am and 125I isotopes has to be calculated.

Concept Introduction:

The rate of reaction is the quantity of formation of product or the quantity of reactant used per unit time.  The rate of reaction doesn’t depend on the sum of amount of reaction mixture used.

The raise in molar concentration of product of a reaction per unit time or decrease in molarity of reactant per unit time is called rate of reaction and is expressed in units of mol/(L.s).

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

    aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

    Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

    ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

Half-life for first order reactions:

The half-life for the first order reaction is constant and it is independent of the reactant concentration.

Half-life period of first order reaction can be calculated using the equation,

    t1/2=0.693k

Explanation

The half-lives of these reactions are calculated as,

  Calculatehalf-lives:_For241Am,k =  0.0016 y-1t1/2 = 0.693k  = 0.6930.0016 y-1 = 433 year.For125I,k =  0

(b)

Interpretation Introduction

Interpretation:

The isotope that decays faster has to be given.

Concept Introduction:

Half-life for first order reactions:

The half-life for the first order reaction is constant and it is independent of the reactant concentration.

Half-life period of first order reaction can be calculated using the equation,

    t1/2=0.693k

(c)

Interpretation Introduction

Interpretation:

The number of atoms that remains after two days has to be calculated.

Concept Introduction:

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

    aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

    Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

    ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 14 Solutions

Show all chapter solutions add

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Beverage consumption represents. a. 19 percent of a young woman's daily calorie intake. b. 7 percent of a young...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Define the following terms: a. chromosome b. chromatin

Human Heredity: Principles and Issues (MindTap Course List)

A thermodynamic process occurs in which the entropy of a system changes by 8 J/K. According to the second law o...

Physics for Scientists and Engineers, Technology Update (No access codes included)

How does heat move from the inner Earth to the surface?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin