Chapter 25.4, Problem 25.5CYU

### Chemistry & Chemical Reactivity

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

Chapter
Section

### Chemistry & Chemical Reactivity

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

# Tritium ( 1 3 H), a radioactive isotope of hydrogen, has a half-life of 12.3 years. (a) Starting with 1.5 mg of this isotope, what mass (mg) remains after 492 years? (b) How long will it take for a sample of tritium to decay to one eighth of its activity? (c) Estimate the length of time necessary for the sample to decay to 1% of its original activity.

a)

Interpretation Introduction

Interpretation: According to rate law that is the concentrations or pressure of the reactants and products of constant parameters is called rate law.

Concept introduction:

Half-life: The time required for a sample to decay half of the initial quantity. It is considered as first-order chemical reaction and is independent of the amount of sample.

Explanation

Given info;

The half-life of tritium (t12)=12.3years

Time t=49.2years

The initial activity of tritium N0=1.5mg

Formula:

According to rate law

Then rate constant

K=0.693t12

K=0.69312.3K=0.0564yâˆ’1

The half-lives of tritium =tt1/2

=49.212.3= 4half-lives

Noâ€‰(1/2)n=â€‰Nâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰

b)

Interpretation Introduction

Interpretation:

The time required for a sample of tritium to decay to one eighth of its activity has to be calculated.

Concept introduction:

Half-life: The time required for a sample to decay half of the initial quantity. It is considered as first-order chemical reaction and is independent of the amount of sample.

According to rate law that is the concentrations or pressure of the reactants and products of constant parameters is called rate law.

c)

Interpretation Introduction

Interpretation:

The length of time necessary for the sample to decay to 1% of its original activity has to be estimated.

Concept introduction:

Half-life: The time required for a sample to decay half of the initial quantity. It is considered as first-order chemical reaction and is independent of the amount of sample.

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