Chapter 25.8, Problem 1.2ACP

### 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

# Rates of decomposition can be measured based on decompositions per min. What is the ratio of the rates of decomposition of the two major uranium isotopes (rate for 238U /rate for 235U)?

Interpretation Introduction

Interpretation: To determine the ratio of the rates of decomposition of the two major isotopes namely, uranium–235 and uranium–238

Concept introduction:

Half–life period: It is the time required for the concentration of a substance to reduce to the one-half of its initial concentration.

The half–life period for first order reaction is as follows:

t1/2=0.693kWhere,k = Rate constantt1/2= half-life

Explanation

Halfâ€“life of 235U is 7.038â€‰Ã—â€‰109â€‰yr

Halfâ€“life of 238U is 4.468â€‰Ã—â€‰1010â€‰yr

The halfâ€“life period for first order reaction is as follows:

â€‚Â t1/2=0.693kâ€Šâ€ŠWhere,kÂ =Â RateÂ constantt1/2=Â half-life

The rate constant of 235U is calculated as follows:

â€‚Â t1/2=0.693kâ€Šâ€Š7.038â€‰Ã—â€‰109â€‰yr=0.693kâ€Šâ€Škâ€‰=â€‰9.8465â€‰Ã—â€‰10âˆ’11yrâˆ’1

The rate constant of 238U is calculated as follows:

â€‚Â t1/2=0

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