   # The element rhenium (Re) bas two naturally occurring isotopes, 185 Re and 187 Re, with an average atomic mass of 186.207 u. Rhenium is 62.60% 187 Re, and the atomic mass of 187 Re is 186.956 u. Calculate the mass of 185 Re. ### 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 5, Problem 39E
Textbook Problem
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## The element rhenium (Re) bas two naturally occurring isotopes, 185Re and 187Re, with an average atomic mass of 186.207 u. Rhenium is 62.60% 187Re, and the atomic mass of 187Re is 186.956 u. Calculate the mass of 185Re.

Interpretation Introduction

Interpretation: The average atomic mass of rhenium (Re) is given. Also atomic mass and percentage abundance of 187Re isotope is given. By using these values, the mass of 185Re is to be calculated.

Concept introduction: The elements having same atomic number but different mass number are called isotopes of that element.

The atomic mass is defined as the sum of number of protons and number of neutrons. If the percentage composition is given, then atomic mass can be calculated by multiplying the mass of element with its percentage composition.

Average atomic mass is defined as the percentage sum of atomic mass of individual atom.

Average atomic mass=Percentageabundanceofeachisotopes×atomicmassofthatisotope

To determine: The mass of 185Re .

### Explanation of Solution

Given

Average mass of rhenium (Re) is 186.207u .

The atomic mass of 187Re is 186.956u .

The percentage abundance of 187Re is 62.60% .

The percentage abundance of Re is,

187Re%+185Re%=100

Substitute the values of 187Re% in above equation.

62.60%+185Re%=100185Re%=37.40%

Formula

The average atomic mass is calculated using the formula,

Average atomic mass=Percentageabundanceofeachisotopes×atomicmassofthatisotope

Substitute the value of average atomic mass, percentage abundance of isotopes of (Re) and its atomic mass in above equation.

Average atomic mass(Re)=(37.40%)(massof185Re)+(62

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