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ChemistryChemistry: An Atoms First Approach2nd Edition
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Natural rubidium has the average mass of 85.4678 u and is composed of isotopes 85 Rb (mass = 84.9117 u) and 87 Rb. The ratio of atoms 85 Rb/ 87 Rb in natural rubidium is 2.591. Calculate the mass of 87 Rb.

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Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

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Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 5, Problem 162CP
Textbook Problem
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Natural rubidium has the average mass of 85.4678 u and is composed of isotopes 85Rb (mass = 84.9117 u) and 87Rb. The ratio of atoms 85Rb/ 87Rb in natural rubidium is 2.591. Calculate the mass of 87Rb.

Interpretation Introduction

Interpretation: The average atomic mass of rubidium (Rb) and atomic mass of isotope (85Rb) is given. Also the ratio of atoms of 85Rb/87Rb is given. The mass of 87Rb  is to be calculated.

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

The mole fraction is defined as ratio of moles of one compound to the total moles in the solution.

To determine: The mass of 87Rb 

Explanation of Solution

Given

Average atomic mass of rubidium (Rb) is 85.4678 u.

The atomic mass of 85Rb  is 84.9117 u.

Formula

The average atomic mass is calculated using the formula,

Average atomic mass  = ∑∑(Mole fraction of isotope) ×(Mass of isotope)Average atomic mass of Rb =(Mole fraction of 85Rb)×(Mass of 85Rb) +(Mole fraction of 87Rb)×(Mass of 87Rb) (1)

The ratio of atoms of 85Rb  and 87Rb  in natural rubidium is,

85Rb87Rb =2.591

Mole fraction of 85Rb  is,

85Rb =85Rb85Rb+87Rb =11+87Rb85Rb

Substitute the value of 85Rb/87Rb in above equation.

85Rb =11+87Rb85Rb =11+12

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