Chapter 2, Problem 23PS

### 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

# Gallium has two naturally occurring isotopes, 69Ga and 71Ga, with masses of 68.9257 u and 70.9249 u, respectively. Calculate the percent abundances of these isotopes of gallium.

Interpretation Introduction

Interpretation:

The percent abundance of isotopes of Gallium has to be determined if the one isotope (69Ga) has a mass of 68.9257u and other isotope (71Ga) has a mass of 70.9249u.

Concept Introduction:

The average weight (atomic weight) of Gallium is 69.723u.

Equation for atomic weight is,

atomic weight=(%abundanceisotope-1100)×(massofisotope-1) +(%abundanceisotope-2100)×(massofisotope-2)+etc

Explanation

There are two isotopes for Gallium atom.

The mass of isotope-1 (69Ga) is 68.9257u

The mass of isotope-2 is (71Ga) is 70.9249u.

Letâ€™s take the percent abundance of 69Ga as â€˜xâ€™ and 71Ga is â€˜100-xâ€™.

Therefore,

Equation for average weight of Gallium is,

Â Â Â Â 69.723â€‰â€‰=â€‰â€‰(x100)â€‰â€‰Ã—â€‰(68.9257)â€‰+â€‰(100-x100)â€‰â€‰Ã—â€‰(70.9249u)69.723â€‰â€‰=â€‰â€‰(68.9257x100)â€‰â€‰+â€‰(7092.49-70.9249x100)69

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