   # Spinel is a mineral that contains 37.9% aluminum, 17.1% magnesium, and 45.0% oxygen, by mass, and has a density of 3.57 g/cm 3 .The edge of the cubic unit cell measures 809 pm. How many of each type of ion are present in the unit cell? ### 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 9, Problem 140CP
Textbook Problem
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## Spinel is a mineral that contains 37.9% aluminum, 17.1% magnesium, and 45.0% oxygen, by mass, and has a density of 3.57 g/cm3.The edge of the cubic unit cell measures 809 pm. How many of each type of ion are present in the unit cell?

Interpretation Introduction

Interpretation:

The mass percentage composition of elements found in a spinel is given and the edge length of the unit cell is given. The number of atoms of each element found in the spinel has to be determined.

Concept introduction:

A spinel is a compound containing at least three elements. One of them is Oxygen. The other two is either metals or one metal and one non-metal.

### Explanation of Solution

Explanation

Deduce the empirical formula of spinel.

Givendata:the spinelcontains37.9%Al,17.1%Mg,45.0%Obymass

No.ofmolesofanelement=weightatomicweight

Assume100gofspinel,No.ofmolesofAl=37.9gAl26.98gAl=1.40molNo.ofmolesofMg=17.1gMg24.31gMg=0.703molNo.ofmolesofO=45.00gO16.00gO=2.81mol

The Moleratiois2:1:4 . Therefore, the empirical formula is Al2MgO4 .

Using the mass percent of the given elements and their respective atomic weight, the number of moles of each element is calculated. Using the number of moles value, the mole ratio is obtained which is useful to deduce the empirical formula of the spinel.

Calculate the number of Al2MgO4 units present in each unit cell to obtain number of each element found in the spinel.

densityofthespinel=3.57g/cm3edgelengthofunitcell=809pm

MolarmassofAl2MgO4=24.31+2(26.98)+4(16)=142.27g/molDensityofunitcell=massofunitcellvolumeofunitcell

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