Chemistry and Chemical Reactivity (9th Edition)

Published by Cengage Learning
ISBN 10: 1133949649
ISBN 13: 978-1-13394-964-0

Chapter 12 The Solid State - Study Questions - Page 467a: 9


707 pm

Work Step by Step

For a face-centered cubic arrangement there are $8 \times 1/8$ atoms in the corners and $6\times1/2$ in the faces, so 4 ions per unit cell. Since the potassium ions are in octahedral holes, there are also 4 potassium ions per unit cell. Mass: $4\times (39.0983+126.905)\ g/mol\div 6.022\times 10^{23}\ ions/mol=1.103\times10^{-21}\ g/cell$ Volume: $1.103\times10^{-21}\ g/cell\div 3.12\ g/cm^3=3.534\times10^{-22}\ cm^3/cell$ Side-length: $\sqrt[3]{3.534\times10^{-22}\ cm^3}=7.07\times10^{-8}\ cm=707\ pm$
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