Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 29 - Molecules and Solids - Problems - Page 854: 14

Answer

0.282 nm.

Work Step by Step

Use the hint. Every ion sits at the corner of a cube of side length s, which is the distance between ions. See Figure 29–20. A cube of side length s is associated with four NaCl pairs. However, only one-eighth of each Na or Cl ion is part of that cube, because 8 cubes meet at that corner. In summary, each cube of side length s has the equivalent of one-half of an NaCl molecule. Calculate the mass per unit volume, i.e., the density. $$\rho=\frac{0.5m_{NaCl}}{s^3}$$ $$s=\left( \frac{0.5m_{NaCl}}{\rho}\right)^{1/3}$$ $$s=\left( \frac{0.5(58.44 g/mole)}{2.165g/cm^3}\frac{mole}{6.02\times10^{23}}\right)^{1/3}$$ $$s=2.82\times10^{-8}cm$$
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