NaF has the same structure as NaCl. (a) Use ionic radii from Chapter 7 to estimate the length of the unit cell edge for NaF. (b) Use the unit cell size calculated in part (a) to estimate the density of \(\mathrm{NaF}\)

First, look up the ionic radii for Na\(^+\) and F\(^-\) ions in the given table or an appropriate reference: - Ionic radius of Na\(^+\): \(102\,\text{pm}\) (picometers) - Ionic radius of F\(^-\): \(133\,\text{pm}\) Remember that 1 pm = \(10^{-12}\,\text{m}\)

NaF has a similar structure to NaCl, which means it has a face-centered cubic (FCC) unit cell. In an FCC structure, the unit cell edge length (a) can be obtained using the following relationship between the ionic radii (r) of the cations and the anions: \(a = 2 \times (r_{\text{cation}} + r_{\text{anion}})\) Using the given values for the ionic radii of Na\(^+\) and F\(^-\) ions, we can calculate the unit cell edge length (a) for NaF: \(a = 2 \times (102\,\text{pm} + 133\,\text{pm})\) \(a = 2 \times 235\,\text{pm}\) \(a = 470\,\text{pm}\)

Next, convert the unit cell edge length from picometers to meters: \(a = 470\,\text{pm} \times \frac{1\,\text{m}}{10^{12}\,\text{pm}}\) \(a = 4.7 \times 10^{-10}\,\text{m}\)

To find the mass and volume of the unit cell, we need to use the given molar masses of Na and F and calculate the mass of one molecule of NaF. Molar mass of Na: \(22.99\,\text{g/mol}\) Molar mass of F: \(19.00\,\text{g/mol}\) Molar mass of NaF: \(22.99\,\text{g/mol} + 19.00\,\text{g/mol} = 41.99\,\text{g/mol}\) Now, since there is one Na\(^+\) and one F\(^-\) ion in each unit cell, we can calculate the mass of one unit cell as follows: Mass of one unit cell: \(\frac{41.99\,\text{g/mol}}{6.022\times 10^{23}\, \text{mol}^{-1}}\) Mass of one unit cell: \(6.98\times 10^{-23}\,\text{g}\) Next, calculate the volume of the unit cell using the unit cell edge length (a): Volume of unit cell: \(a^3\) Volume of unit cell: \((4.7\times 10^{-10}\,\text{m})^3\) Volume of unit cell: \(1.03\times 10^{-28}\,\text{m}^3\)

Finally, we can calculate the density of NaF using the mass and volume of the unit cell: Density: \(\frac{\text{Mass}}{\text{Volume}}\) Density: \(\frac{6.98\times 10^{-23}\,\text{g}}{1.03\times 10^{-28}\,\text{m}^3}\) Density: \(6.78\times 10^{5}\,\text{g/m}^3\) So, the estimated density of NaF is approximately \(6.78\times 10^{5}\,\text{g/m}^3\).