Lithium chloride crystallizes in a face-centered cubic structure.The unit cell length is 5.14 $\times$ 10^-⁸ cm.The chloride ions are touching each other along the face diagonal of the unit cell.The lithium ions fit into the holes between the chloride ions.What is the mass of LiCl in a unit cell? A)7.04 $\times$ 10^-²³ g B)1.41 $\times$ 10^-²² g C)2.82 $\times$ 10^-²² g D)4.22 $\times$ 10^-²² g E)5.63 $\times$ 10^-²² g

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In a face-centered cubic (FCC) structure, the face diagonal is equal to $\sqrt{2}$ times the unit cell length. Given that the chloride ions touch each other along the face diagonal, the length of the face diagonal is $5.14 \times \sqrt{2}$ Å, which is the diameter of two chloride ions. Thus, the radius of a chloride ion is $5.14 \times \sqrt{2} / 2$ Å. Since lithium ions fit into the holes between the chloride ions without changing the overall length, the mass of LiCl in the unit cell can be calculated by considering the number of formula units in the FCC structure and the molar masses of lithium (6.94 g/mol) and chlorine (35.45 g/mol). An FCC unit cell contains 4 formula units of LiCl. The molar mass of LiCl is $6.94 + 35.45 = 42.39$ g/mol. Therefore, the mass of LiCl in a unit cell is $(42.39 \, \text{g/mol}) \times (4 \, \text{formula units}) \times (1 \, \text{mol} / 6.022 \times 10^{23} \, \text{formula units}) = 2.82 \times 10^{-22}$ g.

Lithium Chloride Crystallizes in a Face-Centered Cubic Structure ×\times× 10-8 Cm ×\times×

Lithium Chloride Crystallizes in a Face-Centered Cubic Structure $\times$ 10^-⁸ Cm $\times$