The binary compounds of lithium LiX (X = H, F, Cl, Br, and I) all crystallize in the cubic lattice k — Solid State Chemistry and Periodicity Chemistry Question
Problem Context
The binary compounds of lithium LiX (X = H, F, Cl, Br, and I) all crystallize in the cubic lattice known as the rock salt or NaCl lattice. One unit cell of this structure (small circles = Li, large circles = X) is shown below. The length of the edge of the unit cell is abbreviated a.
Calculate the density of LiCl, a = 513.6 pm.
Model Answer
Volume of one unit cell = a^3 = (513.6 pm)^3 = (513.6 × 10^-10 cm)^3 = 1.355 × 10^-22 cm^3
Mass of one unit cell = 4 LiCl = 4(42.39 g mol^-1)/(6.022 × 10^23 mol^-1) = 2.816 × 10^-22 g
Density = (2.816 × 10^-22 g)/(1.355 × 10^-22 cm^3) = 2.078 g cm^-3
Carbon-hydrogen bonds are invariably shorter than carbon-fluorine bonds (e.g., 108.7 pm in CH4 vs. 132.3 pm in CF4). However, the Li–H distances in LiH are actually slightly longer than the Li–F distances in LiF. Explain why.
Model Answer
A neutral hydrogen atom is somewhat smaller than a neutral fluorine atom (hence the smaller C–H bond compared to a C–F bond). However, Zeff for F is much greater than for H, so addition of an electron to form H– causes a much greater increase in size than addition of an electron to F to form F–. LiH and LiF are both largely ionic, with H– and F– anions, respectively. The H– ion is thus slightly larger in size than the F– ion.
The a values of the lithium halides increase monotonically but not steadily with increasing period: The increase from fluoride to chloride is the largest, with the increase from chloride to bromide the smallest and the increase from bromide to iodide intermediate in size. Explain this pattern. What would you predict about the magnitude of the increase in a from LiI to LiAt?
Model Answer
As the principal quantum number n increases, the size of an atom or ion increases, though the effect generally diminishes in magnitude as n increases. The outlier in this general trend in the lithium halides is thus the LiCl vs. LiBr (n = 3 to n = 4), where the increase is smaller than expected. This is due to the inclusion for the first time of the d block elements (Z = 21 to Z = 30). The addition of these ten extra protons, which are not completely shielded by the ten extra electrons, causes the 4p elements to be anomalously contracted.
This effect is also expected with the astatide ion At–, due to the intervention of the 4f elements (the “lanthanide contraction”). So the increase in size from LiI to LiAt is expected to be rather small, similar to or even smaller than the increase in size from LiCl to LiBr. While data are not available for astatides, this trend is seen in structures of polonides.
The melting points of the lithium halides (filled circles) and of lithium hydride (open square) are graphed as a function of the unit cell edge length a below. Explain the correlation observed among the lithium halides between a value and melting point.
Model Answer
In these ionic crystals, the interionic attractions are proportional to 1/r, where r is the separation between ions. So as a is smaller, the cohesive forces are stronger, which leads to higher melting points.
The melting point of lithium hydride deviates from the value expected based on the correlation shown by the lithium halides. Explain this deviation.
Model Answer
H is much less electronegative than F, so LiH is much less ionic than LiF. Since the cohesive energies are proportional to q1q2/r, and the charges on Li and H in LiH are smaller than those on Li and F in LiF, LiH has a lower melting point.