Crystals of hydrated chromium(III) chloride are green, have an empirical formula of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O},\) and are highly soluble, (a) Write the complex ion that exists in this compound. (b) If the complex is treated with excess \(\mathrm{AgNO}_{3}(a q)\) how many moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in solution? (c) Crystals of anhydrous chromium(III) chloride are violet and insoluble in aqueous solution. The coordination geometry of chromium in these crystals is octahedral, as is almost always the case for \(\mathrm{Cr}^{3+} .\) How can this be the case if the ratio of \(\mathrm{Cr}\) to Clis not 1:6 ?

To identify the complex ion, we first look at the empirical formula of hydrated chromium(III) chloride: \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Since the compound is soluble, the complex ion would be formed by the Cr and the H2O molecules. Hence, the complex ion would be \([{\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6}]^{3+}\).

When hydrated chromium(III) chloride is treated with excess silver nitrate (AgNO3), silver chloride (AgCl) will precipitate. To determine the number of moles of AgCl formed, we need to consider the number of moles of chloride ions, Cl-, in the solution. In the given empirical formula, \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), we have 3 moles of chloride ions for every 1 mole of hydrated chromium(III) chloride. Thus, for every 1 mole of hydrated chromium(III) chloride that dissolves, 3 moles of AgCl will precipitate when treated with excess AgNO3.

According to the information given, anhydrous chromium(III) chloride, CrCl3, has a violet color and is insoluble in water. The coordination geometry of chromium in this compound is octahedral. This means that there are 6 ligands surrounding the chromium ion. It is important to note that the ratio of chromium to chloride in the compound is not 1:6 but 1:3 as given by the formula CrCl3. However, the coordination geometry indicates that there are 6 ligands surrounding chromium. This can be explained by the fact that each chloride ion in the anhydrous chromium(III) chloride can act as a bidentate ligand, binding to the chromium ion in two different places. This way, the six-coordinate positions around the chromium can be occupied by the three chloride ions in an octahedral fashion.