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 Cl is not \(1: 6 ?\)

Step by step solution

01

(a) Identify the complex ion

The given empirical formula of the crystals is \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Since it is stated as a highly soluble compound, the complex ion can be assumed to be hydrated. Therefore, the complex ion that exists is \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\).

02

(b) Calculate moles of AgCl precipitated

When the complex \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) is treated with excess \(\mathrm{AgNO}_{3}(a q)\), the reaction between \(\mathrm{Cl}^{-}\) and \(\mathrm{Ag}^{+}\) ions leads to the precipitation of AgCl. The reaction can be represented as: \[3\mathrm{Ag}^{+} + 3\mathrm{Cl}^{-} \rightarrow 3\mathrm{AgCl}\] For each mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in the solution, there are 3 moles of \(\mathrm{Cl}^{-}\) ions. Therefore, 3 moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in the solution.

03

(c) Explanation of octahedral structure in CrCl3

In the anhydrous \(\mathrm{CrCl}_{3}\), the ratio of Cr to Cl is 1:3. Despite this ratio, the coordination geometry of chromium is found to be octahedral. This is possible because in addition to the chloride ions, there are other non-chloride ligands that complete the octahedral coordination for the chromium ion. For the chromium(III) ion, three chloride ions can be coordinated directly to Cr3+, and the remaining three positions of the octahedral geometry can be occupied by other non-chloride ligands such as water molecules or other counter ions. This explains the octahedral geometry for \(\mathrm{Cr}^{3+}\) in anhydrous chromium(III) chloride even though the ratio of Cr to Cl is not 1:6.

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