Question

(a) A compound with formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?

Short answer

The initial formula for the complex is [Ru(H₂O)₅Cl]₂+ and upon reacting with AgNO₃(aq), 2 moles of AgCl precipitate. After a year, one additional Cl⁻ ion replaces one H₂O ligand, and the final formula becomes [Ru(H₂O)₄Cl₂](+), with 3 moles of AgCl precipitating upon reacting with AgNO₃(aq).

Step-by-step solution

Understand the Initial Reaction

In the initial reaction, upon dissolving the complex compound in water and adding excess AgNO₃(aq), 2 moles of AgCl are precipitated per mole of complex. The compound's given formula is RuCl₃⋅5H₂O. We know that there are 2 moles of Cl⁻ ions replaced per mole of complex, so we need to determine which ligands are still attached to Ru.

Determine the initial formula

Given that the compound is still dissolvable and retains its color, this implies that at least the water molecules remain with the Ru atom. We have 5 water molecules as ligands, and 2 Cl⁻ ions are replaced by Ag⁺ ions. This means that 1 Cl⁻ still remains with the Ru atom. So, the initial formula for the complex is [Ru(H₂O)₅Cl]₂+, with 2 AgCl as the precipitate.

Understand the Reaction After One Year

After a solution of RuCl₃⋅5H₂O has stood for about a year, the addition of AgNO₃(aq) precipitates 3 mol of AgCl per mole of complex. Since we now have 3 moles of AgCl precipitated, this means that during this time, one of the water ligands has been replaced by another Cl⁻ ion.

Determine the Final Formula

Now that we know one additional Cl⁻ ion replaced one of the water ligands, the final formula for the complex after one year would be [Ru(H₂O)₄Cl₂](+), with 3 AgCl as the precipitate.

Summarize the Observations

In summary, the initial compound, when mixed with AgNO₃(aq), precipitates 2 mol of AgCl per mole of complex, and the initial formula is [Ru(H₂O)₅Cl]₂+. After a year, the compound reacts with AgNO₃(aq) to precipitate 3 mol of AgCl per mole of complex, with the final formula being [Ru(H₂O)₄Cl₂](+).