Problem 50 - Chemistry: The Central Science

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?

Step-by-Step Solution

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 1: 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.

Step 2: 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.

Step 3: 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 Since we now have 3 moles of AgCl precipitated, this means that during this time, one of the water ligands has been replaced by another Cl⁻ ion.

Step 4: 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.

Step 5: 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](+).