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(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

01

Understand the Initial Reaction

In the initial reaction, upon dissolving the complex compound in water and adding excess AgNO鈧�(aq), 2 moles of AgCl are precipitated per mole of complex. The compound's given formula is RuCl鈧冣媴5H鈧侽. We know that there are 2 moles of Cl鈦� ions replaced per mole of complex, so we need to determine which ligands are still attached to Ru.

02

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鈦� ions are replaced by Ag鈦� ions. This means that 1 Cl鈦� still remains with the Ru atom. So, the initial formula for the complex is [Ru(H鈧侽)鈧匔l]鈧�+, with 2 AgCl as the precipitate.

03

Understand the Reaction After One Year

After a solution of RuCl鈧冣媴5H鈧侽 has stood for about a year, the addition of AgNO鈧�(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 Since we now have 3 moles of AgCl precipitated, this means that during this time, one of the water ligands has been replaced by another Cl鈦� ion.

04

Determine the Final Formula

Now that we know one additional Cl鈦� ion replaced one of the water ligands, the final formula for the complex after one year would be [Ru(H鈧侽)鈧凜l鈧俔(+), with 3 AgCl as the precipitate.

05

Summarize the Observations

In summary, the initial compound, when mixed with AgNO鈧�(aq), precipitates 2 mol of AgCl per mole of complex, and the initial formula is [Ru(H鈧侽)鈧匔l]鈧�+. After a year, the compound reacts with AgNO鈧�(aq) to precipitate 3 mol of AgCl per mole of complex, with the final formula being [Ru(H鈧侽)鈧凜l鈧俔(+).

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