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 ${\mathrm{AgNO}}_3(aq)$ 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 ${\mathrm{AgNO}}_3(aq)$ precipitates $3\mathrm{mol}$ of $\mathrm{AgCl}$ per mole of complex. What has happened in the ensuing time?

Short answer

In the beginning, the complex compound is $[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_5\mathrm{Cl}{]}^{+2}{\mathrm{Cl}}^{-}$, with 2 chlorines in the coordination sphere. After a year, the complex compound changes to $[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_4{\mathrm{Cl}}_2{]}^{+}{\mathrm{Cl}}^{-}$, indicating that one of the water molecules has been replaced by a chlorine anion, making all 3 chlorines part of the coordination sphere.

Step-by-step solution

Analyzing the formation of original complex compound

We know that the formula of the compound is ${\mathrm{RuCl}}_3\cdot 5{\mathrm{H}}_2\mathrm{O}$. When it is dissolved in water, it forms a solution similar in color to the original complex. Upon reacting with silver nitrate, 2 moles of solid $\mathrm{AgCl}$ form per mole of complex. This implies that 2 of the 3 chlorines are part of the coordination sphere in the original complex and the other one is a counter-ion.

Determine the ligands in the coordination sphere

Since there are 2 moles of $\mathrm{AgCl}$ formed per mole of complex, it means that 2 chlorines are part of the coordination sphere. The remaining chlorine and some water molecules must be outside the coordination sphere acting as counter-ions. Therefore, the formula for the compound with the ligands in the coordination sphere would be: $$[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_5\mathrm{Cl}{]}^{+2}{\mathrm{Cl}}^{-}$$

Analyzing the changes in the complex after a year

After a year, the chemical reaction with silver nitrate forms 3 moles of $\mathrm{AgCl}$ per mole of complex. This suggests that the third chlorine has entered into the coordination sphere of the complex. One of the water ligands from the coordination sphere must have been replaced by the chlorine anion.

Determine the new formula of the complex after a year

After a year, the chemical reaction with silver nitrate forms 3 moles of $\mathrm{AgCl}$ per mole of the complex, indicating that all 3 chlorines are now in the coordination sphere. Therefore, we will have to update the formula of the complex compound: $$[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_4{\mathrm{Cl}}_2{]}^{+}{\mathrm{Cl}}^{-}$$ In conclusion, the initial complex formula is $[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_5\mathrm{Cl}{]}^{+2}{\mathrm{Cl}}^{-}$. After a year, the complex formula has changed to $[\mathrm{Ru}({\mathrm{H}}_2\mathrm{O}{)}_4{\mathrm{Cl}}_2{]}^{+}{\mathrm{Cl}}^{-}$ due to the rearrangement of ligands, with one of the water molecules being replaced by a chlorine anion.