Question

A coordination compound \(CrCl_3 \cdot 6H_2O\) is mixed with excess of \(AgNO_3\) solution, two moles of \(AgCl\) are precipitated per mole of the compound. Write the structural formula of the coordination compound.

Hint:

For hydrated chromium chloride complexes: \[ [Cr(H_2O)_6]Cl_3 \] gives \(3\) moles of \(AgCl\). \[ [Cr(H_2O)_5Cl]Cl_2 \cdot H_2O \] gives \(2\) moles of \(AgCl\). \[ [Cr(H_2O)_4Cl_2]Cl \cdot 2H_2O \] gives \(1\) mole of \(AgCl\). The number of moles of \(AgCl\) formed equals the number of chloride ions present outside the coordination sphere.

Answer 1

Concept: The structural formula of a coordination compound can be determined by studying the number of ions produced in solution and the number of chloride ions that react with silver nitrate. Silver nitrate reacts only with those chloride ions that are present outside the coordination sphere (ionisable chloride ions). Chloride ions present inside the coordination sphere remain coordinated to the metal ion and do not immediately precipitate with silver nitrate. The reaction involved is \[ Ag^+ + Cl^- \rightarrow AgCl \downarrow \] Thus, the number of moles of \(AgCl\) formed gives the number of ionisable chloride ions present outside the coordination sphere.

Step 1: Writing the given compound. The molecular formula is \[ CrCl_3 \cdot 6H_2O \] The compound contains: \[ 1 \; Cr \] \[ 3 \; Cl^- \] \[ 6 \; H_2O \]

Step 2: Using the information provided by the \(AgNO_3\) test. The question states that \[ 2 \text{ moles of } AgCl \] are obtained per mole of the coordination compound. Since each mole of \(AgCl\) requires one mole of free chloride ion, \[ Ag^+ + Cl^- \rightarrow AgCl \] the formation of two moles of \(AgCl\) indicates that \[ \boxed{2 \text{ chloride ions are present outside the coordination sphere}} \] These chloride ions are ionisable and react immediately with silver nitrate.

Step 3: Determining the chloride ions inside the coordination sphere. The compound contains a total of three chloride ions. Out of these, \[ 2 \] chloride ions are outside the coordination sphere. Therefore, \[ 3-2=1 \] chloride ion must be coordinated directly to chromium inside the coordination sphere. Thus, the coordination sphere must contain \[ 1Cl^- \] and the remaining positions are occupied by water molecules.

Step 4: Determining the coordination number of chromium. Chromium(III) generally exhibits coordination number 6. One position is occupied by chloride ion. Hence, the remaining five positions are occupied by water molecules. Therefore, the complex ion becomes \[ [Cr(H_2O)_5Cl]^{2+} \] The two chloride ions remain outside the coordination sphere. Hence, the structural formula is \[ \boxed{[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O} \]

Step 5: Verification. Inside coordination sphere: \[ 1Cl^- + 5H_2O \] Outside coordination sphere: \[ 2Cl^- \] Water molecules: \[ 5+1=6 \] Total chloride ions: \[ 1+2=3 \] Thus, the molecular formula remains \[ CrCl_3 \cdot 6H_2O \] and two chloride ions are available to form two moles of \(AgCl\).

Final Answer: \[ \boxed{[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O} \]