Question

A complex Cr(H$_2$O)$_6$Cl$_3$ shows conductance similar to a 1 : 2 electrolyte in aqueous solution. 9.3 g of this complex is passed through a cation exchanger and excess AgNO$_3$ is added. Find the mass of AgCl precipitated in grams.
[Molar mass of Cr = 52 g/mol]

Hint:

The number of free ions outside the coordination sphere determines electrolyte behavior and precipitation reactions.

Answer 1

Correct Answer: 10

Step 1: Understanding the nature of the complex.
Since the complex shows conductance similar to a 1 : 2 electrolyte, its structure is:
\[ [\text{Cr(H}_2\text{O)}_5\text{Cl}]Cl_2 \cdot H_2O \] This means two chloride ions are present outside the coordination sphere.
Step 2: Reaction with silver nitrate.
Each free chloride ion reacts with AgNO$_3$ to form AgCl:
\[ [\text{Cr(H}_2\text{O)}_5\text{Cl}]Cl_2 \cdot H_2O + 2AgNO_3 \rightarrow 2AgCl + \text{complex} \]
Step 3: Calculation of moles of complex.
Molar mass of complex = $52 + (6 \times 18) + (3 \times 35.5) = 266.5$ g/mol
\[ \text{Moles of complex} = \frac{9.3}{266.5} = 0.0349 \]
Step 4: Calculation of mass of AgCl formed.
Moles of AgCl formed = $2 \times 0.0349 = 0.0698$
Molar mass of AgCl = 143.5 g/mol
\[ \text{Mass of AgCl} = 0.0698 \times 143.5 = 10.015 \approx 10 \text{ g} \]