Core Logic
The 4 L$4 \text{ L}$ solution contains:
0.4 mol$0.4 \text{ mol}$ of [Co(NH₃)₅SO₄]Br$[Co(NH_3)_5SO_4]Br$ $\implies$ Gives 0.4 mol Br^-$0.4 \text{ mol } Br^-$ in solution.
0.4 mol$0.4 \text{ mol}$ of [Co(NH₃)₅Br]SO₄$[Co(NH_3)_5Br]SO_4$ $\implies$ Gives 0.4 mol SO₄²⁻$0.4 \text{ mol } SO_4^{2-}$ in solution.
The solution is divided into two 2 L$2 \text{ L}$ portions. Each 2 L$2 \text{ L}$ portion will contain exactly half the moles of each species:
Moles of Br^-$Br^-$ in 2 L = 0.2 mol$2 \text{ L} = 0.2 \text{ mol}$
Moles of SO₄²⁻$SO_4^{2-}$ in 2 L = 0.2 mol$2 \text{ L} = 0.2 \text{ mol}$
Step 1: Reaction with Silver Nitrate
When the first 2 L$2 \text{ L}$ of the mixture reacts with excess AgNO₃$AgNO_3$:
Ag^+ + Br^- arrow AgBr (Precipitate 'Y')$$Ag^+ + Br^- \rightarrow AgBr \downarrow (\text{Precipitate 'Y'})$$
Since there are 0.2 mol$0.2 \text{ mol}$ of free Br^-$Br^-$ ions, 0.2 mol$0.2 \text{ mol}$ of AgBr$AgBr$ (Y) will be formed.
Step 2: Reaction with Barium Chloride
When the remaining 2 L$2 \text{ L}$ of the mixture reacts with excess BaCl₂$BaCl_2$:
Ba²⁺ + SO₄²⁻ arrow BaSO₄ (Precipitate 'Z')$$Ba^{2+} + SO_4^{2-} \rightarrow BaSO_4 \downarrow (\text{Precipitate 'Z'})$$
Since there are 0.2 mol$0.2 \text{ mol}$ of free SO₄²⁻$SO_4^{2-}$ ions, 0.2 mol$0.2 \text{ mol}$ of BaSO₄$BaSO_4$ (Z) will be formed.
Step 3: Final Conclusion
Checking the options:
(1) 0.2 mol$0.2 \text{ mol}$ of 'Z' is formed $\implies$ True.
(2) 'Y' is BaSO₄$BaSO_4$ and 'Z' is AgBr$AgBr$ $\implies$ False, they are reversed.
(3) 0.4 mol$0.4 \text{ mol}$ of 'Z' is formed $\implies$ False, it's 0.2 mol$0.2 \text{ mol}$.
(4) 0.1 mol$0.1 \text{ mol}$ of 'Y' is formed $\implies$ False, it's 0.2 mol$0.2 \text{ mol}$.
Pattern Recognition
Only the counter-ions (outside the coordination sphere) ionize in water and participate in precipitation reactions. Always account for volume fractions when a solution is split.
Chapter Mix
Class 12 Chemistry: Coordination Compounds
Class 11 Chemistry: Some Basic Concepts of Chemistry