Consider a mixture $X$ which is made by dissolving $0.4$ mol of $[\mathrm{Co(NH_3)_5SO_4}]Br$ and $0.4$ mol of $[\mathrm{Co(NH_3)_5Br}]SO_4$ in water to make $4$ L of solution. When $2$ L of mixture $X$ is allowed to react with excess $\mathrm{AgNO_3}$, it forms precipitate $Y$. The rest $2$ L of mixture $X$ reacts with excess $\mathrm{BaCl_2}$ to form precipitate $Z$. Which of the following statements is CORRECT?
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- $Y$ is $\mathrm{BaSO_4}$ and $Z$ is $\mathrm{AgBr}$
- $0.1$ mol of $Y$ is formed
- $0.2$ mol of $Z$ is formed
$0.4$ mol of $Z$ is formed
The Correct Option is C
Solution and Explanation
Step 1: Understanding the complexes.
$[\mathrm{Co(NH_3)_5SO_4}]Br$ gives Br$^-$ as counter ion in solution.
$[\mathrm{Co(NH_3)_5Br}]SO_4$ gives SO$_4^{2-$} as counter ion in solution.
Step 2: Calculating moles in 2 L solution.
Total volume = $4$ L
So, $2$ L contains half the moles.
\[ \text{Moles of each salt in 2 L} = \frac{0.4}{2} = 0.2 \] Step 3: Reaction with AgNO$_3$.
Only free Br$^-$ reacts with $\mathrm{AgNO_3}$ to form $\mathrm{AgBr}$.
Moles of $\mathrm{AgBr}$ formed:
\[ 0.2\,\text{mol} \] Step 4: Reaction with BaCl$_2$.
Only free SO$_4^{2-}$ reacts with $\mathrm{BaCl_2}$ to form $\mathrm{BaSO_4}$.
Moles of $\mathrm{BaSO_4}$ formed:
\[ 0.2\,\text{mol} \] Step 5: Final conclusion.
The correct statement is that $0.2$ mol of $Z$ is formed.
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