What is the concentration of chloride ion, in molarity, in a solution containing 10.56 gm `BaCl_(2). 8H_(2)O` per litre of solution ? (Ba = 137)

Answer

To find the concentration of chloride ions (Cl⁻) in molarity from a solution containing 10.56 g of BaCl₂·8H₂O per liter, follow these steps:

### Step 1: Calculate the Molar Mass of BaCl₂·8H₂O
- **Barium (Ba)**: 137 g/mol
- **Chlorine (Cl)**: 35.5 g/mol (2 Cl atoms = 2 × 35.5 g/mol = 71 g/mol)
- **Water (H₂O)**: 18 g/mol (8 H₂O molecules = 8 × 18 g/mol = 144 g/mol)

**Total Molar Mass Calculation**:
\[ \text{Molar Mass of BaCl₂·8H₂O} = 137 + 71 + 144 = 352 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of BaCl₂·8H₂O
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{10.56 \text{ g}}{352 \text{ g/mol}} \approx 0.03 \text{ moles} \]

### Step 3: Determine the Molarity of BaCl₂·8H₂O
Molarity (M) is defined as moles of solute per liter of solution. Since the volume of the solution is 1 liter:
\[ \text{Molarity of BaCl₂·8H₂O} = \frac{0.03 \text{ moles}}{1 \text{ L}} = 0.03 \text{ M} \]

### Step 4: Calculate the Molarity of Chloride Ions
From the dissociation of BaCl₂·8H₂O:
\[ \text{BaCl₂} \rightarrow \text{Ba}^{2+} + 2\text{Cl}^- \]
This indicates that 1 mole of BaCl₂ produces 2 moles of Cl⁻. Therefore, the molarity of Cl⁻ ions will be:
\[ \text{Molarity of Cl}^- = 2 \times \text{Molarity of BaCl₂·8H₂O} = 2 \times 0.03 \text{ M} = 0.06 \text{ M} \]

### Final Answer
The concentration of chloride ions in the solution is **0.06 M**.

---