Calculate the volume of water required to dissolve`0.1g` lead (II) chloride to get a saturaed solution `(K_(sp)` of `PbCI_(2) = 3.2 xx 10^(-8)`, atomic mass of `Pb = 207 u)`. Multiply your answer with 10 to get answer.

Answer

To calculate the volume of water required to dissolve 0.1 g of lead (II) chloride (PbCl2) to get a saturated solution, follow these steps:

### Step 1: Write the dissociation equation
Lead (II) chloride dissociates in water as follows:
\[ \text{PbCl}_2 (s) \rightleftharpoons \text{Pb}^{2+} (aq) + 2 \text{Cl}^- (aq) \]

### Step 2: Define solubility (S)
Let the solubility of PbCl2 in water be \( S \) mol/L. Therefore, the concentration of lead ions (\( \text{Pb}^{2+} \)) will be \( S \) and the concentration of chloride ions (\( \text{Cl}^- \)) will be \( 2S \).

### Step 3: Write the expression for Ksp
The solubility product constant (\( K_{sp} \)) for PbCl2 can be expressed as:
\[ K_{sp} = [\text{Pb}^{2+}][\text{Cl}^-]^2 = S \cdot (2S)^2 = 4S^3 \]

### Step 4: Substitute the given Ksp value
Given that \( K_{sp} = 3.2 \times 10^{-8} \):
\[ 3.2 \times 10^{-8} = 4S^3 \]

### Step 5: Solve for S
Rearranging the equation gives:
\[ S^3 = \frac{3.2 \times 10^{-8}}{4} = 0.8 \times 10^{-8} = 8 \times 10^{-9} \]
Now, take the cube root:
\[ S = (8 \times 10^{-9})^{1/3} = 2 \times 10^{-3} \, \text{mol/L} \]

### Step 6: Calculate the number of moles of PbCl2
To find the number of moles of PbCl2 in 0.1 g, use the molar mass:
- Molar mass of Pb = 207 g/mol
- Molar mass of Cl = 35.5 g/mol
- Molar mass of PbCl2 = 207 + (2 × 35.5) = 207 + 71 = 278 g/mol

Now calculate the number of moles:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.1 \, \text{g}}{278 \, \text{g/mol}} \approx 3.60 \times 10^{-4} \, \text{mol} \]

### Step 7: Calculate the volume of water required
Using the molarity (S) we found earlier:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} \]
Rearranging gives:
\[ \text{Volume in L} = \frac{\text{Number of moles}}{S} = \frac{3.60 \times 10^{-4} \, \text{mol}}{2 \times 10^{-3} \, \text{mol/L}} = 0.18 \, \text{L} \]

### Step 8: Convert volume to mL
Since the question asks for the volume in mL, we convert:
\[ 0.18 \, \text{L} = 180 \, \text{mL} \]

### Step 9: Multiply by 10 as per the question
Finally, multiply the volume by 10:
\[ 180 \times 10 = 1800 \]

### Final Answer
The final answer is **1800**.

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