In one litre of pure water, 44.4 g of calcium chloride is dissolved. The number of ions in one mL of the resultant solution is :

Options

A. `7.23 xx 10^(23)`
B. `7.23 xx 10^(20)`
C. `4.82 xx 10^(23)`
D. `4.82 xx 10^(20)`

Explanation

To solve the problem of finding the number of ions in one mL of a solution made by dissolving 44.4 g of calcium chloride (CaCl₂) in one liter of pure water, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Molar Mass of Calcium Chloride (CaCl₂)**:
- The molar mass of calcium (Ca) = 40.08 g/mol
- The molar mass of chlorine (Cl) = 35.45 g/mol
- Therefore, the molar mass of CaCl₂ = 40.08 g/mol + (2 × 35.45 g/mol) = 40.08 g/mol + 70.90 g/mol = 110.98 g/mol

2. **Calculate the Number of Moles of CaCl₂**:
- Number of moles = mass (g) / molar mass (g/mol)
- Number of moles of CaCl₂ = 44.4 g / 110.98 g/mol ≈ 0.400 moles

3. **Determine the Molarity of the Solution**:
- Molarity (M) = number of moles of solute / volume of solution (L)
- Since we have 1 liter of solution, the molarity of the CaCl₂ solution is:
- Molarity = 0.400 moles / 1 L = 0.400 M

4. **Calculate the Number of Moles in 1 mL of Solution**:
- Since 1 L = 1000 mL, the number of moles in 1 mL = (0.400 moles / 1000 mL) × 1 mL = 0.000400 moles

5. **Determine the Number of Ions Produced by Dissociation**:
- Calcium chloride dissociates in water as follows:
\[ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- \]
- For every 1 mole of CaCl₂, it produces 3 moles of ions (1 Ca²⁺ and 2 Cl⁻).
- Therefore, the total number of moles of ions in 1 mL = 0.000400 moles of CaCl₂ × 3 = 0.001200 moles of ions.

6. **Convert Moles of Ions to Number of Ions**:
- Using Avogadro's number (6.022 × 10²³ ions/mol):
- Number of ions = 0.001200 moles × 6.022 × 10²³ ions/mol ≈ 7.22 × 10²⁰ ions.

### Final Answer:
The number of ions in one mL of the resultant solution is approximately **7.22 × 10²⁰ ions**.