A mixture of `CaCl_(2)` and NaCl weighing 4.44g is treated with solution carbonate solution to precipitate all the `Ca^(2+)` ions as calcium carbonate . The calcium carbonate so obtained is heated strongly to get 0.25 g of CaO. The percentage of NaCl in the mixture (Atomic mass of Ca = 40) is.

Options

A. 75
B. 30.5
C. 25
D. 69.4

Explanation

To find the percentage of NaCl in the mixture of CaCl₂ and NaCl weighing 4.44 g, we can follow these steps:

### Step 1: Calculate the mass of CaCO₃ produced
Given that heating CaCO₃ produces CaO, we can use the mass of CaO obtained to find the mass of CaCO₃.

The molar mass of CaO is:
- Ca: 40 g/mol
- O: 16 g/mol
- Total = 40 + 16 = 56 g/mol

From the problem, we know that 0.25 g of CaO is produced.

Using the ratio of the molar masses:
\[ \text{Mass of CaCO}_3 = \left(\frac{100 \text{ g CaCO}_3}{56 \text{ g CaO}}\right) \times 0.25 \text{ g CaO} \]
Calculating this gives:
\[ \text{Mass of CaCO}_3 = \left(\frac{100}{56}\right) \times 0.25 = 0.4464 \text{ g} \]

### Step 2: Calculate the moles of CaCO₃
Next, we can find the moles of CaCO₃ produced:
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + 3 \times 16 = 100 \text{ g/mol} \]
\[ \text{Moles of CaCO}_3 = \frac{0.4464 \text{ g}}{100 \text{ g/mol}} = 0.004464 \text{ mol} \]

### Step 3: Determine the moles of Ca²⁺ ions
Since 1 mole of CaCO₃ is produced from 1 mole of Ca²⁺ ions, the moles of Ca²⁺ ions in the mixture is also 0.004464 mol.

### Step 4: Calculate the mass of CaCl₂ in the mixture
The molar mass of CaCl₂ is:
- Ca: 40 g/mol
- Cl: 35.5 g/mol (2 Cl atoms)
- Total = 40 + 2(35.5) = 111 g/mol

Using the moles of Ca²⁺ to find the mass of CaCl₂:
\[ \text{Mass of CaCl}_2 = \text{Moles} \times \text{Molar mass} = 0.004464 \text{ mol} \times 111 \text{ g/mol} = 0.4968 \text{ g} \]

### Step 5: Calculate the mass of NaCl in the mixture
The total mass of the mixture is given as 4.44 g. Therefore, the mass of NaCl can be calculated as:
\[ \text{Mass of NaCl} = \text{Total mass} - \text{Mass of CaCl}_2 = 4.44 \text{ g} - 0.4968 \text{ g} = 3.9432 \text{ g} \]

### Step 6: Calculate the percentage of NaCl in the mixture
Finally, we can find the percentage of NaCl in the mixture:
\[ \text{Percentage of NaCl} = \left(\frac{\text{Mass of NaCl}}{\text{Total mass}}\right) \times 100 = \left(\frac{3.9432 \text{ g}}{4.44 \text{ g}}\right) \times 100 \approx 88.8\% \]

### Conclusion
The percentage of NaCl in the mixture is approximately **88.8%**.

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