A mixture of `CaCl_(2)` and NaCl weighing 4.44 is treated with sodium carbonate solution to precipitate all the `Ca^(2+)` ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get 0.56 g of `CaO`. The percentage of NaCl in the mixture of (atomic mass of Ca=40) is

Options

A. 75
B. 30.6
C. 25
D. 69.4

Answer

To solve the problem step by step, we will follow the reactions and calculations involved in determining the percentage of NaCl in the mixture of CaCl₂ and NaCl.

### Step 1: Write the reactions
When the mixture of CaCl₂ and NaCl is treated with sodium carbonate (Na₂CO₃), calcium ions (Ca²⁺) from CaCl₂ precipitate as calcium carbonate (CaCO₃):
\[ \text{CaCl}_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + 2\text{NaCl} \]

Upon heating, calcium carbonate decomposes to form calcium oxide (CaO) and carbon dioxide (CO₂):
\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

### Step 2: Calculate moles of CaO produced
Given that 0.56 g of CaO is produced, we need to find the number of moles of CaO. The molar mass of CaO is approximately 56 g/mol.

Using the formula for moles:
\[ \text{Moles of CaO} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Moles of CaO} = \frac{0.56 \, \text{g}}{56 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 3: Relate moles of CaO to moles of CaCO₃
From the reaction, we know that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, the moles of CaCO₃ formed are also 0.01 mol.

### Step 4: Relate moles of CaCO₃ to moles of CaCl₂
From the first reaction, 1 mole of CaCO₃ is produced from 1 mole of CaCl₂. Thus, the moles of CaCl₂ in the mixture are also 0.01 mol.

### Step 5: Calculate the mass of CaCl₂
The molar mass of CaCl₂ is approximately 111 g/mol. Therefore, the mass of CaCl₂ can be calculated as follows:
\[ \text{Mass of CaCl}_2 = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of CaCl}_2 = 0.01 \, \text{mol} \times 111 \, \text{g/mol} = 1.11 \, \text{g} \]

### Step 6: Calculate the mass of NaCl in the mixture
The total mass of the mixture is given as 4.44 g. We can find the mass of NaCl by subtracting the mass of CaCl₂ from the total mass:
\[ \text{Mass of NaCl} = \text{Total mass} - \text{Mass of CaCl}_2 \]
\[ \text{Mass of NaCl} = 4.44 \, \text{g} - 1.11 \, \text{g} = 3.33 \, \text{g} \]

### Step 7: Calculate the percentage of NaCl in the mixture
To find the percentage of NaCl in the mixture, we use the formula:
\[ \text{Percentage of NaCl} = \left( \frac{\text{Mass of NaCl}}{\text{Total mass}} \right) \times 100 \]
\[ \text{Percentage of NaCl} = \left( \frac{3.33 \, \text{g}}{4.44 \, \text{g}} \right) \times 100 \approx 75\% \]

### Final Answer
The percentage of NaCl in the mixture is approximately **75%**.

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