A 10 g sample of a mixture of calcium chloride and sodium chloride is treated with `Na_(2)CO_(3)` to precipitate calcium as calcium carbonate. This `CaCO_(3)` is heated to convert all the calcium to CaO and the final mass of CaO is 1.12gm. Calculate % by mass of NaCl in the original mixture.

Options

A. 0.152
B. 0.321
C. 0.218
D. 0.1107

Answer

To solve the problem step by step, let's follow the outlined process:

### Step 1: Write the reaction for the conversion of calcium carbonate to calcium oxide.
The reaction is:
\[ \text{CaCO}_3 \xrightarrow{\text{heat}} \text{CaO} + \text{CO}_2 \]

### Step 2: Determine the mass of calcium carbonate (CaCO3) from the mass of calcium oxide (CaO).
Given that the mass of CaO produced is 1.12 g, we need to find the amount of CaCO3 that produced this amount of CaO.

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

The molar mass of CaCO3 is:
- Ca: 40 g/mol
- C: 12 g/mol
- O: 16 g/mol (3 O atoms)
- Molar mass of CaCO3 = 40 + 12 + (16 × 3) = 100 g/mol

Using the stoichiometric relationship:
\[ \text{mass of CaCO}_3 = \left(\frac{\text{mass of CaO}}{\text{molar mass of CaO}}\right) \times \text{molar mass of CaCO}_3 \]
Substituting the values:
\[ \text{mass of CaCO}_3 = \left(\frac{1.12 \, \text{g}}{56 \, \text{g/mol}}\right) \times 100 \, \text{g/mol = 2 g} \]

### Step 3: Determine the amount of calcium chloride (CaCl2) in the original mixture.
From the reaction between calcium chloride and sodium carbonate:
\[ \text{CaCl}_2 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 + 2 \text{NaCl} \]
This indicates that 1 mole of CaCl2 produces 1 mole of CaCO3.

Thus, the mass of CaCl2 that corresponds to 2 g of CaCO3 can be calculated using its molar mass:
- Molar mass of CaCl2 = 40 + (35.5 × 2) = 111 g/mol

Using the stoichiometric relationship:
\[ \text{mass of CaCl}_2 = \left(\frac{\text{mass of CaCO}_3}{\text{molar mass of CaCO}_3}\right) \times \text{molar mass of CaCl}_2 \]
Substituting the values:
\[ \text{mass of CaCl}_2 = \left(\frac{2 \, \text{g}}{100 \, \text{g/mol}}\right) \times 111 \, \text{g/mol = 2.22 g} \]

### Step 4: Calculate the mass of sodium chloride (NaCl) in the original mixture.
The total mass of the mixture is 10 g. Therefore, the mass of NaCl can be calculated as:
\[ \text{mass of NaCl} = \text{total mass} - \text{mass of CaCl}_2 \]
Substituting the values:
\[ \text{mass of NaCl} = 10 \, \text{g} - 2.22 \, \text{g} = 7.78 \, \text{g} \]

### Step 5: Calculate the percentage by mass of NaCl in the original mixture.
The percentage by mass of NaCl is given by:
\[ \text{Percentage of NaCl} = \left(\frac{\text{mass of NaCl}}{\text{total mass}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of NaCl} = \left(\frac{7.78 \, \text{g}}{10 \, \text{g}}\right) \times 100 = 77.8\% \]

### Final Answer:
The percentage by mass of NaCl in the original mixture is **77.8%**.