A sample of mixture of `CaCl_(2)` and NaCl weighing 2.22 gm was treated to precipitate all the Ca as `CaCO_(3)` which was then heated and quantitatively converted to 0.84 gm of CaO. Calculate the percentage (by mass )of `CaCl_(2)` in the mixture.

Answer

To solve the problem step by step, we will follow the outlined procedure:

### Step 1: Determine the moles of CaO produced
We know that the mass of CaO produced is 0.84 g. To find the number of moles of CaO, we use the formula:

\[ \text{Moles of CaO} = \frac{\text{mass of CaO}}{\text{molar mass of CaO}} \]

The molar mass of CaO (Calcium Oxide) is calculated as follows:
- Calcium (Ca) = 40 g/mol
- Oxygen (O) = 16 g/mol

Thus, the molar mass of CaO = 40 + 16 = 56 g/mol.

Now, substituting the values:

\[ \text{Moles of CaO} = \frac{0.84 \text{ g}}{56 \text{ g/mol}} = 0.015 \text{ moles} \]

### Step 2: Relate moles of CaO to moles of CaCO3
From the chemical reaction, we know that:

\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

This indicates that 1 mole of CaCO3 produces 1 mole of CaO. Therefore, the moles of CaCO3 produced will also be:

\[ \text{Moles of CaCO}_3 = 0.015 \text{ moles} \]

### Step 3: Relate moles of CaCO3 to moles of CaCl2
Since the reaction shows that 1 mole of CaCl2 produces 1 mole of CaCO3, we can conclude that:

\[ \text{Moles of CaCl}_2 = 0.015 \text{ moles} \]

### Step 4: Calculate the mass of CaCl2
Now, we will calculate the mass of CaCl2 using its molar mass. The molar mass of CaCl2 is calculated as follows:
- Calcium (Ca) = 40 g/mol
- Chlorine (Cl) = 35.5 g/mol (and there are 2 Cl atoms)

Thus, the molar mass of CaCl2 = 40 + (2 × 35.5) = 40 + 71 = 111 g/mol.

Now, we can find the mass of CaCl2:

\[ \text{Mass of CaCl}_2 = \text{Moles of CaCl}_2 \times \text{Molar mass of CaCl}_2 \]

Substituting the values:

\[ \text{Mass of CaCl}_2 = 0.015 \text{ moles} \times 111 \text{ g/mol} = 1.665 \text{ g} \]

### Step 5: Calculate the percentage by mass of CaCl2 in the mixture
Now that we have the mass of CaCl2, we can calculate the percentage by mass of CaCl2 in the original mixture. The total mass of the mixture is given as 2.22 g.

\[ \text{Percentage of CaCl}_2 = \left( \frac{\text{Mass of CaCl}_2}{\text{Total mass of mixture}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage of CaCl}_2 = \left( \frac{1.665 \text{ g}}{2.22 \text{ g}} \right) \times 100 \approx 75.68\% \]

### Final Answer
The percentage by mass of CaCl2 in the mixture is approximately **75.68%**.

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