`10 g` of a sample of a mixture of `CaCl_(2)` and `NaCl` is treated to precipitate all the calcium as `CaCO_(3)`. This `CaCO_(3)` is heated to convert all the `Ca` to `CaO` and the final mass of `CaO` is 1.62 g.The percent by mass of `CaCl_(2)` in the origial mixture is

Options

A. 0.321
B. 0.162
C. 0.218
D. 0.11

Explanation

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate the moles of CaO produced
We know that the mass of CaO produced is 1.62 g. To find the 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 is calculated as follows:
- Atomic mass of Ca = 40 g/mol
- Atomic mass of O = 16 g/mol

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

Now, substituting the values:

\[ \text{Moles of CaO} = \frac{1.62 \, \text{g}}{56 \, \text{g/mol}} = 0.02893 \, \text{mol} \]

### Step 2: Relate moles of CaO to moles of CaCl₂
From the stoichiometry of the reactions:
- 1 mole of CaCl₂ produces 1 mole of CaCO₃, which in turn produces 1 mole of CaO.

Therefore, the moles of CaCl₂ in the mixture is also 0.02893 mol.

### Step 3: Calculate the mass of CaCl₂
To find the mass of CaCl₂, we use the formula:

\[ \text{Mass of CaCl₂} = \text{Moles of CaCl₂} \times \text{Molar mass of CaCl₂} \]

The molar mass of CaCl₂ is calculated as follows:
- Atomic mass of Ca = 40 g/mol
- Atomic mass of 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, substituting the values:

\[ \text{Mass of CaCl₂} = 0.02893 \, \text{mol} \times 111 \, \text{g/mol} = 3.21 \, \text{g} \]

### Step 4: Calculate the percent by mass of CaCl₂ in the original mixture
The percent by mass of CaCl₂ in the mixture can be calculated using the formula:

\[ \text{Percent by mass of CaCl₂} = \left( \frac{\text{Mass of CaCl₂}}{\text{Total mass of mixture}} \right) \times 100 \]

Substituting the values:

\[ \text{Percent by mass of CaCl₂} = \left( \frac{3.21 \, \text{g}}{10 \, \text{g}} \right) \times 100 = 32.1\% \]

### Final Answer
The percent by mass of CaCl₂ in the original mixture is **32.1%**.

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