Theroretically Percentage of `Cl_(2)` in `CaOCl_(2)`

Options

A. `35%`
B. `56%`
C. `85%`
D. `12%`

Explanation

To find the theoretical percentage of \( Cl_2 \) in \( Ca(OCl)_2 \) (bleaching powder), we can follow these steps:

### Step 1: Determine the molar mass of \( Ca(OCl)_2 \)
- The formula for bleaching powder is \( Ca(OCl)_2 \).
- We need to calculate the molar mass by adding the atomic masses of each element in the compound:
- Calcium (Ca): 40 g/mol
- Oxygen (O): 16 g/mol (there are 2 oxygen atoms)
- Chlorine (Cl): 35.5 g/mol (there are 2 chlorine atoms)

### Calculation:
\[ \text{Molar mass of } Ca(OCl)_2 = \text{mass of Ca} + 2 \times \text{mass of O} + 2 \times \text{mass of Cl} \]
\[ = 40 + 2 \times 16 + 2 \times 35.5 \]
\[ = 40 + 32 + 71 = 143 \text{ g/mol} \]

### Step 2: Determine the total mass of chlorine in \( Ca(OCl)_2 \)
- Since there are 2 chlorine atoms in the compound:
\[ \text{Mass of Cl} = 2 \times 35.5 = 71 \text{ g} \]

### Step 3: Calculate the percentage of \( Cl_2 \) in \( Ca(OCl)_2 \)
- The percentage of \( Cl_2 \) in \( Ca(OCl)_2 \) can be calculated using the formula:
\[ \text{Percentage of } Cl_2 = \left( \frac{\text{mass of Cl}}{\text{molar mass of } Ca(OCl)_2} \right) \times 100 \]
\[ = \left( \frac{71}{143} \right) \times 100 \]
\[ \approx 49.65\% \]

### Step 4: Identify the closest option
- The calculated percentage of \( Cl_2 \) is approximately 49.65%.
- Among the options provided (35%, 56%, 85%, 12%), the closest option is 56%.

### Conclusion
Thus, the theoretical percentage of \( Cl_2 \) in \( Ca(OCl)_2 \) is approximately **56%**.

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