An impure sample of `CaCO_(3)` contains 38% of Ca. The percentage
of impurity present in the sample is :

Options

A. `5%`
B. `95%`
C. `10%`
D. `2.5%`

Answer

To solve the problem of finding the percentage of impurity in an impure sample of calcium carbonate (CaCO₃) that contains 38% calcium, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Atomic Mass of Calcium (Ca)**:
- The atomic mass of calcium (Ca) is 40 g/mol.

2. **Calculate the Molecular Mass of Calcium Carbonate (CaCO₃)**:
- The molecular mass of CaCO₃ can be calculated as follows:
- Ca: 40 g/mol
- C: 12 g/mol
- O: 16 g/mol (and there are 3 oxygen atoms)
- Therefore, the molecular mass of CaCO₃ = 40 + 12 + (16 × 3) = 40 + 12 + 48 = 100 g/mol.

3. **Calculate the Percentage of Calcium in Pure CaCO₃**:
- The percentage of calcium in pure CaCO₃ is calculated using the formula:
\[ \text{Percentage of Ca} = \left( \frac{\text{Atomic mass of Ca}}{\text{Molecular mass of CaCO}_3} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of Ca} = \left( \frac{40}{100} \right) \times 100 = 40\% \]

4. **Compare with the Given Percentage of Calcium in the Impure Sample**:
- The impure sample contains 38% calcium.

5. **Calculate the Percentage of Impurity**:
- The percentage of impurity can be calculated by finding the difference between the percentage of calcium in pure CaCO₃ and the percentage of calcium in the impure sample:
\[ \text{Percentage of Impurity} = \text{Percentage of Ca in pure CaCO}_3 - \text{Percentage of Ca in impure sample} \]
- Substituting the values:
\[ \text{Percentage of Impurity} = 40\% - 38\% = 2\% \]

6. **Calculate the Percentage of Impurity Relative to the Pure Sample**:
- To find the percentage of impurity relative to the pure sample:
\[ \text{Percentage of Impurity (relative)} = \left( \frac{\text{Change in Ca}}{\text{Percentage of Ca in pure CaCO}_3} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of Impurity (relative)} = \left( \frac{2}{40} \right) \times 100 = 5\% \]

### Final Answer:
The percentage of impurity present in the sample is **5%**.

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