500 g impure sample of `CaCO_(3)` on heating gives 70 g of `CaO`. Percentage impurities in sample is

Options

A. `25%`
B. `50%`
C. `75%`
D. `80%`

Answer

To find the percentage of impurities in the sample of CaCO₃, we can follow these steps:

### Step 1: Understand the Reaction
When calcium carbonate (CaCO₃) is heated, it decomposes into calcium oxide (CaO) and carbon dioxide (CO₂):
\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

### Step 2: Calculate Molar Masses
- Molar mass of CaCO₃ = 40 (Ca) + 12 (C) + 3 × 16 (O) = 100 g/mol
- Molar mass of CaO = 40 (Ca) + 16 (O) = 56 g/mol
- Molar mass of CO₂ = 12 (C) + 2 × 16 (O) = 44 g/mol

### Step 3: Determine the Mass Ratio
From the balanced equation, 100 g of CaCO₃ produces 56 g of CaO and 44 g of CO₂. Therefore, the total mass of products formed from 100 g of CaCO₃ is:
\[ 56 \, \text{g (CaO)} + 44 \, \text{g (CO₂)} = 100 \, \text{g} \]

### Step 4: Relate the Mass of CaO to CaCO₃
Given that 70 g of CaO is produced, we can set up a proportion to find the mass of CO₂ produced:
\[ \frac{M_{\text{CaO}}}{M_{\text{CO}_2}} = \frac{56}{44} \]
Let \( x \) be the mass of CO₂ produced:
\[ \frac{70}{x} = \frac{56}{44} \]
Cross-multiplying gives:
\[ 70 \times 44 = 56 \times x \]
\[ 3080 = 56x \]
\[ x = \frac{3080}{56} = 55 \, \text{g (CO₂)} \]

### Step 5: Calculate Total Mass of Products
The total mass of products formed (CaO + CO₂) is:
\[ 70 \, \text{g (CaO)} + 55 \, \text{g (CO₂)} = 125 \, \text{g} \]

### Step 6: Determine the Mass of Pure CaCO₃
The mass of pure CaCO₃ that was originally present in the sample is equal to the total mass of products formed:
\[ \text{Mass of pure CaCO}_3 = 125 \, \text{g} \]

### Step 7: Calculate the Mass of Impurities
The mass of impurities in the sample is:
\[ \text{Mass of impurities} = \text{Total mass of sample} - \text{Mass of pure CaCO}_3 \]
\[ \text{Mass of impurities} = 500 \, \text{g} - 125 \, \text{g} = 375 \, \text{g} \]

### Step 8: Calculate Percentage of Impurities
The percentage of impurities in the sample is calculated as:
\[ \text{Percentage of impurities} = \left( \frac{\text{Mass of impurities}}{\text{Total mass of sample}} \right) \times 100 \]
\[ \text{Percentage of impurities} = \left( \frac{375 \, \text{g}}{500 \, \text{g}} \right) \times 100 = 75\% \]

### Final Answer
The percentage of impurities in the sample is **75%**.

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