`CaCO_3` decomposes to give `CaO` and `CO_2`, if the masses of CaO and` CO_2` produced are 5.6 g and 4.4 g respectively by heating 12 g of an impure `CaCO_3` sample then the` % `impurity of the sample will be

Options

A. `33.33%`
B. `16.67%`
C. `83.33%`
D. `20%`

Answer

To solve the problem, we need to determine the percentage of impurity in the impure calcium carbonate sample. Here’s a step-by-step solution:

### Step 1: Write the decomposition reaction
The decomposition of calcium carbonate (CaCO₃) can be represented by the following chemical equation:
\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

### Step 2: Calculate the total mass of products
From the problem, we know the masses of the products formed:
- Mass of CaO = 5.6 g
- Mass of CO₂ = 4.4 g

Now, we can calculate the total mass of the products:
\[ \text{Total mass of products} = \text{Mass of CaO} + \text{Mass of CO}_2 \]
\[ \text{Total mass of products} = 5.6 \, \text{g} + 4.4 \, \text{g} = 10.0 \, \text{g} \]

### Step 3: Determine the mass of impurity
The mass of the original impure sample of CaCO₃ is given as 12 g. To find the mass of the impurity, we subtract the total mass of the products from the mass of the original sample:
\[ \text{Mass of impurity} = \text{Mass of impure sample} - \text{Total mass of products} \]
\[ \text{Mass of impurity} = 12 \, \text{g} - 10.0 \, \text{g} = 2.0 \, \text{g} \]

### Step 4: Calculate the percentage of impurity
To find the percentage of impurity in the sample, we use the formula:
\[ \text{Percentage of impurity} = \left( \frac{\text{Mass of impurity}}{\text{Mass of impure sample}} \right) \times 100 \]
\[ \text{Percentage of impurity} = \left( \frac{2.0 \, \text{g}}{12 \, \text{g}} \right) \times 100 \]
\[ \text{Percentage of impurity} = \left( \frac{2.0}{12} \right) \times 100 = 16.67\% \]

### Final Answer
The percentage of impurity in the sample is **16.67%**.

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