`CaCO_3` decomposes to give CaO and `CO_2`, if the masses of CaO and CO2 produced are 5.6 g and 4.4 g respectively by heating 12 g of an impure CaCO3 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 of determining the percentage of impurity in the sample of calcium carbonate (CaCO₃), we will follow these steps:

### Step 1: Write the decomposition reaction
The decomposition of calcium carbonate 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 impure sample of CaCO₃ is given as 12 g. According to the law of conservation of mass, the mass of the reactants should equal the mass of the products. Therefore, we can find the mass of impurity by subtracting the total mass of products from the mass of the impure sample:
\[ \text{Mass of impurity} = \text{Mass of impure sample} - \text{Total mass of products} \]
\[ \text{Mass of impurity} = 12 \, \text{g} - 10 \, \text{g} = 2 \, \text{g} \]

### Step 4: Calculate the percentage of impurity
To find the percentage of impurity in the sample, we use the formula:
\[ \text{Percentage of impurity} = \left( \frac{\text{Mass of impurity}}{\text{Mass of impure sample}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage of impurity} = \left( \frac{2 \, \text{g}}{12 \, \text{g}} \right) \times 100 \]
\[ \text{Percentage of impurity} = \left( \frac{2}{12} \right) \times 100 = 16.67\% \]

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

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