Four gram of mixture of calcium carbonate and sand is treated with excess of HCl and 0.880 g of carbon-di-oxide is produced. What is the percentage of calcium carbonate in original mixture ?

Options

A. `40%`
B. `50%`
C. `55%`
D. `45%`

Explanation

To find the percentage of calcium carbonate in the original mixture, we can follow these steps:

### Step 1: Write the chemical reaction
When calcium carbonate (CaCO₃) reacts with hydrochloric acid (HCl), it produces calcium chloride (CaCl₂), water (H₂O), and carbon dioxide (CO₂). The balanced chemical equation is:

\[ \text{CaCO}_3 (s) + 2 \text{HCl} (aq) \rightarrow \text{CaCl}_2 (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g) \]

### Step 2: Determine the molar mass of calcium carbonate and carbon dioxide
- The molar mass of calcium carbonate (CaCO₃) is approximately 100 g/mol.
- The molar mass of carbon dioxide (CO₂) is approximately 44 g/mol.

### Step 3: Use the mass of CO₂ produced to find the mass of CaCO₃
From the reaction, we know that 1 mole of CaCO₃ produces 1 mole of CO₂. Therefore, we can set up a proportion based on the masses:

If 100 g of CaCO₃ produces 44 g of CO₂, then we can find how much CaCO₃ corresponds to the 0.880 g of CO₂ produced:

\[ \text{Mass of CaCO}_3 = \left( \frac{100 \, \text{g CaCO}_3}{44 \, \text{g CO}_2} \right) \times 0.880 \, \text{g CO}_2 \]

Calculating this gives:

\[ \text{Mass of CaCO}_3 = \frac{100 \times 0.880}{44} = 2 \, \text{g} \]

### Step 4: Calculate the percentage of calcium carbonate in the original mixture
The total mass of the mixture is 4 g. To find the percentage of calcium carbonate in the mixture, we use the formula:

\[ \text{Percentage of CaCO}_3 = \left( \frac{\text{Mass of CaCO}_3}{\text{Total mass of mixture}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Percentage of CaCO}_3 = \left( \frac{2 \, \text{g}}{4 \, \text{g}} \right) \times 100 = 50\% \]

### Final Answer
The percentage of calcium carbonate in the original mixture is **50%**.