Which of the following statement is/are correct
1.0 g mixture of CaCO 3 ​ (s) and glass beads liberate 0.22 g of CO 2 ​ upon treatment with excess of HCl. Glass does not react with HCl.

Options

A. The weight of `CaCO_(3)` in the original mixture is `0.5 g`.
B. The weight of calcium in the original mixture is `0.2 g`
C. The weight percent of calcium in the original mixture is 40% `Ca`
D. The weight percent of `Ca` in the original mixture is 20% `Ca`

Explanation

To determine which statements are correct regarding the given mixture of CaCO₃ and glass beads, we can follow these steps:

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

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

### Step 2: Calculate Moles of CO₂ Produced
We know that 0.22 g of CO₂ is produced. To find the moles of CO₂, we use the molar mass of CO₂, which is approximately 44 g/mol.

\[ \text{Moles of CO}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{0.22 \, \text{g}}{44 \, \text{g/mol}} = 0.005 \, \text{mol} \]

### Step 3: Relate Moles of CO₂ to Moles of CaCO₃
From the balanced equation, we see that 1 mole of CaCO₃ produces 1 mole of CO₂. Therefore, the moles of CaCO₃ that reacted is also 0.005 mol.

### Step 4: Calculate the Mass of CaCO₃
Now, we can calculate the mass of CaCO₃ using its molar mass, which is approximately 100 g/mol.

\[ \text{Mass of CaCO}_3 = \text{moles} \times \text{molar mass} = 0.005 \, \text{mol} \times 100 \, \text{g/mol} = 0.5 \, \text{g} \]

### Step 5: Determine the Composition of the Mixture
Since the total mass of the mixture is 1.0 g and we have found that the mass of CaCO₃ is 0.5 g, we can find the mass of glass beads in the mixture.

\[ \text{Mass of glass beads} = \text{Total mass} - \text{Mass of CaCO}_3 = 1.0 \, \text{g} - 0.5 \, \text{g} = 0.5 \, \text{g} \]

### Step 6: Calculate the Percentage of CaCO₃ in the Mixture
To find the percentage of CaCO₃ in the mixture:

\[ \text{Percentage of CaCO}_3 = \left( \frac{\text{Mass of CaCO}_3}{\text{Total mass}} \right) \times 100 = \left( \frac{0.5 \, \text{g}}{1.0 \, \text{g}} \right) \times 100 = 50\% \]

### Conclusion
Based on the calculations:
- The weight of CaCO₃ in the original mixture is 0.5 g.
- The glass beads do not react with HCl.

Thus, the correct statements are:
1. The weight of CaCO₃ in the original mixture is 0.5 g (Correct).
2. The glass does not react with HCl (Correct).