When 200 g of lime strongly heated , it undergoes thermal decomposition to form 112 g of lime and unknown mass of carbon dioxide gas as `underset(200 g)(CaCO_(3))rarr underset(112 g)(CaO)+underset(?)(CO_(2))`
What will be the mass of `CO_(2)` formed ?

Options

A. 88 g
B. 24 g
C. 64 g
D. 40 g

Answer

To solve the problem of finding the mass of carbon dioxide (CO₂) formed when 200 g of calcium carbonate (CaCO₃) undergoes thermal decomposition, we can follow these steps:

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

### Step 2: Calculate the molar mass of calcium carbonate (CaCO₃)
To find the molar mass of CaCO₃, we add the atomic masses of its constituent elements:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (3 atoms of oxygen)

Calculating the total:
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + (16 \times 3) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 3: Calculate the molar mass of carbon dioxide (CO₂)
Next, we calculate the molar mass of CO₂:
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (2 atoms of oxygen)

Calculating the total:
\[ \text{Molar mass of CO}_2 = 12 + (16 \times 2) = 12 + 32 = 44 \text{ g/mol} \]

### Step 4: Determine the mass of CO₂ produced from 200 g of CaCO₃
From the balanced equation, we see that 100 g of CaCO₃ produces 44 g of CO₂. We need to find out how much CO₂ is produced from 200 g of CaCO₃.

Using a proportion:
\[ \frac{100 \text{ g CaCO}_3}{44 \text{ g CO}_2} = \frac{200 \text{ g CaCO}_3}{x \text{ g CO}_2} \]

Cross-multiplying gives:
\[ 100x = 200 \times 44 \]
\[ 100x = 8800 \]
\[ x = \frac{8800}{100} = 88 \text{ g CO}_2 \]

### Conclusion
The mass of carbon dioxide (CO₂) formed is **88 grams**.

---