How many grams of calcium oxide is obtained on heating 100 g of `CaCO_(3)(s)`?

Options

A. 50g
B. 40g
C. 56g
D. 44g

Answer

To determine how many grams of calcium oxide (CaO) are obtained from heating 100 g of calcium carbonate (CaCO₃), we can follow these steps:

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation**:
The decomposition of calcium carbonate upon heating can be represented by the following balanced equation:
\[ \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \]
This equation indicates that 1 mole of calcium carbonate produces 1 mole of calcium oxide and 1 mole of carbon dioxide.

2. **Calculate the Molar Mass of Calcium Carbonate (CaCO₃)**:
To find the molar mass of CaCO₃, we need to sum the atomic masses of its constituent elements:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (and there are 3 oxygen atoms in CaCO₃)

Therefore, the molar mass of CaCO₃ is:
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + (16 \times 3) = 40 + 12 + 48 = 100 \text{ g/mol} \]

3. **Determine the Moles of Calcium Carbonate**:
Since we have 100 g of calcium carbonate, we can calculate the number of moles using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{100 \text{ g}}{100 \text{ g/mol}} = 1 \text{ mole} \]

4. **Use Stoichiometry to Find Moles of Calcium Oxide Produced**:
From the balanced equation, we know that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, heating 1 mole of CaCO₃ will yield:
\[ 1 \text{ mole of CaO} \]

5. **Calculate the Molar Mass of Calcium Oxide (CaO)**:
Now, we need to find the molar mass of CaO:
- Calcium (Ca): 40 g/mol
- Oxygen (O): 16 g/mol

Thus, the molar mass of CaO is:
\[ \text{Molar mass of CaO} = 40 + 16 = 56 \text{ g/mol} \]

6. **Calculate the Mass of Calcium Oxide Produced**:
Since we have 1 mole of CaO produced from the decomposition of 1 mole of CaCO₃, the mass of CaO produced is:
\[ \text{Mass of CaO} = \text{Number of moles} \times \text{Molar mass} = 1 \text{ mole} \times 56 \text{ g/mol} = 56 \text{ g} \]

### Final Answer:
Thus, the mass of calcium oxide obtained from heating 100 g of calcium carbonate is **56 g**.

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