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

Options

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

Answer

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

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

### Step 2: Determine the molar mass of CaCO₃.
The molar mass of calcium carbonate (CaCO₃) can be calculated as follows:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (3 oxygen atoms)

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 number of moles of CaCO₃ in 100 grams.
Using the formula:
\[ \text{Moles of CaCO}_3 = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Moles of CaCO}_3 = \frac{100 \text{ g}}{100 \text{ g/mol}} = 1 \text{ mole} \]

### Step 4: Use the stoichiometry of the reaction to find moles of CaO produced.
From the balanced equation, we see that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, if we start with 1 mole of CaCO₃, we will also produce 1 mole of CaO.

### Step 5: Calculate the molar mass of CaO.
The molar mass of calcium oxide (CaO) is calculated as follows:
- Calcium (Ca): 40 g/mol
- Oxygen (O): 16 g/mol

Calculating the total:
\[ \text{Molar mass of CaO} = 40 + 16 = 56 \text{ g/mol} \]

### Step 6: Calculate the mass of CaO produced.
Since we have 1 mole of CaO produced, we can find the mass:
\[ \text{Mass of CaO} = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of CaO} = 1 \text{ mole} \times 56 \text{ g/mol} = 56 \text{ g} \]

### Conclusion:
Thus, the mass of calcium oxide obtained from heating 100 grams of calcium carbonate is **56 grams**.

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