Limestone (`CaCO_(3)`) decomposes into quicklime (CaO) on strong heating. How much quantity of limestone will be required to prepare 100 kg of quicklime?

Explanation

To determine how much limestone (CaCO₃) is required to prepare 100 kg of quicklime (CaO), we can follow these steps:

### Step 1: Write the decomposition reaction
The decomposition of calcium carbonate (CaCO₃) into calcium oxide (CaO) and carbon dioxide (CO₂) can be represented by the following chemical equation:

\[ \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \]

### Step 2: Calculate the molar masses
Next, we need to calculate the molar masses of the compounds involved:

- Molar mass of CaCO₃:
- Ca: 40 g/mol
- C: 12 g/mol
- O: 16 g/mol × 3 = 48 g/mol
- Total: 40 + 12 + 48 = 100 g/mol

- Molar mass of CaO:
- Ca: 40 g/mol
- O: 16 g/mol
- Total: 40 + 16 = 56 g/mol

### Step 3: Determine the stoichiometry
From the balanced equation, we see that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, the molar ratio is 1:1.

### Step 4: Calculate the amount of CaCO₃ needed for 100 kg of CaO
We need to find out how many grams of CaCO₃ are required to produce 100 kg (or 100,000 g) of CaO.

Using the molar masses calculated:
- 1 mole of CaO (56 g) is produced from 1 mole of CaCO₃ (100 g).

Now, we can set up a proportion to find the required mass of CaCO₃:

\[ \text{Mass of CaCO}_3 = \left( \frac{\text{Mass of CaCO}_3}{\text{Mass of CaO}} \right) \times \text{Mass of CaO} \]

Substituting the known values:

\[ \text{Mass of CaCO}_3 = \left( \frac{100 \, \text{g}}{56 \, \text{g}} \right) \times 100,000 \, \text{g} \]

### Step 5: Perform the calculation
Calculating the above expression:

\[ \text{Mass of CaCO}_3 = \left( \frac{100}{56} \right) \times 100,000 \]

\[ = 1.7857 \times 100,000 \approx 178,570 \, \text{g} \]

### Step 6: Convert to kg
To convert grams to kilograms:

\[ \text{Mass of CaCO}_3 = \frac{178,570 \, \text{g}}{1000} \approx 178.57 \, \text{kg} \]

### Final Answer
Approximately **178.57 kg** of limestone (CaCO₃) is required to prepare 100 kg of quicklime (CaO).

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