Question

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12

Hint:

When calculating mass from moles, always use the correct molar masses and conversion factors (grams to kilograms) to ensure accurate results.

Answer 1

Correct Answer: 63

To determine the amount of calcium oxide (CaO) produced from heating 150 kg of limestone (CaCO₃), knowing the limestone is 75% pure, we follow these steps:

1. Calculate the mass of pure CaCO₃: The limestone is 75% pure, so the mass of pure CaCO₃ is 75% of 150 kg. 
Mass of pure CaCO₃ = 0.75 × 150 kg = 112.5 kg.

2. Use the chemical reaction:
CaCO₃ (s) → CaO (s) + CO₂ (g)

3. Calculate the molar masses: 
Ca = 40, C = 12, O = 16 (given). 
Molar mass of CaCO₃ = 40 + 12 + (16×3) = 100 g/mol.
Molar mass of CaO = 40 + 16 = 56 g/mol.

4. Convert mass of CaCO₃ to moles: 
Moles of CaCO₃ = \(\frac{112,500\, \text{g}}{100\, \text{g/mol}}\) = 1125 moles.

5. Moles of CaCO₃ to moles of CaO: The reaction shows a 1:1 molar ratio, so moles of CaO = 1125 moles.

6. Calculate the mass of CaO: 
Mass of CaO = moles of CaO × molar mass of CaO = 1125 moles × 56 g/mol = 63000 g = 63 kg.

7. Verify the range: The computed mass of CaO is 63 kg, which fits perfectly within the given range of 63-63 kg.

Therefore, the amount of calcium oxide produced is 63 kg.

Answer 2

Given that: \[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \] We start by calculating the mass of CaCO$_3$: \[ \text{mass of CaCO}_3 = \frac{150 \times 75}{100} = 112.5 \, \text{kg} \] Next, calculate the moles of CaCO$_3$: \[ n_{\text{CaCO}_3} = \frac{\text{mass}}{\text{molar mass of CaCO}_3} = \frac{1125000}{100} = 1125 \, \text{moles} \] Since each mole of CaCO$_3$ produces 1 mole of CaO, the moles of CaO formed will be the same: \[ n_{\text{CaO}} = 1125 \, \text{moles} \] Now, we calculate the mass of CaO: \[ \text{mass of CaO} = n_{\text{CaO}} \times \text{molar mass of CaO} = 1125 \times 56 = 63000 \, \text{grams} = 63 \, \text{kg} \] 
Thus, the amount of calcium oxide produced is 63 kg.