Calculate the weight of lime `(CaO)` obtained by heating `200` kg of `95%` pure lime stone `(CaCO_(3)).`

Options

A. `104.4 kg`
B. `105.4 kg`
C. `212.8kg`
D. `106.4 kg`

Answer

To solve the problem of calculating the weight of lime (CaO) obtained by heating 200 kg of 95% pure limestone (CaCO₃), we will follow these steps:

### Step 1: Calculate the mass of pure CaCO₃
Given that the limestone is 95% pure, we first need to find the mass of pure calcium carbonate (CaCO₃) in the 200 kg sample.

\[ \text{Mass of pure CaCO₃} = \text{Total mass} \times \text{Purity} \]
\[ \text{Mass of pure CaCO₃} = 200 \, \text{kg} \times \frac{95}{100} = 190 \, \text{kg} \]

### Step 2: Convert the mass of pure CaCO₃ to grams
Since the molar mass calculations are easier in grams, we convert the mass from kilograms to grams.

\[ \text{Mass of pure CaCO₃ in grams} = 190 \, \text{kg} \times 1000 \, \text{g/kg} = 190000 \, \text{g} \]

### Step 3: Calculate the number of moles of CaCO₃
Next, we need to calculate the number of moles of calcium carbonate using its molar mass. The molar mass of CaCO₃ is calculated as follows:

- Molar mass of Ca (Calcium) = 40 g/mol
- Molar mass of C (Carbon) = 12 g/mol
- Molar mass of O (Oxygen) = 16 g/mol (3 O atoms = 48 g/mol)

\[ \text{Molar mass of CaCO₃} = 40 + 12 + 48 = 100 \, \text{g/mol} \]

Now, we can calculate the number of moles of CaCO₃:

\[ \text{Number of moles of CaCO₃} = \frac{\text{Mass of pure CaCO₃}}{\text{Molar mass of CaCO₃}} = \frac{190000 \, \text{g}}{100 \, \text{g/mol}} = 1900 \, \text{mol} \]

### Step 4: Determine the number of moles of CaO produced
From the balanced chemical equation for the decomposition of calcium carbonate:

\[ \text{CaCO₃} \rightarrow \text{CaO} + \text{CO₂} \]

We see that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, the number of moles of CaO produced will be the same as the number of moles of CaCO₃:

\[ \text{Number of moles of CaO} = 1900 \, \text{mol} \]

### Step 5: Calculate the mass of CaO produced
Now, we calculate the mass of CaO produced using its molar mass. The molar mass of CaO is:

- Molar mass of Ca (Calcium) = 40 g/mol
- Molar mass of O (Oxygen) = 16 g/mol

\[ \text{Molar mass of CaO} = 40 + 16 = 56 \, \text{g/mol} \]

Now we can find the mass of CaO produced:

\[ \text{Mass of CaO} = \text{Number of moles of CaO} \times \text{Molar mass of CaO} \]
\[ \text{Mass of CaO} = 1900 \, \text{mol} \times 56 \, \text{g/mol} = 106400 \, \text{g} \]

### Step 6: Convert the mass of CaO to kilograms
Finally, we convert the mass of CaO from grams to kilograms:

\[ \text{Mass of CaO in kg} = \frac{106400 \, \text{g}}{1000 \, \text{g/kg}} = 106.4 \, \text{kg} \]

### Final Answer
The weight of lime (CaO) obtained by heating 200 kg of 95% pure limestone (CaCO₃) is **106.4 kg**.

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