Calculate the weight of lime (CaO) obtained by heating 190kg of 95% pure lime stone (`CaCO_3`).
`CaCO_3​→CaO+CO_2` ​

Options

A. 101Kg
B. 202Kg
C. 303Kg
D. 404Kg

Explanation

To calculate the weight of lime (CaO) obtained by heating 190 kg of 95% pure limestone (CaCO₃), we can follow these steps:

### Step 1: Calculate the amount of pure CaCO₃
First, we need to determine the amount of pure CaCO₃ in the limestone. Since the limestone is 95% pure, we calculate:

\[ \text{Pure CaCO}_3 = 95\% \text{ of } 190 \text{ kg} \]

\[ \text{Pure CaCO}_3 = \frac{95}{100} \times 190 = 180.5 \text{ kg} \]

### Step 2: Convert kg to grams
Next, we convert the amount of pure CaCO₃ from kilograms to grams, since the molar masses are typically expressed in grams.

\[ \text{Pure CaCO}_3 = 180.5 \text{ kg} \times 1000 \text{ g/kg} = 180500 \text{ g} \]

### Step 3: Write the balanced chemical equation
The decomposition of calcium carbonate (CaCO₃) can be represented by the following equation:

\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \]

From this equation, we see that 1 mole of CaCO₃ produces 1 mole of CaO.

### Step 4: Determine the molar masses
Next, we need the molar masses of CaCO₃ and CaO:

- Molar mass of CaCO₃ = 100 g/mol
- Molar mass of CaO = 56 g/mol

### Step 5: Calculate the amount of CaO produced
Using the stoichiometry of the reaction, we can find out how much CaO is produced from the amount of CaCO₃ we have. The ratio of CaO produced to CaCO₃ is:

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

Substituting in the values we have:

\[ \text{Mass of CaO} = \left(\frac{56 \text{ g}}{100 \text{ g}}\right) \times 180500 \text{ g} \]

Calculating this gives:

\[ \text{Mass of CaO} = 0.56 \times 180500 = 101080 \text{ g} \]

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

\[ \text{Mass of CaO} = \frac{101080 \text{ g}}{1000 \text{ g/kg}} = 101.08 \text{ kg} \]

### Final Answer
The weight of lime (CaO) obtained by heating 190 kg of 95% pure limestone is approximately **101.08 kg**.

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