Calculate the weight of lime (CaO) obtained by heating 290kg of 95% pure lime stone (`CaCO_3`).
`CaCO_3​→CaO+CO_2` ​

Options

A. 185Kg
B. 158Kg
C. 154Kg
D. 198Kg

Explanation

To solve the problem of calculating the weight of lime (CaO) obtained by heating 290 kg of 95% pure limestone (CaCO₃), we will follow these steps:

### Step 1: Calculate the amount of pure limestone (CaCO₃)
Given that the limestone is 95% pure, we can calculate the amount of pure CaCO₃ in the 290 kg sample.

\[ \text{Amount of pure CaCO}_3 = \left(\frac{95}{100}\right) \times 290 \text{ kg} = 275.5 \text{ kg} \]

### Step 2: Convert the amount of pure CaCO₃ to grams
To work with molar masses, we will convert kilograms to grams.

\[ \text{Amount of pure CaCO}_3 = 275.5 \text{ kg} \times 1000 \text{ g/kg} = 275500 \text{ g} \]

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

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

### Step 4: Determine the molar masses
The molar mass of CaCO₃ is approximately 100 g/mol, and the molar mass of CaO is approximately 56 g/mol.

### Step 5: Calculate the amount of CaO produced
From the balanced equation, we see that 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, we can set up a proportion based on the molar masses:

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

Substituting the known values:

\[ \text{Weight of CaO} = \left(\frac{56 \text{ g}}{100 \text{ g}}\right) \times 275500 \text{ g} \]

### Step 6: Perform the calculation
Calculating the weight of CaO:

\[ \text{Weight of CaO} = 0.56 \times 275500 \text{ g} = 154280 \text{ g} \]

### Step 7: Convert grams back to kilograms
To express the weight of CaO in kilograms:

\[ \text{Weight of CaO} = \frac{154280 \text{ g}}{1000 \text{ g/kg}} = 154.28 \text{ kg} \]

### Final Answer
The weight of lime (CaO) obtained by heating 290 kg of 95% pure limestone is approximately **154.28 kg**.

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