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Calculate the number of moles of calcium chloride that can be obtained from 50 g of limestone in the presence of excess hydrogen chloride.

[tex]
[ \text{Ca} = 40, \text{C} = 12, \text{O} = 16, \text{H} = 1, \text{Cl} = 35.5]
[/tex]

Sagot :

To calculate the number of moles of calcium chloride (CaCl₂) obtained from 50 grams of limestone (CaCO₃) in the presence of excess hydrogen chloride (HCl), we need to follow a series of steps. Here's a detailed, step-by-step solution:

### Step 1: Determine the Molar Mass of Calcium Carbonate (CaCO₃)

We are given the atomic masses of:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol

Calcium carbonate (CaCO₃) consists of:
- 1 atom of Calcium
- 1 atom of Carbon
- 3 atoms of Oxygen

Thus, the molar mass of CaCO₃ is calculated as:
[tex]\[ \text{Molar mass of } CaCO_3 = 40 \, (\text{for Ca}) + 12 \, (\text{for C}) + 3 \times 16 \, (\text{for O}) = 100 \, \text{g/mol} \][/tex]

### Step 2: Calculate the Moles of Calcium Carbonate (CaCO₃)

We have 50 grams of limestone (CaCO₃). To find the number of moles of CaCO₃, we use the formula:
[tex]\[ \text{Moles of } CaCO_3 = \frac{\text{mass of } CaCO_3}{\text{molar mass of } CaCO_3} \][/tex]
[tex]\[ \text{Moles of } CaCO_3 = \frac{50 \, \text{g}}{100 \, \text{g/mol}} = 0.5 \, \text{moles} \][/tex]

### Step 3: Determine the Relation in the Chemical Reaction

The balanced chemical equation for the reaction between CaCO₃ and HCl is:
[tex]\[ CaCO_3 + 2HCl \rightarrow CaCl_2 + CO_2 + H_2O \][/tex]

From the equation, we can see that:
- 1 mole of CaCO₃ reacts to produce 1 mole of CaCl₂

Thus, the number of moles of CaCl₂ produced is directly equal to the number of moles of CaCO₃ reacted.

### Step 4: Calculate the Moles of Calcium Chloride (CaCl₂)

Given that we have 0.5 moles of CaCO₃, the number of moles of CaCl₂ produced will be:
[tex]\[ \text{Moles of } CaCl_2 = 0.5 \, \text{moles} \][/tex]

### Conclusion

So, the number of moles of calcium chloride (CaCl₂) that can be obtained from 50 grams of limestone (CaCO₃) in the presence of excess hydrogen chloride (HCl) is:
[tex]\[ 0.5 \, \text{moles} \][/tex]