To determine the amount of polyethylene obtained from 64.0 kg of calcium carbide (CaC₂), we will follow these steps:
### Step 1: Calculate the number of moles of CaC₂
First, we need to convert the mass of calcium carbide from kilograms to grams:
\[
64.0 \, \text{kg} = 64000 \, \text{g}
\]
Next, we will use the molar mass of CaC₂ to find the number of moles. The molar mass of CaC₂ is 64 g/mol.
Using the formula for moles:
\[
\text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\]
\[
\text{Number of moles of CaC₂} = \frac{64000 \, \text{g}}{64 \, \text{g/mol}} = 1000 \, \text{moles}
\]
### Step 2: Determine the number of moles of C₂H₂ produced
From the reaction:
\[
\text{CaC}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + \text{C}_2\text{H}_2
\]
1 mole of CaC₂ produces 1 mole of C₂H₂. Therefore, the number of moles of C₂H₂ produced is also 1000 moles.
### Step 3: Determine the number of moles of C₂H₄ produced
Next, C₂H₂ reacts with hydrogen to form C₂H₄:
\[
\text{C}_2\text{H}_2 + \text{H}_2 \rightarrow \text{C}_2\text{H}_4
\]
Again, 1 mole of C₂H₂ produces 1 mole of C₂H₄. Thus, the number of moles of C₂H₄ produced is also 1000 moles.
### Step 4: Calculate the mass of C₂H₄
The molar mass of C₂H₄ (ethylene) is 28 g/mol. We can find the mass of C₂H₄ produced:
\[
\text{Mass of C}_2\text{H}_4 = \text{Number of moles} \times \text{Molar mass}
\]
\[
\text{Mass of C}_2\text{H}_4 = 1000 \, \text{moles} \times 28 \, \text{g/mol} = 28000 \, \text{g}
\]
### Step 5: Convert the mass of C₂H₄ to polyethylene
Since the reaction to form polyethylene from C₂H₄ is a 1:1 ratio:
\[
\text{Mass of polyethylene} = \text{Mass of C}_2\text{H}_4 = 28000 \, \text{g}
\]
### Step 6: Convert grams to kilograms
Finally, we convert the mass of polyethylene from grams to kilograms:
\[
28000 \, \text{g} = 28 \, \text{kg}
\]
### Final Answer
The amount of polyethylene obtained from 64.0 kg of CaC₂ is **28 kg**.
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