Formation of polyethylene from calcium carbide takes place as follows
`CaC_(2)+2H_(2)OrarrCa(OH)_(2)_C_(2)H_(2)`
`C_(2)H_(2)+H_(2)rarrC_(2)H_(4)`
`n(C_(2)H_(4))rarr(-CH_(2)-CH_(2)-)_(n)`
The mass of polyethylene obtained in kg from 64 kg `CaC_(2)` is

Answer

To find the mass of polyethylene obtained from 64 kg of calcium carbide (CaC₂), we can follow these steps:

### Step 1: Determine the moles of calcium carbide (CaC₂)
First, we need to calculate the molar mass of calcium carbide (CaC₂):
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol × 2 = 24 g/mol (since there are 2 carbon atoms)

So, the molar mass of CaC₂ = 40 g/mol + 24 g/mol = 64 g/mol.

Now, we convert the mass of CaC₂ from kg to grams:
\[ 64 \text{ kg} = 64000 \text{ g} \]

Next, we calculate the moles of CaC₂:
\[ \text{Moles of CaC₂} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{64000 \text{ g}}{64 \text{ g/mol}} = 1000 \text{ moles} \]

### Step 2: Calculate the moles of acetylene (C₂H₂) produced
From the reaction:
\[ \text{CaC₂} + 2 \text{H₂O} \rightarrow \text{Ca(OH)₂} + \text{C₂H₂} \]
1 mole of CaC₂ produces 1 mole of C₂H₂. Therefore, 1000 moles of CaC₂ will produce:
\[ 1000 \text{ moles of C₂H₂} \]

### Step 3: Calculate the moles of ethylene (C₂H₄) produced
From the reaction:
\[ \text{C₂H₂} + \text{H₂} \rightarrow \text{C₂H₄} \]
1 mole of C₂H₂ produces 1 mole of C₂H₄. Thus, 1000 moles of C₂H₂ will produce:
\[ 1000 \text{ moles of C₂H₄} \]

### Step 4: Determine the moles of polyethylene (C₂H₄)n
The polymerization reaction is:
\[ n \text{(C₂H₄)} \rightarrow (-\text{CH₂-CH₂}-)_n \]
This means that the moles of C₂H₄ will directly correspond to the moles of polyethylene produced. Therefore, we have:
\[ 1000 \text{ moles of C₂H₄} \rightarrow 1000 \text{ moles of polyethylene} \]

### Step 5: Calculate the mass of polyethylene produced
The molar mass of polyethylene (C₂H₄) is:
\[ \text{C} = 12 \text{ g/mol} \times 2 + \text{H} = 1 \text{ g/mol} \times 4 = 24 \text{ g/mol} \]

Now, we calculate the total mass of polyethylene produced:
\[ \text{Mass of polyethylene} = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of polyethylene} = 1000 \text{ moles} \times 28 \text{ g/mol} = 28000 \text{ g} \]

Convert grams to kilograms:
\[ \text{Mass of polyethylene} = \frac{28000 \text{ g}}{1000} = 28 \text{ kg} \]

### Final Answer:
The mass of polyethylene obtained from 64 kg of calcium carbide is **28 kg**.

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