Polythene can be produced from calcium carbide according to the following sequence of reactions.
`CaC_(2)+2H_(2)Orarr Ca(OH)_(2)+C_(2)H_(2), C_(2)H_(2)+H_(2)rarr C_(2)H_(4), nC_(2)H_(4)rarr(C_(2)H_(4))n`
The mass of polythene which can be produced from `"20.0 kg of "CaC_(2)` is :

Options

A. 8.75 kg
B. 20 kg
C. 16.5 kg
D. 9.65 kg

Answer

To find the mass of polythene that can be produced from 20.0 kg of calcium carbide (CaC₂), we will follow these steps:

### Step 1: Convert the mass of CaC₂ to grams
Given:
- Mass of CaC₂ = 20.0 kg

To convert kilograms to grams:
\[ \text{Mass in grams} = 20.0 \, \text{kg} \times 1000 \, \text{g/kg} = 20000 \, \text{g} \]

### Step 2: Calculate the molar mass of CaC₂
The molar mass of CaC₂ can be calculated as follows:
- Atomic mass of Calcium (Ca) = 40 g/mol
- Atomic mass of Carbon (C) = 12 g/mol
- Therefore, the molar mass of CaC₂ = 40 + (2 × 12) = 40 + 24 = 64 g/mol

### Step 3: Calculate the number of moles of CaC₂
Using the formula:
\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]
\[ \text{Number of moles of CaC₂} = \frac{20000 \, \text{g}}{64 \, \text{g/mol}} = 312.5 \, \text{moles} \]

### Step 4: Determine the number of moles of C₂H₂ produced
From the reaction:
\[ \text{CaC₂} + 2 \text{H₂O} \rightarrow \text{Ca(OH)₂} + \text{C₂H₂} \]
The stoichiometry shows that 1 mole of CaC₂ produces 1 mole of C₂H₂. Therefore:
\[ \text{Moles of C₂H₂} = \text{Moles of CaC₂} = 312.5 \, \text{moles} \]

### Step 5: Determine the number of moles of C₂H₄ produced
From the reaction:
\[ \text{C₂H₂} + \text{H₂} \rightarrow \text{C₂H₄} \]
Again, the stoichiometry shows that 1 mole of C₂H₂ produces 1 mole of C₂H₄. Therefore:
\[ \text{Moles of C₂H₄} = \text{Moles of C₂H₂} = 312.5 \, \text{moles} \]

### Step 6: Calculate the molar mass of C₂H₄
The molar mass of C₂H₄ can be calculated as follows:
- Molar mass of C₂H₄ = (2 × 12) + (4 × 1) = 24 + 4 = 28 g/mol

### Step 7: Calculate the mass of polythene produced
Using the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
\[ \text{Mass of polythene} = 312.5 \, \text{moles} \times 28 \, \text{g/mol} = 8750 \, \text{g} \]

### Step 8: Convert grams to kilograms
To convert grams to kilograms:
\[ \text{Mass in kg} = \frac{8750 \, \text{g}}{1000} = 8.75 \, \text{kg} \]

### Final Answer
The mass of polythene that can be produced from 20.0 kg of CaC₂ is **8.75 kg**.

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