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. 22.4 litres
B. 2.24 litres
C. 20.16 litres
D. 2.016 litres

Answer

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

### Step 1: Determine the molar mass of calcium carbide (CaC₂)
- The molar mass of calcium (Ca) = 40 g/mol
- The molar mass of carbon (C) = 12 g/mol
- Since there are 2 carbon atoms in calcium carbide, we calculate:
\[ \text{Molar mass of CaC}_2 = 40 + (2 \times 12) = 40 + 24 = 64 \text{ g/mol} \]

### Step 2: Determine the molar mass of ethene (C₂H₄)
- The molar mass of hydrogen (H) = 1 g/mol
- The molar mass of ethene (C₂H₄) is calculated as follows:
\[ \text{Molar mass of C}_2\text{H}_4 = (2 \times 12) + (4 \times 1) = 24 + 4 = 28 \text{ g/mol} \]

### Step 3: Calculate the amount of ethene produced from 20.0 kg of calcium carbide
- From the reaction, 1 mole of CaC₂ produces 1 mole of C₂H₄.
- We need to find out how many moles of CaC₂ are in 20.0 kg:
\[ \text{Mass of CaC}_2 = 20.0 \text{ kg} = 20000 \text{ g} \]
\[ \text{Number of moles of CaC}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{20000 \text{ g}}{64 \text{ g/mol}} \approx 312.5 \text{ moles} \]

### Step 4: Calculate the mass of ethene produced
- Since 1 mole of CaC₂ produces 1 mole of C₂H₄, the number of moles of ethene produced is also 312.5 moles.
- Now, calculate the total mass of ethene produced:
\[ \text{Mass of C}_2\text{H}_4 = \text{Number of moles} \times \text{Molar mass} = 312.5 \text{ moles} \times 28 \text{ g/mol} \approx 8750 \text{ g} = 8.75 \text{ kg} \]

### Step 5: Calculate the mass of polythene produced
- The final step is to recognize that polythene is produced from ethene through polymerization. The mass of polythene produced will be the same as the mass of ethene produced:
\[ \text{Mass of polythene} \approx 8.75 \text{ kg} \]

### Final Answer
The mass of polythene which can be produced from 20.0 kg of calcium carbide is approximately **8.75 kg**.

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