Question

Calcium carbide produces acetylene on reaction with water. Ethylene can be obtained by reduction of C2H2. Polythene is produced by polymerization of C4H4 . Calculate the theoretical yield of polythene per kilogram of CaC2:-​

Answer 1

There needs to be a minor correction in the given question.

Polythene is produced by the polymerization of C₂H₄, and not C₄H₄.

The theoretical yield of polythene per kilogram of CaC₂ is 437.5 g by weight.

• The synthesis of polythene from CaC₂ takes place through the following reactions :

(i) CaC₂ + 2H₂O → C₂H₂ (acetylene) + Ca(OH)₂

(ii) C₂H₂ + H₂ → C₂H₄  (ethylene)

(iii) nC₂H₄ → (C₂H₄)n (polythene)

• From reaction (i), we see that 1 mole of CaC₂ yields 1 mole of C₂H₂.

• Now, Atomic weight of Ca = 40 g

Atomic weight of C = 12 g

Therefore, molar weight of CaC₂ = Atomic weight of Ca + 2 × Atomic weight of C

Or, Molar weight of CaC₂ = 40 g + 2 × 12 g = 40 g + 24 g = 64 g

• Now, molar weight of C₂H₂ =  2 × Atomic weight of C + 2 × Atomic weight of H

Or, Molar weight of C₂H₂ = (2 × 12 g) + (2 × 1 g) = (24 + 2) g = 26 g

• Therefore, we see that 44 g of CaC₂ yields 26 g of C₂H₂.

• Now, reduction of acetylene means reaction of acetylene with hydrogen. Therefore, reaction (ii) shows that reduction of 1 mole of acetylene (C₂H₂) gives 1 mole ethylene (C₂H₄).

• Molar weight of C₂H₄ = 2 × atomic weight of C + 4 × atomic weight of H

Or, Molar weight of C₂H₄ = 2 × 12 g + 4 × 1 g = (24 + 4) g = 28 g

• Therefore, 26 g of C₂H₂ yields 28 g of C₂H₄.

• Further, the polymerization of ethylene into polyethylene or polythene is shown in reaction (iii).

Polymerization is the combination of n number of smaller molecules called monomers to form one large molecule called polymer.

• Since one molecule of C₂H₄ weighs 28 g, n molecules of C₂H₄ will weigh n × 28 g = 28n g.

• Comparing with the starting compound CaC₂, we find that 64 g of CaC₂ yields 28n g of polythene.

• Now, 1 kg of CaC₂ = 1000 g of CaC₂

 1 g of CaC₂ yields (28n / 64) g of polythene

=> 1000 g of CaC₂ will yield {(28n × 1000) / 64 } g of polythene

Or, 1000 g of CaC₂ will yield 437.5n g of polythene.