Problem 16 - Chemistry in 30 days

Question

Formation of polyethylene from calcium carbide takes place as follows: \(\mathrm{CaC}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{C}_{2} \mathrm{H}_{2}\) \(\mathrm{C}_{2} \mathrm{H}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4}\) \(n \mathrm{C}_{2} \mathrm{H}_{4} \rightarrow\left(-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right)_{n}\) the amount of polyethylene obtained from \(64.1 \mathrm{~kg}\) of \(\mathrm{CaC}_{2}\) is (a) \(7 \mathrm{~kg}\) (b) \(14 \mathrm{~kg}\) (c) \(21 \mathrm{~kg}\) (d) \(28 \mathrm{~kg}\)

Step-by-Step Solution

Answer

(d) 28 kg

Step 1: Understanding the Reaction Pathway

The formation of polyethylene from calcium carbide (\(\text{CaC}_2\) is a multi-step process:1. First, calcium carbide reacts with water (\(\text{H}_2\text{O}\) to produce acetylene (\(\text{C}_2\text{H}_2\) and calcium hydroxide (\(\text{Ca(OH)}_2\).2. Acetylene then reacts with hydrogen (\(\text{H}_2\) to form ethylene (\(\text{C}_2\text{H}_4\).3. Finally, ethylene undergoes polymerization to form polyethylene (\((-\text{CH}_2-\text{CH}_2-)_{n}\).We need to determine how much polyethylene can be formed from 64.1 kg of \(\text{CaC}_2\).

Step 2: Calculate Moles of Calcium Carbide

First, we calculate the number of moles of calcium carbide (\(\text{CaC}_2\)) using its molar mass. The molar mass of \(\text{CaC}_2\) is \(40.08 \, \text{g/mol} + 2 \times 12.01 \, \text{g/mol} = 64.10 \, \text{g/mol}\).The number of moles of \(\text{CaC}_2\) is calculated as:\[\text{Moles of } \text{CaC}_2 = \frac{64100 \, \text{g}}{64.10 \, \text{g/mol}} = 1000 \, \text{moles}\]

Step 3: Determine Moles of Ethylene Produced

From the first reaction, each mole of \(\text{CaC}_2\) produces one mole of \(\text{C}_2\text{H}_2\). From the second reaction, each mole of \(\text{C}_2\text{H}_2\) produces one mole of \(\text{C}_2\text{H}_4\) (ethylene).Thus, 1000 moles of \(\text{CaC}_2\) produce 1000 moles of \(\text{C}_2\text{H}_4\).

Step 4: Calculate Mass of Polyethylene Produced

Polyethylene is formed from \(\text{C}_2\text{H}_4\) with a molar mass of \(28.05 \, \text{g/mol}\) (for the \(\text{CH}_2\text{CH}_2\) unit). Thus, the mass of the polyethylene produced will be:\[\text{Mass of polyethylene} = 1000 \, \text{moles} \times 28.05 \, \text{g/mol} = 28050 \, \text{g} = 28.05 \, \text{kg}\]

Step 5: Final Answer

From the calculations, 28.05 kg of polyethylene can be obtained from 64.1 kg of \(\text{CaC}_2\). Therefore, the answer is (d) 28 kg.

Key Concepts

Calcium Carbide

Calcium carbide, \( \text{CaC}_2 \), is a compound that plays a crucial role in the chemical industry. It is mainly used for the production of acetylene gas, which is an essential precursor to ethylene, and eventually, polyethylene production. Calcium carbide is formed via the combination of calcium and carbon at very high temperatures. When introduced to water, it reacts to produce acetylene and calcium hydroxide. This reaction is represented by the equation:

\(\mathrm{CaC}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}+ \mathrm{C}_{2} \mathrm{H}_{2}\)

• Highly reactive and requires careful handling
• Used in various industrial processes beyond acetylene production
• Important precursor for polyethylene

Acetylene

Acetylene, represented chemically as \( \text{C}_2\text{H}_2 \), is a hydrocarbon and a building block for various organic compounds. Known for its high reactivity due to the triple bond between the carbon atoms, acetylene is not only used for welding and cutting in its gaseous state but is also crucial in chemical synthesis.

When acetylene is produced from calcium carbide, it serves as an intermediate in synthesizing ethylene. This transformation involves a hydrogenation reaction where acetylene reacts with hydrogen gas to form ethylene:

\( \mathrm{C}_{2} \mathrm{H}_{2}+ \mathrm{H}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \)

• Contains carbon-carbon triple bonds
• Very versatile in organic chemistry
• Crucial step towards creating ethylene and polyethylene

Ethylene

Ethylene, \( \text{C}_2\text{H}_4 \), is an unsaturated hydrocarbon with a double bond between its carbon atoms. It is one of the most important raw materials in the petrochemical industry. Ethylene serves as a precursor to polyethylene, the most widely used plastic in the world.

Ethylene is produced from acetylene through the addition of hydrogen. This compound is highly reactive, allowing it to polymerize easily. The resulting reaction is a polymerization process that transforms multiple ethylene molecules into polyethylene.

• Double-bonded carbon structure
• Major feedstock for plastic production
• Interface between simple hydrocarbons and complex polymers

Polymerization

Polymerization is the chemical process that transforms small molecules, known as monomers, into large chain-like structures called polymers. In the case of polyethylene production, ethylene serves as the monomer, and the polymerization process involves linking these molecules to form long chains of polyethylene.

The polymerization of ethylene occurs through a reaction that repeatedly joins ethylene units:

\( n \mathrm{C}_2\mathrm{H}_4 \rightarrow (-\mathrm{CH}_2-\mathrm{CH}_2-)_{n} \)

• Results in formation of high molecular weight compounds
• Key process in manufacturing various types of plastics
• Enables control over the properties of the final product through reaction conditions