Problem 36 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The polymerisation of ethylene to linear polyethylene is represented by the reaction [1994 - 2 Marks] \(n \mathrm{CH}_{2}=\mathrm{CH}_{2} \longrightarrow \mathrm{E} \mathrm{CH}_{2}-\mathrm{CH}_{2} \frac{1}{\pi}\) where \(n\) has a large integral value. Given that the average enthalpies of bond dissociation for \(\mathrm{C}=\mathrm{C}\) and \(\mathrm{C}-\mathrm{C}\) at \(298 \mathrm{~K}\) are \(+590\) and \(+331 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\), respectively, calculate the enthalpy of polymerisation per mole of ethylene at \(298 \mathrm{~K}\).

Step-by-Step Solution

Answer

Enthalpy of polymerization per mole of ethylene is +259 kJ/mol at 298 K.

Step 1: Write the Reaction Equation

The polymerization of ethylene can be represented as the conversion of multiple ethylene units, initially having a double bond, into a single polyethylene chain, where monomers are linked by single bonds. The reaction can be denoted as \( n \text{CH}_2=\text{CH}_2 \rightarrow \text{E} \text{CH}_2-\text{CH}_2 \). For simplicity, consider one repeating unit \( \text{CH}_2=\text{CH}_2 \rightarrow \text{CH}_2-\text{CH}_2 \).

Step 2: Identify Bond Changes

In this reaction, the transformation involves the breaking of one \( \text{C}=\text{C} \) double bond and the formation of one \( \text{C}-\text{C} \) single bond for the polymerization of one ethylene unit.

Step 3: Calculate Energy Changes per Mole

The energy required to break one \( \text{C}=\text{C} \) bond is \(+590 \text{ kJ/mol}\). The energy released in forming one \( \text{C}-\text{C} \) bond is \(-331 \text{ kJ/mol}\).

Step 4: Determine Enthalpy Change of Reaction

The enthalpy of polymerization per mole of ethylene can be calculated as the difference between the energy required to break the double bond and the energy released when forming a single bond. Therefore, the enthalpy change \( \Delta H \) is: \[ \Delta H = (+590 - 331) \text{ kJ/mol} = +259 \text{ kJ/mol} \]

Step 5: Interpret the Result

The positive sign of the calculated enthalpy change indicates endothermic polymerization per mole of ethylene at \( 298 \text{ K} \), meaning that energy is absorbed from the surroundings during the process.

Key Concepts

Ethylene Polymerization

Ethylene polymerization is a fascinating chemical reaction where ethylene molecules (also known as ethene or \( \text{C}_2\text{H}_4 \)) are transformed into polyethylene, a type of plastic. During this process, the double bonds in ethylene molecules break, and these molecules link together forming long chains, creating polyethylene. This polymerization is crucial because polyethylene is widely used in products like packaging, containers, and even pipes. This process is usually initiated by heat, pressure, or catalysts, enabling the growth of large polymer chains from smaller ethylene units. Understanding this transformation is key to learning how essential materials are manufactured.

Bond Dissociation Energy

Bond dissociation energy is a measure of the strength of a chemical bond. It refers to the amount of energy needed to break a bond in a molecule, separating it into individual atoms. In ethylene polymerization, we consider the dissociation energy of carbon-carbon bonds.

• Breaking Bonds: Higher bond dissociation energy means a stronger bond and more energy needed to break it.
• Reformulation: Conversely, bonds with lower dissociation energy break more easily.

In the context of polymerization, understanding and calculating bond dissociation energies helps determine the energy required and released during the transformation, making it easier to control and optimize the process.

C=C Double Bond

The \( \text{C}=\text{C} \) double bond plays a central role in the polymerization of ethylene. It consists of one sigma bond and one pi bond, making it stronger and requiring more energy to break than a single bond. This is why such bonds have higher bond dissociation energy values.

• Structure: The double bond restricts rotation around it, giving molecules like ethylene a specific shape.
• Reactivity: Despite their strength, double bonds are reactive under the right conditions, as observed in polymerization.

Breaking a \( \text{C}=\text{C} \) bond is the first step in forming polyethylene, enabling the linking of carbon atoms in a single bond format.

C-C Single Bond

In polyethylene, the \( \text{C}-\text{C} \) single bond is central to forming the polymer chain from ethylene units. The single bond is comprised solely of a sigma bond, making it less strong than a double bond yet very stable under normal conditions.

• Energy Aspect: Forming a \( \text{C}-\text{C} \) bond releases energy, usually less compared to breaking a \( \text{C}=\text{C} \).
• Flexibility: Single bonds allow for rotation around the bond axis, contributing to the diversity in polymer chain structure.

This bond is crucial in stabilizing the polymer structure and also contributes to the solid properties of materials like plastic.

Endothermic Reaction

An endothermic reaction involves the absorption of energy from the surroundings. In the context of ethylene polymerization, the conversion is observed as endothermic, meaning the process consumes energy rather than releasing it. This energy is necessary to break the substantial \( \text{C}=\text{C} \) bonds and form new \( \text{C}-\text{C} \) bonds.

• Energy Profile: The energy required to break the double bond surpasses the energy released during single bond formation.
• Real-world Implication: Such reactions typically require external energy sources like heat to proceed efficiently.

Understanding endothermic processes aids in designing energy-efficient synthesis methods for materials like polyethylene, informing choices about industrial conditions.