Problem 4 - Chemistry and Chemical Reactivity

Question

Ethene, \(\mathrm{C}_{2} \mathrm{H}_{4},\) is unstable with respect to decomposition to the elements \(\left(\Delta_{f} H^{\circ}=52.47 \mathrm{kJ} / \mathrm{mol}\right) .\) It is also unstable with respect to polymerization to polyethylene. Nevertheless, samples of ethane can be stored without decomposition essentially forever. Why is this so?

Step-by-Step Solution

Answer

Ethene's decomposition is hindered by high activation energy, despite its thermodynamic instability.

Step 1: Understanding Instability

Ethene is thermodynamically unstable because its formation has a positive enthalpy change (\( \Delta_{f} H^{\circ}=52.47 \text{kJ/mol} \)). This means that decomposing into elements or polymerizing would release energy.

Step 2: Kinetic Stability

Despite being thermodynamically unstable, ethene doesn't decompose easily because the reaction rates are extremely slow at room temperature. The high activation energy barrier prevents the reaction from occurring spontaneously.

Step 3: Reaction Pathway and Energy Barrier

For ethene to decompose, sufficient energy must be supplied to overcome the activation energy, which is often not available at typical storage conditions.

Key Concepts

Ethene Decomposition

Ethene, known chemically as \(\mathrm{C}_2\mathrm{H}_4\), can decompose into its elemental forms: carbon and hydrogen. This decomposition is thermodynamically favorable because it results in a reduction in free energy due to the release of 52.47 kJ/mol of energy. This positive \(\Delta_{f} H^{\circ}\) value suggests that energy could be released into the surrounding environment as the chemical bonds of ethene break down into simpler forms. However, despite being energetically favorable under the right conditions, this reaction does not happen spontaneously at room temperature because it is held back by other factors such as kinetic barriers.

Thermodynamic Stability

Thermodynamic stability refers to whether a substance can remain in its current state without energy input from the surroundings. For ethene, its thermodynamic instability is indicated by a positive enthalpy of formation. This suggests that ethene does not exist in the lowest energy state possible and that it could ideally convert into its components or polymerize. Yet, achieving this conversion requires more energy than typically found at room temperature.
This condition implies that while ethene at room temperature is in a state that is not the lowest possible energy, it doesn't just change to a more stable state on its own without assistance.

Activation Energy

Activation energy is the minimum energy required to initiate a chemical reaction. For ethene, a significant activation energy barrier exists between its current form and its decomposed elements or polymerized form.
This energy barrier is like a wall that the molecules must climb over to react. The larger the barrier, the slower the rate of reaction at a given temperature. Ethene, having such a high activation energy, means that it requires considerable energy to start breaking its molecular bonds. This barrier prevents spontaneous decomposition of ethene at standard conditions.

Polymerization

Polymerization involves chaining monomers like ethene together to form a large molecule, such as polyethylene. Although ethene can theoretically form a polymer more stable than the monomer itself, the process requires overcoming the activation energy barrier similar to its decomposition.
Without a catalyst or elevated temperature to provide the necessary energy, the polymerization of ethene does not occur at room temperature, allowing ethene to be stored as it is without converting spontaneously into polymer or decomposing. This showcases how kinetic factors, the practical conditions of temperature and catalysis, dramatically influence the stability and reactivity of ethene in real-world scenarios.