Question

Consider the feasibility of a free-radical chain mechanism for hydrogenation of ethylene in the vapor state at \(25^{\circ}\) by the following propagation steps: $$ \begin{aligned} &\mathrm{CH}_{3}-\mathrm{CH}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{CH}_{3}-\mathrm{CH}_{3}+\mathrm{H} \\ &\mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{H} \cdot \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \end{aligned} $$

Short answer

In conclusion, the proposed free-radical chain mechanism for hydrogenation of ethylene in the vapor state at \(25^{\circ}\) might not be feasible due to several factors. These factors include the high reactivity of free radical species (H·) leading to competing side reactions, high energy barriers, and low selectivity towards the desired ethane product (CH3-CH3).

Step-by-step solution

Understanding the Hydrogenation of Ethylene

In this process, ethylene (or ethene), which is a double-bonded carbon compound (CH2=CH2), undergoes hydrogenation to form ethane (CH3-CH3). This means a hydrogen molecule (H2) is added across the double bond of the ethylene molecules, breaking the bond and then forming new single bonds with the carbons.

Identify the Free Radical

A free radical is a highly reactive molecule with an unpaired electron. In this case, the hydrogen atom (H·) is acting as a free radical due to its unpaired electron.

Examine the Propagation Steps

The given propagation steps for this hydrogenation mechanism involve the following reactions: 1. An ethyl radical CH3-CH2 reacts with a hydrogen (H2) molecule, forming ethane (CH3-CH3) and releasing a new free-radical hydrogen atom (H·). 2. The free-radical hydrogen atom (H·) reacts with ethylene (CH2=CH2) to form the ethyl radical (CH3-CH2).

Determine the Feasibility of the Mechanism

For this mechanism to be feasible, the reactions should be thermodynamically favorable, which means the overall Gibbs free energy change of the process should be negative. Additionally, the reaction rates should be satisfactory and the selectivity (i.e., the prevalence of ethane as a product over other possible by-products) should be high. However, hydrogenation of alkenes using atomic hydrogen is known to be slow and not very feasible due to energy barriers, competing side reactions, and low solubility of gaseous hydrogen in liquids. Radicals like H· are also likely to react with the starting materials, intermediates, or products, leading to the formation of other compounds. Furthermore, the hydrogen free radical is highly reactive, and it can react with other compounds in the vapor state, potentially leading to the formation of side products, which would decrease the selectivity towards the desired ethane product. In conclusion, although it is theoretically possible for a free-radical chain mechanism to occur, the proposed hydrogenation of ethylene in the vapor state at 25°C involving this mechanism might not be feasible. Reasons include the high reactivity of free radical species leading to competing side reactions, high energy barriers, and low selectivity towards the desired end product.

Key concepts

Hydrogenation of Ethylene

Hydrogenation of ethylene is a chemical reaction where ethene (C\(_2\)H\(_4\)), often referred to by its systematic name ethylene, undergoes a process that transforms it into ethane (C\(_2\)H\(_6\)). In this reaction, a hydrogen molecule (H\(_2\)) interacts with ethylene's double bond.

• This bond is initially composed of strong pi bonds, which are broken during hydrogenation.
• The hydrogen atoms then form new single bonds with each carbon atom originally part of the double bond in ethylene.

To visualize, imagine ethylene as two carbons connected by a double bond. The hydrogenation process "adds" a hydrogen atom to each of these carbons, thus saturating the bond and resulting in ethane, a saturated alkane with all single bonds.The hydrogenation process is crucial in various industrial applications, such as producing edible oils and various fuels, where unsaturated hydrocarbons are converted into their saturated counterparts.

Reaction Propagation Steps

Propagation steps are the heart of any free radical mechanism, including the hydrogenation of ethylene. These steps are sequences of reactions crucial to maintaining the cycle of the mechanism. In our context, the propagation steps include critical transformations that sustain the radical chain reaction.

• First, an ethyl radical (\( \text{CH}_3-\text{CH}_2 \)) reacts with a hydrogen molecule (\( \text{H}_2 \)), yielding ethane (\( \text{CH}_3-\text{CH}_3 \)) and another radical hydrogen atom (H\(\cdot\)).
• Second, this free radical hydrogen (H\(\cdot\)) subsequently reacts with another ethylene molecule to regenerate the ethyl radical, completing the cycle.

These steps create a cyclical chain where the radical is continuously regenerated. In essence, the propagation step ensures that once the reaction has been initiated, it can perpetuate under certain conditions, ensuring the continuous production of ethane from ethylene.

Feasibility of Reaction Mechanism

Evaluating the feasibility of a reaction mechanism is essential to understand whether a proposed chemical reaction can occur under given conditions. In the case of the hydrogenation of ethylene via a free radical mechanism, several factors must be considered. For this mechanism to be considered feasible:

• The energy required to initiate and sustain the reaction must be relatively low.
• The intermediate and final products should not favor reverse reactions.

However, some practical barriers exist. The high reactivity of the hydrogen radical leads to several side reactions that can consume the radicals, thus reducing the efficiency and selectivity towards the desired product. Coupled with high activation energy barriers and low solubility of hydrogen gas, these issues contribute to why such a mechanism may not be feasible under standard conditions or without particular catalysts or environmental adjustments.

Thermodynamic Favorability

Thermodynamic favorability is a crucial aspect when analyzing the feasibility of any chemical reaction. It involves the assessment of energy changes that determine whether a reaction is spontaneous or not. For a reaction to be thermodynamically favorable:

• The change in Gibbs free energy (\( \Delta G \)) must be negative, indicating that the reaction can proceed spontaneously under ideal conditions.
• Exothermic reactions typically boost favorability, as energy is released during the conversion process.

In the context of the hydrogenation of ethylene, while the formation of ethane from ethylene and hydrogen is typically exothermic, the free radical pathway has its challenges.

• High energy barriers associated with radical formation and propagation can offset the exothermic benefits, making the reaction complex.
• Moreover, the formation of unwanted side products can influence overall \( \Delta G \), complicating evaluations of thermodynamic favorability.

To optimize such reactions, chemists often use specific catalysts or alter reaction conditions to ensure that the desired path is favored, thereby increasing the reaction’s practical feasibility.