Calculating ΔHrxn For Ethylene Hydrogenation Using Average Bond Energies

In the realm of chemical thermodynamics, understanding the enthalpy change (${\Delta H}$) of a reaction is crucial for predicting its heat transfer and spontaneity. For gas-phase reactions, a practical method for estimating the enthalpy change involves utilizing average bond energies. This approach provides valuable insights into the energy required to break and form chemical bonds during a reaction. In this article, we will delve into the application of average bond energies to calculate the enthalpy change for the hydrogenation of ethylene, a fundamental reaction in organic chemistry.

Understanding Average Bond Energies

Before we embark on the calculation, it's essential to grasp the concept of average bond energies. Average bond energy is the amount of energy required to break one mole of a particular bond in the gaseous phase, averaged over a variety of molecules. These values are typically tabulated and provide a reasonable approximation for bond strengths in different chemical environments. It's crucial to recognize that these are average values, and the actual bond energy in a specific molecule can deviate slightly due to factors like molecular structure and neighboring atoms. However, for many calculations, average bond energies offer a convenient and reliable approach.

The fundamental principle behind using average bond energies to calculate reaction enthalpy lies in Hess's Law. Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken and depends only on the initial and final states. In the context of bond energies, we can envision a reaction proceeding in two steps: first, breaking all the bonds in the reactants, which requires energy (endothermic, positive ${\[\Delta H}$), and second, forming all the bonds in the products, which releases energy (exothermic, negative ${\[\Delta H}$). The overall enthalpy change of the reaction is then the sum of these two energy changes.

The formula for calculating the enthalpy change of a reaction (${\Delta H_{rxn}}$) using average bond energies is:

${ \Delta H_{rxn} = \sum{(\text{Bond energies of bonds broken})} - \sum{(\text{Bond energies of bonds formed})} }$

This equation essentially quantifies the difference between the energy invested in breaking bonds and the energy released upon forming new bonds. A negative ${\[\Delta H_{rxn}}$ indicates an exothermic reaction, where more energy is released than consumed, while a positive ${\[\Delta H_{rxn}}$ signifies an endothermic reaction, where more energy is consumed than released.

The Hydrogenation of Ethylene

Hydrogenation, a cornerstone reaction in organic chemistry, involves the addition of hydrogen (${H_2}$) to an unsaturated compound, typically an alkene or alkyne, to produce a saturated compound. This process is widely employed in various industrial applications, including the production of margarine from vegetable oils and the synthesis of various organic chemicals.

The specific reaction we will analyze is the hydrogenation of ethylene (${H_2C=CH_2}$) to form ethane (${H_3C-CH_3}$):

${ H_2C=CH_2(g) + H_2(g) \rightarrow H_3C-CH_3(g) }$

Ethylene, a simple alkene with a carbon-carbon double bond, readily reacts with hydrogen gas in the presence of a suitable catalyst, such as palladium or platinum, to yield ethane, a saturated alkane with a carbon-carbon single bond. This reaction is of significant industrial importance as it represents a fundamental step in the production of numerous chemicals and polymers.

Calculating ΔHrxn for Ethylene Hydrogenation

Now, let's apply the average bond energy method to calculate the enthalpy change for the hydrogenation of ethylene. The first step involves identifying all the bonds broken and formed during the reaction. To do this accurately, it's helpful to draw the Lewis structures of the reactants and products:

Reactants:

• Ethylene (${H_2C=CH_2}$): Contains 1 C=C double bond, 4 C-H single bonds, 1 H-H single bond
• Hydrogen (${H_2}$): Contains 1 H-H single bond

Product:

• Ethane (${H_3C-CH_3}$): Contains 1 C-C single bond, 6 C-H single bonds

Bonds Broken:

• 1 C=C double bond
• 1 H-H single bond

Bonds Formed:

• 1 C-C single bond
• 2 C-H single bonds

Note that we only consider the net change in bonds. For example, while ethylene has 4 C-H bonds and ethane has 6 C-H bonds, only 2 additional C-H bonds are formed during the reaction.

Next, we need to look up the average bond energies for each of these bonds. Here are typical values (in kJ/mol):

• C=C: 614
• C-C: 348
• C-H: 413
• H-H: 436

Now, we can plug these values into our equation:

${ \Delta H_{rxn} = \sum{(\text{Bond energies of bonds broken})} - \sum{(\text{Bond energies of bonds formed})} }$ ${ \Delta H_{rxn} = [(1 \times 614 \text{ kJ/mol}) + (1 \times 436 \text{ kJ/mol})] - [(1 \times 348 \text{ kJ/mol}) + (2 \times 413 \text{ kJ/mol})] }$ ${ \Delta H_{rxn} = [614 + 436] \text{ kJ/mol} - [348 + 826] \text{ kJ/mol} }$ ${ \Delta H_{rxn} = 1050 \text{ kJ/mol} - 1174 \text{ kJ/mol} }$ ${ \Delta H_{rxn} = -124 \text{ kJ/mol} }$

Therefore, the calculated enthalpy change for the hydrogenation of ethylene using average bond energies is -124 kJ/mol. This negative value indicates that the reaction is exothermic, meaning it releases heat.

Significance of the Result

The calculated ${\[\Delta H_{rxn}}$ of -124 kJ/mol provides valuable information about the energetics of the ethylene hydrogenation reaction. The negative sign confirms that the reaction is exothermic, which aligns with experimental observations. Exothermic reactions tend to be thermodynamically favorable, meaning they are more likely to occur spontaneously.

This result also suggests that the products (ethane) are more stable than the reactants (ethylene and hydrogen) due to their lower energy state. The energy released during the reaction is a consequence of the formation of stronger bonds in the product (C-C and C-H) compared to the bonds broken in the reactants (C=C and H-H).

It's important to remember that this calculation is an estimation based on average bond energies. The actual enthalpy change can vary slightly depending on the specific reaction conditions and the presence of catalysts. More accurate methods, such as calorimetry or computational chemistry techniques, can provide more precise values.

Conclusion

In this article, we've demonstrated how to calculate the enthalpy change (${\Delta H_{rxn}}$) for a chemical reaction using average bond energies. By applying this method to the hydrogenation of ethylene, we determined an approximate ${\[\Delta H_{rxn}}$ of -124 kJ/mol, indicating an exothermic reaction. This approach provides a valuable tool for understanding the energetics of chemical reactions and predicting their thermodynamic feasibility. While average bond energies offer a convenient estimation, it's crucial to recognize their limitations and consider more precise methods when higher accuracy is required. The principles and calculations discussed here are fundamental to understanding chemical thermodynamics and its applications in various scientific and industrial fields.