Problem 50 - Chemistry: An Atoms-Focused Approach

Question

Using the average bond strengths given in Appendix 4 estimate the molar heat of hydrogenation, \(\Delta H_{\text {hydrogenation }},\) for the conversion of \(\mathrm{C}_{2} \mathrm{H}_{2}\) to \(\mathrm{C}_{2} \mathrm{H}_{6}\) $$\mathrm{CH} \equiv \mathrm{CH}(g)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)$$

Step-by-Step Solution

Answer

Question: Estimate the molar heat of hydrogenation for the conversion of acetylene (C2H2) to ethane (C2H6) using the given average bond strengths. Answer: The estimated molar heat of hydrogenation for the conversion of acetylene to ethane is 371 kJ/mol.

Step 1: Calculate the bond energy of reactants

To calculate the bond energy of reactants, we need to consider the bonds present in acetylene (C2H2) and the two hydrogen molecules (H2). In acetylene, there is a carbon-carbon triple bond (C≡C) and two carbon-hydrogen single bonds (C-H). For the hydrogen molecules, there are two hydrogen-hydrogen single bonds (H-H). We need to sum these energies to get the total bond energy of the reactants. Bond energy of reactants \(= E_{C \equiv C} + 2E_{C-H} + 2E_{H-H}\). Refer to Appendix 4, and find the average bond strengths for each bond as follows: \(E_{C\equiv C} = 837\ \text{kJ/mol}, E_{C-H} = 413\ \text{kJ/mol}, E_{H-H} = 436\ \text{kJ/mol}\) Then, calculate the bond energy of reactants: Bond energy of reactants \(= 837\ \text{kJ/mol} + 2(413\ \text{kJ/mol}) + 2(436\ \text{kJ/mol}) = 2535\ \text{kJ/mol}\).

Step 2: Calculate the bond energy of products

To calculate the bond energy of products, we need to consider the bonds present in ethane (C2H6). In ethane, there is a carbon-carbon single bond (C-C) and six carbon-hydrogen single bonds (C-H). We need to sum these energies to get the total bond energy of the products. Bond energy of products \(= E_{C-C} + 6E_{C-H}\). Refer to Appendix 4, and find the average bond strengths for each bond as follows: \(E_{C-C} = 348\ \text{kJ/mol}, E_{C-H} = 413\ \text{kJ/mol}\) Then, calculate the bond energy of products: Bond energy of products \(= 348\ \text{kJ/mol} + 6(413\ \text{kJ/mol}) = 2906\ \text{kJ/mol}\).

Step 3: Calculate the molar heat of hydrogenation

To calculate the molar heat of hydrogenation, we need to find the difference between the bond energy of reactants and the bond energy of products. Molar heat of hydrogenation \(\Delta H_{\text {hydrogenation }} = \text{Bond energy of products} - \text{Bond energy of reactants}\). \(\Delta H_{\text {hydrogenation }} = 2906\ \text{kJ/mol} - 2535\ \text{kJ/mol}= 371\ \text{kJ/mol}\). This is the estimated molar heat of hydrogenation for the conversion of acetylene to ethane.

Key Concepts

Bond Energy

Bond energy refers to the measure of energy required to break one mole of bonds in gaseous molecules. It represents the strength of a chemical bond. The stronger the bond, the higher the bond energy. To understand the process of hydrogenation in terms of bond energies, we analyze the bonds broken and formed in the reaction.

• In chemical reactions, bonds in the reactants are broken and new bonds in the products are formed.
• The total energy change depends on the difference between the energy needed to break bonds and the energy released when new bonds are formed.
• A negative change indicates that energy is released, making the reaction exothermic.

For the conversion of acetylene to ethane, understanding bond energy helps estimate the heat change involved in the process.

Acetylene

Acetylene, with the formula \$\(C_2H_2\)\, is a simple alkyne and a common fuel in welding due to its high flame temperature. It is characterized by a carbon-carbon triple bond, the focus of many energy calculations in chemistry. A triple bond consists of:

• One sigma (\(\sigma\)) bond.
• Two pi (\(\pi\)) bonds.

This bond arrangement makes acetylene highly reactive and leads to its prominent role in reactions like hydrogenation. The energy needed to break a carbon-carbon triple bond (\(E_{C\equiv C}=837\ \text{kJ/mol}\)) is notably higher than for single or double bonds, contributing significantly to the overall energy calculations in reactions involving acetylene.

Ethane

Ethane, \(C_2H_6\), is a simple alkane, consisting of a carbon-carbon single bond and six carbon-hydrogen bonds. This molecule is a product of the hydrogenation of acetylene. Ethane's single bonds:

• Include one carbon-carbon bond.
• Are each associated with a carbon-hydrogen bond (\(E_{C-H}=413\ \text{kJ/mol}\)).

The energy required to form these bonds in ethane contributes to the total energy calculations in the reaction, which helps to determine the molar heat of hydrogenation. In such reactions, the energy released upon forming ethane's single bonds is compared against the energy consumed while breaking acetylene's triple bonds.

Average Bond Strength

Average bond strength reflects the typical energy needed to break a type of chemical bond. It is an important factor in estimating reaction energies, as it simplifies calculations by providing standard values for each bond type. In hydrogenation:

• Standard bond strengths, such as \(E_{C\equiv C}\) and \(E_{C-H}\), are utilized to calculate bond energies for reactants and products.
• This estimate is compared to the actual reaction heat to understand the energetics involved in transforming reactants into products.

By using average bond strengths from tables or appendices, chemists can efficiently estimate reaction enthalpies, like the molar heat of hydrogenation, to predict whether a reaction is exothermic or not.