Problem 49 - 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 \(\mathrm{C}_{2} \mathrm{H}_{4}\) to \(\mathrm{C}_{2} \mathrm{H}_{6}\) $$\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)$$

Step-by-Step Solution

Answer

Question: Estimate the molar heat of hydrogenation for the conversion of ethene (C2H4) to ethane (C2H6) using the given average bond strengths in Appendix 4. Answer: The molar heat of hydrogenation for the conversion of ethene (C2H4) to ethane (C2H6) is approximately -128 kJ/mol.

Step 1: 1. Identify the bonds broken and formed in the reaction

In this reaction, a double bond between the two carbon atoms in ethene (C=C) will be broken and replaced with a single bond (C-C). Two hydrogen atoms will be added to the molecules as well, breaking the bond in the H2 molecule. So, we have these bonds being broken and formed in the reaction: Bonds broken: 1 C=C bond in ethene 1 H-H bond in H2 Bonds formed: 1 C-C bond in ethane 2 C-H bonds in ethane

Step 2: 2. Find the average bond strengths in Appendix 4

In Appendix 4, find the average bond strengths for C=C, C-C, C-H, and H-H bonds. (use the given values from appendix 4; if it's not given, assume C=C: 610 kJ/mol, C-C: 348 kJ/mol, C-H: 413 kJ/mol, H-H: 436 kJ/mol as an example) C=C: 610 kJ/mol C-C: 348 kJ/mol C-H: 413 kJ/mol H-H: 436 kJ/mol

Step 3: 3. Calculate the energy of bonds broken

Add up the bond strengths for the bonds that are broken in the reaction. This will give us the energy needed to break these bonds. Energy of bonds broken = Energy of 1 C=C bond + Energy of 1 H-H bond Energy of bonds broken = 610 kJ/mol + 436 kJ/mol Energy of bonds broken = 1046 kJ/mol

Step 4: 4. Calculate the energy of bonds formed

Add up the bond strengths for the bonds that are formed in the reaction. This will give us the energy released when these bonds are formed. Energy of bonds formed = Energy of 1 C-C bond + Energy of 2 C-H bonds Energy of bonds formed = 348 kJ/mol + 2(413 kJ/mol) Energy of bonds formed = 348 kJ/mol + 826 kJ/mol Energy of bonds formed = 1174 kJ/mol

Step 5: 5. Calculate the molar heat of hydrogenation

The molar heat of hydrogenation is the difference between the energy of bonds broken and the energy of bonds formed. \(\Delta H_{\text {hydrogenation }}\) = Energy of bonds broken - Energy of bonds formed \(\Delta H_{\text {hydrogenation }}\) = 1046 kJ/mol - 1174 kJ/mol \(\Delta H_{\text {hydrogenation }}\) = -128 kJ/mol The molar heat of hydrogenation for the conversion of \(\mathrm{C}_{2} \mathrm{H}_{4}\) to \(\mathrm{C}_{2} \mathrm{H}_{6}\) is -128 kJ/mol, which means that 128 kJ of energy is released per mole of ethene converted to ethane.

Key Concepts

Molar Heat of Hydrogenation

The molar heat of hydrogenation is an important concept in understanding the energy changes during chemical reactions, specifically for the conversion of unsaturated hydrocarbons to saturated ones. In this process, an unsaturated compound (like an alkene) reacts with hydrogen gas, and the double bond in the compound becomes a single bond. During the reaction from ethene (\( \mathrm{C}_{2} \mathrm{H}_{4} \)) to ethane (\( \mathrm{C}_{2} \mathrm{H}_{6} \)), a double bond breaks to form a stronger single bond.
When calculating the molar heat of hydrogenation, we look at the difference between the energy required to break bonds (endothermic process) and the energy released when new bonds form (exothermic process). The energies involved depend on the specific bonds in the molecules participating in the reaction.
The overall reaction in this case is exothermic, meaning that more energy is released when forming bonds than is consumed breaking them. That's why the calculated molar heat of hydrogenation in this example is -128 kJ/mol, indicating that 128 kJ of energy is released when one mole of ethene is converted to ethane.

Average Bond Strengths

Average bond strengths refer to the typical amount of energy required to break certain types of chemical bonds. These average values are crucial for estimating energy changes in chemical reactions. Bonds of different types involve different amounts of energy, which is typically measured in kJ/mol.
In this particular exercise, the average bond strengths used are those for the C=C, C-C, C-H, and H-H bonds. These values are often found in a reference section of textbooks or can be derived from empirical data. For the reaction between ethene and hydrogen gas, it's vital to calculate both the energy needed to break the initial bonds and the energy released when new bonds form.
This involves identifying:

• one C=C bond in ethene, which typically requires 610 kJ/mol to break,
• one H-H bond in hydrogen, requiring about 436 kJ/mol,
• a C-C bond and two C-H bonds in the resulting ethane, which release 348 kJ/mol and 826 kJ/mol, respectively, when formed.

Thus, calculating these can give us insightful observations about the reaction’s energy profile.

Enthalpy Change

Enthalpy change (\( \Delta H \)) is a measure of the total energy change in a chemical reaction, reflecting both the energy absorbed to break bonds and the energy released when new bonds form.
For the hydrogenation process, the enthalpy change is the difference between these energies. This calculation tells us if the overall process is exothermic (releases energy) or endothermic (absorbs energy). In this case, with the reaction from (\( \mathrm{C}_{2} \mathrm{H}_{4} \)) to (\( \mathrm{C}_{2} \mathrm{H}_{6} \)), the enthalpy change is calculated by taking the total energy of bonds broken (1046 kJ/mol) and subtracting the total energy of bonds formed (1174 kJ/mol).
This results in an enthalpy change of -128 kJ/mol, indicating that energy is released in this exothermic reaction. Understanding enthalpy changes helps in predicting the feasibility and spontaneity of reactions, as those with lower energy states are generally more stable.