Question

At \(298 \mathrm{~K}\), the standard enthalpies of formation for \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\) are \(227 \mathrm{~kJ} / \mathrm{mol}\) and \(49 \mathrm{~kJ} / \mathrm{mol}\), respectively. a. Calculate \(\Delta H^{\circ}\) for $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) $$ b. Both acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) can be used as fuels. Which compound would liberate more energy per gram when combusted in air?

Short answer

a. The ∆H° for the given reaction C6H6(l) → 3 C2H2(g) is 632 kJ/mol. b. Acetylene (C2H2) releases more energy per gram (8.72 kJ/g) when combusted in air than benzene (C6H6) (0.63 kJ/g).

Step-by-step solution

Write the general formula for calculating ∆H°

Recalling the formula for ∆H° of reaction: ∆H°(reaction) = Σn∆H°f(products) - Σm∆H°f(reactants) Where n and m are the stoichiometric coefficients of the products and reactants, respectively, and ∆H°f represents their standard enthalpies of formation.

Apply the formula to the given reaction

For the reaction: C6H6(l) → 3 C2H2(g) ∆H°(reaction) = 3*(∆H°f(C2H2(g))) - (∆H°f(C6H6(l))) Using the given data: ∆H°f(C2H2) = 227 kJ/mol and ∆H°f(C6H6) = 49 kJ/mol ∆H°(reaction) = 3*(227 kJ/mol) - 49 kJ/mol

Calculate ∆H°(reaction)

Calculating the value of ∆H°(reaction): ∆H°(reaction) = 681 kJ/mol - 49 kJ/mol ∆H°(reaction) = 632 kJ/mol a. The ∆H° for the given reaction C6H6(l) → 3 C2H2(g) is 632 kJ/mol b. Identify the compound that liberates more energy per gram when combusted in air

Calculate the molar mass of C2H2 and C6H6

The molar mass of C2H2 is 2*12.01 g/mol (C) + 2*1.01 g/mol (H) = 26.04 g/mol The molar mass of C6H6 is 6*12.01 g/mol (C) + 6*1.01 g/mol (H) = 78.12 g/mol

Calculate the energy released per gram for each compound

Energy per gram for C2H2: (∆H°f(C2H2) / Molar mass of C2H2) = (227 kJ/mol) / (26.04 g/mol) Energy per gram for C6H6: (∆H°f(C6H6) / Molar mass of C6H6) = (49 kJ/mol) / (78.12 g/mol)

Compare the energy per gram values

Energy per gram for C2H2: 8.72 kJ/g Energy per gram for C6H6: 0.63 kJ/g Comparing the energy per gram values, we find that C2H2 releases more energy per gram (8.72 kJ/g) when combusted in air than C6H6 (0.63 kJ/g).

Key concepts

Enthalpy Change Calculation

Enthalpy change, denoted as \( \Delta H \), helps us understand how heat energy changes during a chemical reaction.
For example, when a substance is formed from its elements under standard conditions, it has a specific enthalpy of formation \( (\Delta H^\circ_f) \). This value indicates the heat absorbed or released when one mole of a compound is formed from its elements in their standard states. In chemical reactions, we often calculate the enthalpy change \( (\Delta H^\circ) \) using the formula:

• \( \Delta H^\circ_{\text{reaction}} = \Sigma n\Delta H^\circ_f(\text{products}) - \Sigma m\Delta H^\circ_f(\text{reactants}) \)

This equation represents how, by knowing the enthalpies of formation of the reactants and products and their stoichiometric coefficients, we can find out the total energy change.
In our problem, the reaction is \( \text{C}_6\text{H}_6(\text{l}) \rightarrow 3\text{C}_2\text{H}_2(\text{g}) \), where we solve for the heat change by inserting known values and simplifying.

Combustion Energy Comparison

Combustion reactions involve burning fuels in oxygen to release energy. Different compounds release varying amounts of energy due to their unique chemical compositions and structures.
When comparing energies, we focus on energy output per gram of fuel. This consideration helps in evaluating which compound is a more efficient energy source.To determine the more energy-effective fuel between acetylene \( (\text{C}_2\text{H}_2) \) and benzene \( (\text{C}_6\text{H}_6) \):

• Calculate the molar mass of each compound: \( \text{C}_2\text{H}_2 \) is 26.04 g/mol and \( \text{C}_6\text{H}_6 \) is 78.12 g/mol.
• Find energy released per gram by dividing standard enthalpy of formation \((\Delta H^\circ_f)\) by molar mass.
• Compare the values to see which releases more energy per gram.

The calculations show \( \text{C}_2\text{H}_2 \) provides **8.72 kJ/g**, while \( \text{C}_6\text{H}_6 \) gives **0.63 kJ/g**. This means acetylene releases more energy per gram, making it a more potent fuel.

Thermochemistry

Thermochemistry focuses on the study of heat changes in chemical reactions. It provides insights into reaction pathways, stability of compounds, and potential energy sources.
Understanding thermochemistry involves recognizing how energy is transferred in reactions. Two key concepts are:

• Exothermic reactions: These release heat to the surroundings, indicated by negative \( \Delta H \) values, and often feel warm.
• Endothermic reactions: These require heat input from the surroundings, resulting in positive \( \Delta H \) values, and often feel cold.

By calculating enthalpy changes, we can predict the heat absorption or release during reactions. This knowledge is crucial for designing energy-efficient processes.
In our exercise, the transformation from benzene to acetylene involved using these principles to calculate the total energy change. This helped us understand the potential heat released when these compounds combust.