Problem 48 - Chemistry The Central Science In Si Units

Question

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(I),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{~kJ} $$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\), would you expect the magnitude of \(\Delta H\) to increase, decrease, of stay the same? Explain.

Step-by-Step Solution

Answer

(a) -630 kJ; (b) +210 kJ/mol; (c) Reverse reaction; (d) Increase in 94H.

Step 1: Determine Enthalpy Change for Reverse Reaction

The enthalpy change for the reverse reaction is the negative of the forward reaction's enthalpy change. Since the forward reaction has an \( \Delta H = +630 \, \text{kJ} \), the reverse reaction will have \( \Delta H = -630 \, \text{kJ} \).

Step 2: Calculate Enthalpy Change for Formation of 1 mol Acetylene

The reaction given, \( \text{C}_6 \text{H}_6(l) \rightarrow 3 \text{C}_2 \text{H}_2(g) \), emits 630 kJ for 3 moles of acetylene. To find the enthalpy change for 1 mole of acetylene, divide the total heat change by 3: \((630 \, \text{kJ}) / 3 = 210 \, \text{kJ/mol}\). So, \( \Delta H = +210 \, \text{kJ/mol}\).

Step 3: Assess Thermodynamic Favorability

The forward reaction is endothermic (absorbs heat), while the reverse is exothermic (releases heat). Generally, exothermic reactions are more thermodynamically favorable. Thus, the reverse reaction is more likely favored.

Step 4: Consider Effect of State Change on Enthalpy

The enthalpy difference between liquid benzene and gaseous benzene involves vaporization enthalpy. If \( \text{C}_6 \text{H}_6(g) \) were consumed instead of \( \text{C}_6 \text{H}_6(l) \), additional energy would be required to vaporize the liquid. This means the magnitude of \( \Delta H\) for the forward reaction would increase.

Key Concepts

Thermodynamics

Thermodynamics is the study of energy, its transformations and its relationship with matter. It encompasses concepts such as heat, work, and energy flow. In the context of chemical reactions, thermodynamics helps us understand how energy changes impact the occurrence and direction of reactions.

• The First Law of Thermodynamics: This law essentially states that energy cannot be created or destroyed, only transformed. This is a crucial concept when considering chemical reactions, where energy is often transformed from one form to another.
• Energy and Stability: In general, systems tend to move towards a state of lower energy, which is typically more stable. This principle plays a role in determining whether reactions are likely to occur spontaneously.

In our exercise, the energy absorbed by the chemical bonds during the decomposition of benzene (8 630 kJ) is a key concept from thermodynamics, guiding us to the understanding of enthalpy changes and their implications on reaction favorabilities.

Chemical Reactions

Chemical reactions involve the breaking and forming of bonds. This process involves energy changes that can be analyzed to determine the overall enthalpy change of the reaction. Understanding these changes is crucial for predicting the outcome and feasibility of reactions.

• Forward vs. Reverse Reactions: In any reaction, we can think about both the forward and reverse processes. An important factor to consider is the enthalpy changes associated with each direction. For instance, in the benzene decomposition exercise, the forward reaction absorbs heat, making it endothermic, while the reverse one releases heat, making it exothermic.
• Reaction Pathways: Sometimes the pathway or mechanism by which reactants turn into products involves multiple steps. These steps can themselves have individual enthalpy changes which collectively determine the overall change for the reaction.

Chemical reactions are governed by more than just energy changes, including factors such as entropy and the physical states of reactants and products.

Heat of Reaction

The heat of reaction, or enthalpy change (9H), is a critical concept in thermodynamics and chemical reactions. It quantifies the heat absorbed or released during a chemical reaction at constant pressure.

• Endothermic vs. Exothermic: If a reaction absorbs heat (9H > 0), it is endothermic. Conversely, if it releases heat (9H < 0), it is exothermic. In our benzene to acetylene decomposition exercise, the forward reaction is endothermic with 9H = +630 kJ.
• Molar Enthalpy: It's common to measure enthalpy changes on a per-mole basis. For example, in the decomposition of benzene, the reaction releases 630 kJ for every three moles of acetylene produced, translating to 210 kJ for one mole.
• Influence of Physical State: The physical state (solid, liquid, gas) of reactants and products can affect enthalpy changes. For example, converting liquid benzene to gas requires additional energy, influencing the magnitude of 9H.

Understanding the heat of reaction is essential for assessing reaction spontaneity and designing processes that either minimize or utilize energy inputs effectively.