Problem 82 - Chemistry and Chemical Reactivity

Question

For each of the following processes, give the algebraic sign of \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ} .\) No calculations are necessary; use your common sense. (a) The decomposition of liquid water to give gaseous oxygen and hydrogen, a process that requires a considerable amount of energy. (b) Dynamite is a mixture of nitroglycerin, \(C_{3} H_{5} N_{3} O_{9},\) and diatomaceous earth. The explosive decomposition of nitroglycerin gives gaseous products such as water, CO \(_{2}\), and others; much heat is cvolved. (c) The combustion of gasoline in the engine of your car, as exemplified by the combustion of octane. \(2 \mathrm{C}_{8} \mathrm{H}_{1 \mathrm{s}}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Step-by-Step Solution

Answer

(a) \( \Delta H^{\circ} > 0 \), \( \Delta S^{\circ} > 0 \), \( \Delta G^{\circ} > 0 \); (b) \( \Delta H^{\circ} < 0 \), \( \Delta S^{\circ} > 0 \), \( \Delta G^{\circ} < 0 \); (c) \( \Delta H^{\circ} < 0 \), \( \Delta S^{\circ} > 0 \), \( \Delta G^{\circ} < 0 \).

Step 1: Analyze the Water Decomposition Reaction

In the decomposition of liquid water to produce gaseous oxygen and hydrogen, the process requires energy input. This indicates an endothermic reaction, so \( \Delta H^{\circ} > 0 \). Additionally, transitioning from liquid to gas increases disorder, suggesting \( \Delta S^{\circ} > 0 \). Since energy is required (endothermic and non-spontaneous under standard conditions), \( \Delta G^{\circ} > 0 \).

Step 2: Analyze the Explosive Decomposition of Nitroglycerin

The explosive decomposition of nitroglycerin releases a significant amount of heat, indicating the process is exothermic, so \( \Delta H^{\circ} < 0 \). The production of gaseous products from a liquid increases randomness, resulting in \( \Delta S^{\circ} > 0 \). The release of energy suggests the process is spontaneous, making \( \Delta G^{\circ} < 0 \).

Step 3: Analyze the Combustion of Octane

In the combustion of octane, heat is released, making the reaction exothermic with \( \Delta H^{\circ} < 0 \). The conversion of reactants into gaseous products increases the entropy, so \( \Delta S^{\circ} > 0 \). The spontaneous nature (exergonic) of combustion indicates \( \Delta G^{\circ} < 0 \).

Key Concepts

Understanding Enthalpy

Enthalpy is an important concept in thermodynamics that reflects the total heat content of a system. It is represented by the symbol \( H \) and is associated with heat exchange under constant pressure.
When a chemical reaction occurs, the heat absorbed or released is denoted by \( \Delta H \). Here are the key points:

• If \( \Delta H > 0 \), the process is endothermic; energy is absorbed from the surroundings.
• If \( \Delta H < 0 \), the process is exothermic; energy is released to the surroundings.

In the context of the given exercises:

• For water decomposition, \( \Delta H > 0 \), indicating it requires energy input.
• For nitroglycerin decomposition and octane combustion, \( \Delta H < 0 \), showing energy is released.

Exploring Entropy

Entropy, denoted by \( S \), measures the system's randomness or disorder. It gives insight into how energy is distributed among particles and how reversible a process might be.
During a reaction, entropy change \( \Delta S \) tells us about the change in disorder. Consider:

• If \( \Delta S > 0 \), the system becomes more disordered.
• If \( \Delta S < 0 \), the system becomes more ordered.

In the exercises provided:

• For all reactions—water decomposition, nitroglycerin decomposition, and octane combustion—\( \Delta S > 0 \), due to the increase in gas molecules, increasing disorder.

Decoding Gibbs Free Energy

Gibbs free energy, symbolized by \( G \), determines the spontaneity of a reaction under constant temperature and pressure. The change in Gibbs free energy \( \Delta G \) provides essential information about whether reactions occur spontaneously.
Here's how to interpret \( \Delta G \):

• If \( \Delta G < 0 \), the reaction is spontaneous (exergonic).
• If \( \Delta G > 0 \), the reaction is non-spontaneous (endergonic).

For the exercises:

• The decomposition of water is non-spontaneous with \( \Delta G > 0 \).
• The decomposition of nitroglycerin and the combustion of octane are spontaneous with \( \Delta G < 0 \).