Problem 94 - Chemistry and Chemical Reactivity

Question

For each of the following processes, predict the algebraic sign of \(\Delta_{r} H^{\circ}, \Delta_{r} S^{\circ},\) and \(\Delta_{r} G^{\circ} .\) 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, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}_{3} \mathrm{O}_{9},\) and diatomaceous earth. The explo- sive decomposition of nitroglycerin gives gaseous products such as water, \(\mathrm{CO}_{2}\), and others; much heat is evolved. (c) The combustion of gasoline in the engine of your car, as exemplified by the combustion of octane. $$2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

Step-by-Step Solution

Answer

(a) \( \Delta_{r} H^{\circ} > 0, \Delta_{r} S^{\circ} > 0, \Delta_{r} G^{\circ} > 0 \) (b) \( \Delta_{r} H^{\circ} < 0, \Delta_{r} S^{\circ} > 0, \Delta_{r} G^{\circ} < 0 \) (c) \( \Delta_{r} H^{\circ} < 0, \Delta_{r} S^{\circ} > 0, \Delta_{r} G^{\circ} < 0 \)

Step 1: Analyze the Decomposition of Liquid Water

The decomposition of liquid water into gaseous oxygen and hydrogen is an endothermic process, meaning it requires energy. Therefore, \( \Delta_{r} H^{\circ} > 0 \) or positive. Since the reaction involves the transition from a liquid to gases, the disorder or entropy increases, making \( \Delta_{r} S^{\circ} > 0 \) or positive. Because it requires energy input, the process is typically non-spontaneous under standard conditions, so \( \Delta_{r} G^{\circ} > 0 \) or positive.

Step 2: Analyze the Explosive Decomposition of Nitroglycerin

The decomposition of nitroglycerin is highly exothermic, releasing a significant amount of heat. Thus, \( \Delta_{r} H^{\circ} < 0 \) or negative. The reaction produces gaseous products from liquid reactants, leading to an increase in entropy, so \( \Delta_{r} S^{\circ} > 0 \) or positive. Since the process releases energy and is spontaneous, \( \Delta_{r} G^{\circ} < 0 \) or negative.

Step 3: Analyze the Combustion of Octane

The combustion of octane is an exothermic process, where a large amount of heat is released. Therefore, \( \Delta_{r} H^{\circ} < 0 \) or negative. The reaction forms gaseous products, leading to an increase in entropy. Consequently, \( \Delta_{r} S^{\circ} > 0 \) or positive. With both a release of energy and increased disorder, the reaction is spontaneous, resulting in \( \Delta_{r} G^{\circ} < 0 \) or negative.

Key Concepts

Enthalpy Change

Enthalpy change is the measure of heat absorbed or released during a chemical process at constant pressure. It's denoted as \( \Delta H \). When we talk about reactions, if the enthalpy change is positive, the reaction is endothermic, meaning it absorbs heat. Conversely, a negative enthalpy change indicates an exothermic reaction, where heat is released.

In the decomposition of liquid water, \( \Delta_{r} H^{\circ} > 0 \) suggests energy is needed, making it endothermic. For the explosive decomposition of nitroglycerin and the combustion of octane, \( \Delta_{r} H^{\circ} < 0 \) because both reactions release substantial heat and are exothermic.

• Positive \( \Delta H \): Endothermic reaction
• Negative \( \Delta H \): Exothermic reaction

Entropy Change

Entropy is a measure of randomness or disorder within a system, represented as \( \Delta S \). If entropy increases, \( \Delta S > 0 \) is positive, indicating greater disorder. A decrease means \( \Delta S < 0 \) is negative, implying more order.

All three processes in the exercise involve positive entropy change. In the decomposition of water, gases form from a liquid, increasing disorder. In the decomposition of nitroglycerin and combustion of octane, gases are produced from solids or liquids, again raising disorder. These transitions naturally lead to higher entropy.

• Positive \( \Delta S \): Increase in randomness
• Negative \( \Delta S \): Increase in order

Gibbs Free Energy

Gibbs free energy, denoted \( \Delta G \), combines enthalpy and entropy to predict the spontaneity of a process. It is calculated as \( \Delta G = \Delta H - T \Delta S \), where \( T \) is temperature. If \( \Delta G < 0 \), the process is spontaneous. Conversely, \( \Delta G > 0 \) indicates a non-spontaneous process.

The decomposition of water requires energy, making \( \Delta G > 0 \) under standard conditions, thus non-spontaneous. In contrast, \( \Delta G < 0 \) for both nitroglycerin decomposition and octane combustion, aligning with their fast and spontaneous reactions.

• Negative \( \Delta G \): Spontaneous reaction
• Positive \( \Delta G \): Non-spontaneous reaction

Endothermic Process

An endothermic process is one in which energy is absorbed from the surroundings, leading to a positive enthalpy change \( \Delta H \). This often results in a temperature decrease of the environment as heat flows into the system.

For the decomposition of water to gaseous hydrogen and oxygen, energy must be input to break bonds in water molecules. This is a prime example of an endothermic process.

• Energy absorbed: Reaction vessel may feel cooler
• Common in reactions needing external heat

Exothermic Reaction

Exothermic reactions release energy, usually in the form of heat, into the surroundings. This release lowers the system's enthalpy \( \Delta H \), often making the surroundings feel warmer.

For nitroglycerin decomposition and octane combustion, significant heat is released, making these reactions exothermic. The spontaneity and intensity of energy release in these reactions are not only characteristic of exothermic reactions but also critical for practical applications like fuel combustion and explosives.

• Energy released: Surroundings may feel warmer
• Includes many combustion and explosive reactions