Problem 63 - Chemistry The Central Science In Si Units

Question

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low \(T\) but not spontaneous at high \(T\); (iv) spontaneous at high T but not spontaneous at low \(T\). $$ \text { (a) } \begin{array}{l} \mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g) \\\ \Delta H^{\circ}=-249 \mathrm{~kJ} ; \Delta S^{\circ}=-278 \mathrm{~J} / \mathrm{K} \\ \text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g) \\ \Delta H^{\circ}=460 \mathrm{~kJ} ; \Delta S^{\circ}=-275 \mathrm{~J} / \mathrm{K} \end{array} $$ (c) \(\mathrm{N}_{2} \mathrm{~F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)\) $$ \Delta H^{\circ}=85 \mathrm{~kJ} ; \Delta S^{\circ}=198 \mathrm{~J} / \mathrm{K} $$

Step-by-Step Solution

Answer

(a) Spontaneous at low T (iii); (b) Not spontaneous at any T (ii); (c) Spontaneous at high T (iv).

Step 1: Understand the Gibbs Free Energy Equation

To determine the spontaneity of a reaction at different temperatures, use the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). When \( \Delta G < 0 \), the reaction is spontaneous. When \( \Delta G > 0 \), the reaction is non-spontaneous.

Step 2: Analyze Reaction (a)

For reaction (a), \( \Delta H^{\circ} = -249 \text{ kJ} \) and \( \Delta S^{\circ} = -278 \text{ J/K} = -0.278 \text{ kJ/K} \). Because \( \Delta H \) is negative and \( \Delta S \) is negative, the reaction is spontaneous at low temperatures where the entropy term \( -T \Delta S \) is less significant.

Step 3: Classify Reaction (a)

With both \( \Delta H < 0 \) and \( \Delta S < 0 \), reaction (a) is spontaneous at low temperatures but not at high temperatures, making it a type (iii) reaction.

Step 4: Analyze Reaction (b)

For reaction (b), \( \Delta H^{\circ} = 460 \text{ kJ} \) and \( \Delta S^{\circ} = -275 \text{ J/K} = -0.275 \text{ kJ/K} \). Both \( \Delta H \) and \( \Delta S \) are positive, suggesting \( \Delta G \) will be positive at all temperatures, as the positive enthalpy cannot be overcome by the entropy term.

Step 5: Classify Reaction (b)

With \( \Delta H > 0 \) and \( \Delta S < 0 \), reaction (b) is not spontaneous at any temperature, classifying it as a type (ii) reaction.

Step 6: Analyze Reaction (c)

For reaction (c), \( \Delta H^{\circ} = 85 \text{ kJ} \) and \( \Delta S^{\circ} = 198 \text{ J/K} = 0.198 \text{ kJ/K} \). Since \( \Delta H > 0 \) and \( \Delta S > 0 \), the reaction is not spontaneous at low temperatures, but as temperature increases, the entropy term \( -T \Delta S \) can become larger, making \( \Delta G < 0 \).

Step 7: Classify Reaction (c)

With \( \Delta H > 0 \) and \( \Delta S > 0 \), reaction (c) is spontaneous at high temperatures but not at low temperatures, making it a type (iv) reaction.

Key Concepts

Spontaneity of reactions

Understanding the spontaneity of chemical reactions is a fundamental aspect of chemistry. It tells us if a reaction can occur without the need for continuous external energy input. The Gibbs free energy (9G) formula is crucial in determining reaction spontaneity. This is expressed as: \( \Delta G = \Delta H - T \Delta S \), where \( \Delta G \) represents Gibbs free energy change, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

• If \( \Delta G < 0 \), the reaction is spontaneous and can proceed on its own.
• If \( \Delta G > 0 \), the reaction is non-spontaneous, meaning it requires energy to proceed.
• If \( \Delta G = 0 \), the system is at equilibrium, and no net reaction occurs.

The spontaneity nature of reactions is guided by both enthalpy and entropy controls, and these elements are influenced significantly by temperature variations.

Types of reactions

Chemical reactions can be categorized based on their spontaneity changes with temperature. Understanding these types helps predict how reactions behave under different temperature conditions:

• **Type (i) reactions** are spontaneous at all temperatures. This involves reactions where both \( \Delta H < 0 \) and \( \Delta S > 0 \), focusing on exothermic reactions with increasing disorder.
• **Type (ii) reactions** are non-spontaneous at any temperature. Here, \( \Delta H > 0 \) and \( \Delta S < 0 \), typical of reactions that are both endothermic and involve decreases in disorder.
• **Type (iii) reactions** are spontaneous at low temperatures but non-spontaneous at high temperatures. For such reactions, \( \Delta H < 0 \) and \( \Delta S < 0 \), favoring low temperatures where the entropy term is less impactful.
• **Type (iv) reactions** occur only at high temperatures. This involves \( \Delta H > 0 \) and \( \Delta S > 0 \), where the positive entropy change overcomes the enthalpy when temperature rises.

These classifications help chemists strategically plan for reactions and understand environmental impacts on chemical processes.

Entropy

Entropy (9S) is a measure of disorder or randomness within a system. In chemical terms, it reflects the number of ways molecules can be arranged. High entropy typically means more disorder: - **Increase in entropy:** Reactions that result in more products than reactants or involve gaseous products from solid or liquid reactants often show an increase in entropy. An example is when a solid dissolves in a liquid, leading to a more disordered system. - **Decrease in entropy:** If a reaction forms a solid from gaseous or liquid reactants, the entropy generally decreases, indicating a more ordered system. In essence, entropy is a powerful concept in understanding how particles behave. It becomes a key predictor of whether a reaction might occur spontaneously, with entropy changes being especially impactful at higher temperatures.

Enthalpy

Enthalpy (9H) is the heat content of a system, representing the total energy. A reaction's enthalpy change reflects if it absorbs or releases heat:- **Exothermic reactions:** These reactions release heat, shown by \( \Delta H < 0 \). They're usually spontaneous, as the system loses energy to the surroundings. Combustion is a classic example.- **Endothermic reactions:** With \( \Delta H > 0 \), these absorb heat, needing continuous energy to proceed. Photosynthesis is a natural endothermic process, where plants absorb sunlight to produce glucose.Understanding enthalpy is critical in predicting how energy changes within a reaction. While exothermic reactions tend to be spontaneous due to energy release, endothermic ones may rely on external conditions like temperature to occur.