Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontaneous 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.
(c) N₂F₄(g) ⟶ 2 NF₂(g) ΔH° = 85 kJ; ΔS° = 198 J/K

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Identify the given values: \( \Delta H^\circ = 85 \text{ kJ} \) and \( \Delta S^\circ = 198 \text{ J/K} \).

Convert \( \Delta S^\circ \) from \( \text{J/K} \) to \( \text{kJ/K} \) by dividing by 1000, so \( \Delta S^\circ = 0.198 \text{ kJ/K} \).

Use the Gibbs free energy equation: \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \).

Determine the sign of \( \Delta G^\circ \) at different temperatures: \( \Delta G^\circ \) is positive when \( \Delta H^\circ > T \Delta S^\circ \) and negative when \( \Delta H^\circ < T \Delta S^\circ \).

Since \( \Delta H^\circ > 0 \) and \( \Delta S^\circ > 0 \), the reaction is spontaneous at high temperatures but not at low temperatures.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG suggests non-spontaneity.

Enthalpy and Entropy

Enthalpy (ΔH) is a measure of the total heat content of a system, while entropy (ΔS) quantifies the degree of disorder or randomness in a system. In chemical reactions, the balance between enthalpy and entropy changes determines whether a reaction is spontaneous. For example, reactions that release heat (exothermic, ΔH < 0) and increase disorder (ΔS > 0) are typically spontaneous.

Temperature Dependence of Spontaneity

The spontaneity of a reaction can depend on temperature, as indicated by the Gibbs Free Energy equation. At low temperatures, reactions with negative ΔH and positive ΔS are favored, while at high temperatures, reactions with positive ΔS can become spontaneous even if ΔH is positive. Understanding this temperature dependence is crucial for classifying reactions into the four types of spontaneity.

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Related Practice

Textbook Question

Sulfur dioxide reacts with strontium oxide as follows: SO₂(g) + SrO(g) → SrSO₃(s) (a) Without using thermochemical data, predict whether ΔG° for this reaction is more negative or less negative than ΔH°.

Textbook 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.

(a) N₂(g) + 3 F₂(g) → 2 NF₃₍g) ΔH° = -249 kJ; ΔS° = -278 J/K

(b) N₂(g) + 3 Cl₂(g) → 2 NCl₃(g) ΔH° = 460 kJ; ΔS° = -275 J/K

Textbook Question

From the values given for ΔH° and ΔS°, calculate ΔG° for each of the following reactions at 298 K. If the reaction is not spontaneous under standard conditions at 298 K, at what temperature (if any) would the reaction become spontaneous?

a. 2 PbS(s) + 3 O₂(g) → 2 PbO(s) + 2 SO₂(g) ΔH° = −844 kJ; ΔS° = −165 J/K

b. 2 POCl₃(g) → 2 PCl₃(g) + O₂(g) ΔH° = 572 kJ; ΔS° = 179 J/K

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Textbook Question

A certain constant-pressure reaction is barely nonspontaneous at 45 °C. The entropy change for the reaction is 72 J/K. Estimate ΔH.