Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

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McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problema 120

Capitolo 18, Problema 120

Ammonium nitrate is dangerous because it decomposes (sometimes explosively) when heated: (a) Using the data in Appendix B, show that this reaction is spontaneous at 25 °C.

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insert step 1> Identify the chemical reaction for the decomposition of ammonium nitrate: \( \text{NH}_4\text{NO}_3(s) \rightarrow \text{N}_2\text{O}(g) + 2\text{H}_2\text{O}(g) \).

insert step 2> Use Appendix B to find the standard enthalpy change (\( \Delta H^\circ \)) and the standard entropy change (\( \Delta S^\circ \)) for the reaction.

insert step 3> Calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) at 25 °C using the equation: \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \), where \( T \) is the temperature in Kelvin (298 K).

insert step 4> Determine if the reaction is spontaneous by checking if \( \Delta G^\circ \) is negative. A negative \( \Delta G^\circ \) indicates a spontaneous reaction.

insert step 5> Conclude that the decomposition of ammonium nitrate is spontaneous at 25 °C if \( \Delta G^\circ \) is negative.

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Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict whether a reaction will occur spontaneously at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (ΔG) is negative. The relationship is given by 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.

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01:51

Gibbs Free Energy of Reactions

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. For a reaction to be spontaneous, the increase in entropy must outweigh the enthalpy change at a given temperature. Understanding how these two factors interact is crucial for analyzing the spontaneity of chemical reactions.

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02:46

Entropy in Thermodynamics

Temperature's Role in Spontaneity

Temperature plays a critical role in determining the spontaneity of a reaction. As temperature increases, the TΔS term in the Gibbs Free Energy equation becomes more significant. This means that reactions with a positive entropy change can become spontaneous at higher temperatures, even if they are endothermic (positive ΔH) at lower temperatures.

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01:17

Spontaneity and Temperature

Pratica correlata

Domanda del libro di testo

Consider the Haber synthesis of gaseous NH₃ (∆H°_f = -46.1 kJ/mol; ∆G°_f = -16.5 kJ/mol: (d) What are the equilibrium constants K_p and K_c for the reaction at 350 K? Assume that ∆H° and ∆S° are independent of temperature.

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Domanda del libro di testo

Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.

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Domanda del libro di testo

Use the data in Appendix B to calculate the equilibrium pressure of CO₂ in a closed 1 L vessel that contains each of the following samples:

(a) 15 g of MgCO₃ and 1.0 g of MgO at 25 °C

(b) 15 g of MgCO3 and 1.0 g of MgO at 280 °C .

Assume that ∆H° and ∆S° are independent of temperature.

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