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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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 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.

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.

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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Spontaneity and Temperature

Related Practice

Textbook Question

Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction Given that ∆G° = -13.6 kJ, calculate ∆G at 25 °C for the following sets of conditions. .(a) 10 atm NH3, 10 atm CO2, 1.0 M NH2CONH2(b) 0.10 atm NH3, 0.10 atm CO2, 1.0 M NH2CONH2Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

Textbook Question

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.

Textbook Question

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.

Textbook Question

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