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.

Verified step by step guidance

1. insert step 1> Identify the chemical reaction for the decomposition of ammonium nitrate: \( \text{NH}_4\text{NO}_3(s) \rightarrow \text{N}_2\text{O}(g) + 2\text{H}_2\text{O}(g) \).
2. 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.
3. 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).
4. 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.
5. insert step 5> Conclude that the decomposition of ammonium nitrate is spontaneous at 25 °C if \( \Delta G^\circ \) is negative.

Key Concepts

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.