91Ó°ÊÓ

For a process to be endothermic, it must absorb heat from its surroundings, and for it to be spontaneous, the process should occur without any external intervention. Two examples of endothermic processes that are spontaneous are: 1. Melting of ice at temperatures above 0°C: When ice absorbs heat from the surroundings at temperatures above 0°C, it melts into water. This is an endothermic and spontaneous process. 2. Dissolution of ammonium nitrate in water: When ammonium nitrate (\(NH_4NO_3\)) is dissolved in water, it absorbs heat from the surroundings and causes the temperature of the solution to decrease. This is an endothermic process that occurs spontaneously.

The Gibbs free energy change, \(\Delta G\), can be used to determine the spontaneity of a process. The equation for Gibbs free energy change is: \[\Delta G = \Delta H - T \Delta S\] where \(\Delta H\) is the enthalpy change, \(T\) is the temperature, and \(\Delta S\) is the entropy change. A process is spontaneous when \(\Delta G < 0\), nonspontaneous when \(\Delta G > 0\), and at equilibrium when \(\Delta G = 0\). One example of a process that is spontaneous at one temperature but nonspontaneous at a different temperature is the dissolution of calcium sulfate in water. The dissolution of calcium sulfate (\(CaSO_4\)) is an endothermic process (\(\Delta H > 0\)) with an associated increase in entropy (\(\Delta S > 0\)). At low temperatures, the entropy term (\(T \Delta S\)) will be smaller than the enthalpy term (\(\Delta H\)), resulting in a positive \(\Delta G\) value, making the process nonspontaneous. However, at higher temperatures, the entropy term (\(T \Delta S\)) becomes more significant and can outweigh the enthalpy term (\(\Delta H\)), resulting in a negative \(\Delta G\) value and making the process spontaneous. In summary, the dissolution of calcium sulfate in water is an example of a process that is spontaneous at high temperatures but nonspontaneous at low temperatures.