Final answer:
The melting of ice at 0°C is thermodynamically favorable due to the heat absorbed from the surroundings (enthalpy of fusion) and the increase in entropy as the ice melts into water at constant temperature.
Step-by-step explanation:
When an ice cube at 0°C is placed in a room at 22°C, it absorbs heat from its surroundings due to the enthalpy of fusion, which is an endothermic process. The enthalpy of fusion is the amount of heat required to convert ice into water without changing the temperature. Specifically, 6.01 kJ of heat is absorbed for every mol of ice that melts at this temperature and pressure.
The process of melting increases the entropy of the system since the molecules in liquid water have more freedom to move than in the solid state, which corresponds to higher disorder or randomness. According to the second law of thermodynamics, natural processes tend to move towards a state of higher total entropy.
This increase in entropy is an important factor when considering whether a process is thermodynamically favorable. The Gibbs free energy (ΔG) of the system decreases during the melting process, which can be comprehended from the Gibbs free energy equation (ΔG = ΔH - TΔS), where ΔH is the change in enthalpy and TΔS is the temperature times the change in entropy. Since ΔS is positive and ΔH is also positive (endothermic) but TΔS is larger at this higher temperature, the Gibbs free energy will be negative, signaling a spontaneous process.