Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2}\);(c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

Understanding the spontaneity of phase changes such as the melting of ice involves considering the thermodynamic principles at play. For a process to be spontaneous, it must occur without the input of external energy under the given conditions. During phase changes, such as freezing and melting, energy and molecular arrangement are key factors.

For instance, under normal atmospheric pressure, the transition from solid ice to liquid water happens without external intervention at temperatures above 0°C. The thermal energy at this temperature is sufficient to overcome the molecular forces holding the ice structure together. However, at -10°C, additional energy is required to raise the temperature of the ice to the melting point, meaning the process is not spontaneous at this temperature and pressure. The spontaneity of any phase change depends on both the prevailing temperature and pressure conditions relative to the substance's phase diagram.

Separating a gaseous mixture into its pure components, such as nitrogen (N_{2}) and oxygen (O_{2}), may appear straightforward, but is not spontaneous. From a thermodynamic perspective, gases naturally mix and spread out to maximize entropy, a measure of disorder. Separation contradicts this trend by reducing entropy, as it creates a more ordered system. Attempting to separate these gases into two pure forms requires work and an input of energy, whether by a mechanical separator or a process such as fractional distillation.

This concept goes hand-in-hand with the second law of thermodynamics, which states that the overall entropy of an isolated system can never decrease over time. The separation of gas mixtures represents an organized state that is less probable without intervention.

When iron filings are exposed to a magnetic field, they experience a force that causes them to align along the magnetic field lines. This spontaneous alignment increases the order within the system, seemingly at odds with the concept of entropy. However, the magnetic field is an external influence that reduces the energy of the system as a whole when the iron particles align – this is a lower energy and more stable state.

Although local entropy decreases when the filings align, the system's total entropy does not necessarily decrease. In this context, the 'system' includes the magnetic field, which is doing work on the filings to align them. The energy changes associated with the magnetic field compensate for the gain in orderliness of the iron filings.

In exothermic reactions, substances react to form products while releasing heat to the surroundings, often leading to increased spontaneity. The reaction of hydrogen gas with oxygen gas to form water vapor, for example, releases energy, making it favorable or spontaneous under the right conditions. A fundamental tenet of thermodynamics is that spontaneous reactions at constant temperature and pressure tend to lower the Gibbs free energy of the system.

This principle helps us understand why exothermic reactions like the combustion of hydrogen are generally spontaneous. They not only release heat, thereby increasing the overall entropy of the surroundings, but also typically result in a decrease in Gibbs free energy, which is a criterion for spontaneity.

The process of dissolution, particularly regarding hydrochloric acid (HCl(g)) in water, can be spontaneous based on its thermodynamic properties. During dissolution, energy is released (exothermic) and the disorder of the system increases as ions become more dispersed in the solution. These factors contribute to spontaneity.

Spontaneous dissolution is also associated with a concept called 'solvation,' where solvent molecules surround and interact with solute particles, like when HCl gas dissolves in water. The increase in entropy due to the distribution of ions throughout the solution and the exothermic nature of the process often make dissolution spontaneous, provided that the Gibbs free energy change is negative.

Gibbs free energy (G) is the defining thermodynamic property in determining the spontaneity of processes. It takes into account both enthalpy (heat content) and entropy, and is governed by the equation G = H - TS, where H represents enthalpy, T is temperature, and S is entropy. A negative change in Gibbs free energy (ΔG) indicates that a process is spontaneous at constant temperature and pressure.

Students often find it challenging to grasp how both energy and disorder interplay in the spontaneity of processes. An important key to understanding is that a negative ΔG can result from a large increase in entropy (even with an endothermic reaction) or from a release of energy (as in an exothermic reaction). Therefore, both factors must be considered when predicting whether a chemical or physical process will occur spontaneously.