Explain why liquid water at 273.0 \(\mathrm{K}\) will not melt in terms of Gibbs energy.

Phase transition refers to the transformation of matter from one state to another, such as solid to liquid, liquid to gas, and vice versa. Key factors influencing these transitions are temperature and pressure. At specific temperature and pressure conditions, known as the phase equilibrium, multiple phases can coexist.

For instance, consider water turning into ice. At the freezing point, 0°C (273.15 K), under standard atmospheric pressure, both water and ice have the same Gibbs energy. This equilibrium situation means that any tiny fluctuation that favors ice would be counterbalanced by another that favors liquid water. Only a change in the conditions, like a drop in temperature, can drive the system towards a complete phase transition into ice or another into water if the temperature rises.

In thermodynamics, a process is said to be spontaneous if it occurs naturally without the need for continuous external influence. The spontaneity of a process can be predicted using the Gibbs free energy. When the change in Gibbs energy (ΔG) is negative, the process is spontaneous, meaning it's energetically favorable. If ΔG is positive, the process is non-spontaneous and requires energy to proceed.

To illustrate, a ball rolling downhill spontaneously moves to a lower energy state. If liquid water at 273 K attempted to freeze, this would necessitate an increase in Gibbs energy, hence it is non-spontaneous; the ball would have to 'roll uphill', which doesn't occur without added energy.

Thermodynamics is the science that deals with heat, work, and the forms of energy associated with chemical and physical processes. The first law of thermodynamics states energy cannot be created or destroyed, only transformed. The second law introduces the concept of entropy, indicating the natural tendency of systems to progress towards disorder.

The Gibbs energy combines these principles to predict process spontaneity by factoring in both enthalpy (heat content) and entropy (disorder). A key point here is that at constant temperature and pressure, the spontaneity of a phase change, or any reaction, can be assessed by determining whether there's a decrease in the system's Gibbs energy.