Which of the following phase transitions gives off more heat: (a) 1 mole of steam to 1 mole of water at \(100^{\circ} \mathrm{C},\) or (b) 1 mole of water to 1 mole of ice at \(0^{\circ} \mathrm{C} ?\)

Understanding phase transitions is crucial to grasp many everyday phenomena, from ice melting to the steam rising from a hot cup of coffee. These transitions refer to the change of a substance from one state of matter to another. The most common states are solid, liquid and gas.

There are several types of phase transitions, such as melting (solid to liquid), freezing (liquid to solid), vaporization (liquid to gas), condensation (gas to liquid), sublimation (solid to gas), and deposition (gas to solid). Each transition involves the absorption or release of energy, impacting the temperature and physical properties of the substance. In the context of the textbook exercise, we look at condensation and freezing as examples of exothermic phase transitions, where heat is released into the surroundings.

When a substance changes from a liquid to a gas, it must absorb a significant amount of heat without changing its temperature. This hidden energy is known as the latent heat of vaporization. It's 'latent' because it's a form of energy transfer that doesn't affect the temperature.

For water, this process occurs at 100°C under standard atmospheric pressure, and the latent heat of vaporization is about 40.79 kJ/mol. Understanding this concept is pivotal when solving problems involving boiling, evaporation, or condensation, such as the transition of steam to water in the exercise. This high energy requirement reflects the strong hydrogen bonds that need to be overcome to allow water molecules to escape into the air as gas.

In contrast to vaporization, the latent heat of fusion is concerned with the change from solid to liquid or from liquid to solid. For water being frozen into ice, this latent heat is around 6.01 kJ/mol and involves heat being released as the water transitions to a more orderly solid state.

This process occurs at 0°C under standard conditions. The latent heat of fusion is less than that of vaporization because changing from a liquid to a solid requires overcoming less internal energy compared to that required for liquid to gas transition. These concepts explain part (b) of the exercise, where freezing water into ice emits heat into the environment.

Heat transfer plays a fundamental role in changing the state of a substance during phase transitions. It is a process by which thermal energy is exchanged between physical systems, depending on the temperature difference and the properties of the materials involved.

Three primary modes of heat transfer exist: conduction (direct contact), convection (fluid movement), and radiation (electromagnetic waves). When we talk about the latent heat of vaporization or fusion, we're addressing how this energy transfer is necessary to overcome intermolecular forces without causing a change in temperature. So, in the steam condensing to water (part a), and water freezing to ice (part b), heat transfer continues until the phase transition is complete.

Lastly, all of the above concepts are foundational pillars of thermodynamics, a branch of physics that deals with heat, work, and energy. Thermodynamics tells us how energy transformations, including phase changes, obey certain laws, such as the conservation of energy.

In terms of the exercise at hand, using the first law of thermodynamics, we can deduce that the heat released during a phase change must be equivalent to the latent heat for a given amount of substance, assuming no other work is done. Therefore, in thermodynamics, understanding how energy is stored in chemical bonds and intermolecular forces leads to a comprehension of how energy is released or absorbed during phase transitions.