Calculate the entropy change for the conversion of following: (a) \(1 \mathrm{~g}\) ice to water at \(273 \mathrm{~K}, \Delta H_{\mathrm{f}}\) for ice \(=6.025 \mathrm{~kJ} \mathrm{~mol}^{-1}\). (b) \(36 \mathrm{~g}\) water to vapour at \(373 \mathrm{~K} ; \Delta H_{\mathrm{v}}\) for \(\mathrm{H}_{2} \mathrm{O}=40.63 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

Enthalpy change, denoted as \( \(\Delta H\) \), represents the total heat content of a system and its variation during a process such as a chemical reaction, heating, melting, or vaporization. During a phase transition, the change in enthalpy is particularly important as it quantifies the energy required for a substance to transition from one phase to another at constant pressure.

For instance, when ice melts into water or water evaporates into vapor, the system absorbs energy from the surroundings, which is reflected as the enthalpy of fusion (\( \(\Delta H_{\mathrm{f}}\) \)) and the enthalpy of vaporization (\( \(\Delta H_{\mathrm{v}}\) \)), respectively. These values are usually expressed per mole of the substance undergoing the phase change.

In practice, to calculate the entropy change for these processes, one must first understand the enthalpy change. Entropy change may then be calculated by dividing the enthalpy change (converted to joules if necessary) by the temperature in kelvins. This relationship is vital for understanding the thermodynamic favorability and spontaneity of phase transitions.

Phase transition is a physical process where a substance changes from one state of matter to another, such as solid to liquid (melting) or liquid to gas (vaporization). During such transitions, properties such as temperature and pressure play a crucial role.

The entropy of a system, denoted by \( \(\Delta S\) \), measures the disorder or randomness of the particles in the system and changes significantly during phase transitions. For melting ice or evaporating water, the entropy increases because the molecules move from a more ordered state (solid or liquid) to a less ordered state (liquid or gas, respectively).

To calculate entropy change, it's essential to consider the energy absorbed or released and the phase transition's temperature. An important consideration in thermodynamic calculations, including the second law of thermodynamics, is that the total entropy of a closed system tends to increase over time, indicating that phase transitions tend towards more disordered states.

A mole is a fundamental unit in chemistry that represents a specific number of particles, typically atoms or molecules, and is indispensable in stoichiometric calculations. The mole concept allows chemists to convert between mass and number of entities (atoms, molecules, etc.) enabling precise chemical manipulations and predictions.

The molar mass is the mass in grams of one mole of a substance and serves as a conversion factor between grams and moles. By using the formula \( n = \frac{m}{M} \), one can determine the number of moles \( n \) in a given mass \( m \) of substance, where \( M \) represents the molar mass.

When calculating the entropy change for phase transitions, as in the textbook exercise, moles calculation is a preliminary step. Accurate determination of the quantity in moles is critical for applying the entropy change formula correctly and arriving at the precise thermodynamic properties of the system.