The vapour pressures of water and ice at \(-10^{\circ} \mathrm{C}\) are \(0.28\) and \(0.26 \mathrm{~Pa}\), respectively. What is the free energy change for the process? \(\mathrm{H}_{2} \mathrm{O} \quad\left(1, \quad-10^{\circ} \mathrm{C}, \quad 0.28 \quad \mathrm{~Pa}, \quad 1 \quad\right.\) mole \()\) \(\rightarrow \mathrm{H}_{2} \mathrm{O}\left(\mathrm{s},-10^{\circ} \mathrm{C}, 0.26 \mathrm{~Pa}, 1 \mathrm{~mole}\right)\) (a) \(R \times 263 \times \ln \frac{14}{13}\) (b) \(R \times 263 \times \ln \frac{13}{14}\) (c) \(R \times 10 \times \ln \frac{13}{14}\) (d) \(R \times 10 \times \ln \frac{14}{13}\)

Vapour pressure is an essential concept in the field of chemistry, particularly when discussing substances in different states of matter. It refers to the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.

The vapour pressure of a substance is dependent on the temperature; as the temperature increases, so does the vapour pressure. This is because molecules gain kinetic energy with rising temperature, which allows more molecules to escape from the liquid or solid phase into the gaseous phase.

• Higher temperature leads to higher vapour pressure.
• Different substances at the same temperature have different vapour pressures based on their intermolecular forces.

For instance, in the given exercise, we compared the vapour pressures of water in two different phases, solid and liquid, at the same temperature. Understanding vapour pressure is crucial when studying phase transitions, such as boiling, evaporation, sublimation, and condensation since these processes involve a change between gaseous and condensed phases.

Phase transition thermodynamics is a field that analyzes the energy changes that occur during transitions between different states of matter. The transitions include melting, freezing, boiling, and sublimation, among others.

Each phase transition is associated with an energy change, specifically enthalpy and entropy changes. When a substance transitions from one phase to another, energy is either absorbed or released. This is significant in the context of free energy change, represented by the Gibbs free energy equation.

The phase transition between water and ice at a given temperature, as in our exercise, involves a calculation of the free energy change, which determines the spontaneity of the transition, as well as the equilibrium between the two phases at that temperature.

• Melting and boiling require energy input (endothermic).
• Freezing and condensation release energy (exothermic).

The calculation of free energy change incorporates entropy and enthalpy, considering both the energy difference and the temperature, providing a comprehensive picture of the thermodynamic process involved in phase transitions.

Chemical potential is a term used to describe the energy that particles contribute to a system and is a measure of the potential for a substance to change, such as undergoing a phase transition or reacting chemically.

It directly relates to free energy, as it is the change in Gibbs free energy with respect to the change in the number of molecules or moles at constant pressure and temperature. In the context of our exercise, the chemical potential governs the direction of the phase change from liquid water to solid ice.

When the chemical potential of the two phases reaches equilibrium, no net change occurs, and the system is at equilibrium. Vapor pressure is one way to understand changes in chemical potential, as a substance with higher vapour pressure at a given temperature has a higher chemical potential and is more likely to go into the gas phase.

• Chemical potential guides the direction of phase transitions.
• A difference in chemical potential between phases drives the phase change.

Understanding chemical potential is vital for accurately determining the conditions under which phase transitions will occur, making it a cornerstone concept in the study of phase transition thermodynamics.