Module 6.1: Phase Transitions

6.1.1 Introduction

I phase transition: the change of a substance's phase, from one phase into another

1. a phase transition occurs when two phases are in equilibrium

   1. both phases at equilibrium (during a phase transition) coexist

2. when energy is transferred as heat during a phase transition, this raises the potential energy of the system instead of the kinetic energy of the system

   1. the kinetic energy of a system is related to its temperature

   2. phase transitions result in increase or decrease of intermolecular forces between molecules of a substance, which determines its potential energy

II phase transitions and their dependence on temperature can be explained by using Gibbs energy.

1. the molar entropy of a system decreases as a substance becomes more condensed.

   1. For a certain substance, the molar entropy is: solid < liquid << gas.

2. the molar enthalpy of a system decreases as a substance becomes more condensed.

   1. This is only true for the molar enthalpy of three different phases of the same substance at the same temperature.

   2. A solid is much lower in potential energy than a gas (due to intermolecular forces) and therefore has less internal energy and less enthalpy.



3. If the Gibbs free energy of the three phases are graphed against temperature, Figure 72 is observed.

   1. The direction of spontaneous change is the direction of decreasing Gibbs free energy.

   2. Therefore, those with greater molar entropies should have larger negative slopes, which is observed in Figure 72.

   3. The temperatures where the Gibbs free energy of the two substances are equal are where phase transitions occur. This is known as the equilibrium point.

   4. Although liquid is more stable at the blue range of temperatures, some of the substance may be in other phases, such as the vapor phase. This is especially true when the difference in Gibbs free energy between phases is small.

III phase transitions and their dependence on pressure can also be explained by using Gibbs energy.

1. the gas phase has a considerably larger molar volume ($\textrm{V}_{m}$) compared to other condensed phases and therefore is the most sensitive to changes in pressure

2. At low pressures, the gas phase is most stable, but condensed phases become most stable with increasing pressure (the distance between molecules decrease as pressure increases, thus IMFs increase)

6.1.2 Vapor pressure

IV vapor pressure: the pressure exerted by the vapor when the vapor and condensed phase (such as liquid or solid) are in dynamic equilibrium

1. the two phases are in dynamic equilibrium when the rates of evaporation and condensation (if the condensed phase is liquid) are equal

   1. phase transitions are also in dynamic equilibrium

2. the vapor pressure is dependent on the difference of $\textrm{G}_{m}$ (vapor) and $\textrm{G}_{m}$ (condensed phase)

V substances with weak intermolecular forces have high vapor pressures

1. molecules with weak IMFs can easily escape from the condensed phase

VI substances with strong intermolecular forces have low vapor pressures

1. molecules with strong IMFs cannot easily escape from the condensed phase

VII vapor pressure also depends on temperature

1. increase in temperature = more kinetic energy = more energy to overcome IMFs

   1. therefore, an increase in temperature can be expected to increase vapor pressure

   2. as vapor pressure increases, the gap between $\textrm{G}_{m}$ (vapor) and $\textrm{G}_{m}$ (liquid) closes.

2. the dependence of vapor pressure and temperature is quantitatively represented by the Clausius-Clapeyron equation $\textrm{ln} \frac{\textrm{P}_{2}}{\textrm{P}_{1}} = - \frac{\Delta \textrm{H}_{vap}^{\Theta}}{\textrm{R}} (\frac{1}{\textrm{T}_{2}} - \frac{1}{\textrm{T}_{1}})$ (Eq. 101)

6.1.3 Boiling and freezing

VIII When the vapor pressure is equal to the external pressure, the substance boils

1. When the external pressure is equal to the atmospheric pressure (1 atm), this is known as the normal boiling point ($\textrm{T}_{b}$) of a substance, where $\Delta \textrm{G}^{\Theta} = 0$.

2. when external pressures are greater than 1 atm, the boiling point is higher than Tb as it requires higher temperatures for the vapor pressure to match $\textrm{P}_{ex}$.

3. vaporization occurs throughout the liquid, as vapor formed in the liquid rises rapidly to the surface (bubbles)

IX normal freezing point ($\textrm{T}_{f}$): the temperature when the liquid and solid phase are in dynamic equilibrium (at 1 atm)

1. unlike the boiling point, the freezing point only varies slightly as the pressure changes

X supercooling: the process of lowering the temperature of a liquid below $\textrm{T}_{f}$ without it freezing

1. in order for a substance to freeze, a nucleation site is required; this could be a crystal, impurity, or even molecular vibration that triggers the phase transition

2. supercooling frequently occurs when the temperature is lowered rapidly

   1. if the substance is very pure and is cooled very quickly and carefully (avoiding any vibration), substances like water can be supercooled up to $-42 \degree \textrm{C}$!

XI superheating: the process of raising the temperature of a liquid above $\textrm{T}_{b}$ without it boiling

1. similar to supercooling, a nucleation site is required for the substance to boil.

2. superheating frequently occurs when the temperature is raised rapidly

3. superheating can be dangerous, and boiling chips (nucleation site) are added to prevent superheating.

6.1.4 Phase Diagrams

XII phase diagram: a diagram that shows the most stable phase at a certain pressure and temperature

XIII phase boundaries: lines separating the regions in a phase diagram

1. the difference in Gibbs free energy of two different states equals zero (Ref. Figure 72)

2. solid-liquid phase boundaries are steep; a drastic increase in pressure barely affects its melting point

   1. positive solid-liquid slope: solid phase is more dense than liquid phase

   2. negative solid-liquid slope: solid phase is less dense than liquid phase

   3. remember that increasing external pressure causes molecules to get closer to each other; the denser phase is favored as pressure increases

XIV triple point: a specific temperature ($\textrm{T}_{tp}$) and pressure ($\textrm{P}_{tp}$) where three phases are in equilibrium

1. all three phases will coexist in equilibrium

2. every compound has a unique triple point; cannot be altered by changing conditions

XV critical point: an endpoint that terminates the liquid-vapor boundary and becomes a supercritical fluid

1. supercritical fluid: fills the entire container but has similarly density to a liquid

   1. supercritical $\textrm{CO}_{2}$ is frequently used as a solvent; non-toxic, no contamination, and environmentally friendly

2. critical temperature ($\textrm{T}_{c}$): the temperature boundary where vapor can no longer be condensed into liquid at any pressure

   1. a vapor that cannot be condensed at all pressures is known as a gas