Phase Equilibria Notes

Phase Equilibria

Definition of Phase

• A phase is a region of space where all physical properties of a material are essentially uniform.
• The term "phase" is sometimes used synonymously with "state of matter."

Phase Equilibrium

• The rate of passage from one phase to another depends on:
  • The surface area of contact between the two phases.
  • The concentration of substance in the phase of origin.

Evaporation and Closed Containers

• Evaporation occurs only on the surface of the liquid.
• In a closed container, there is constant evaporation from the surface.
• Particles break away from the liquid's surface but are trapped in the space above.

Equilibrium in a Closed System

• Gaseous particles bounce around, and some hit the liquid surface and get trapped.
• Equilibrium is established when the number of particles leaving the surface equals the number returning.

Vapor Pressure

• In equilibrium, there's a fixed number of gaseous particles above the liquid.
• These particles exert pressure when they hit the container walls.
• The pressure exerted by a vapor in dynamic equilibrium with its liquid is called the vapor pressure.
• Liquids with high vapor pressures at room temperature are volatile; those with very low vapor pressures are non-volatile.

Vapor Pressure and Boiling Point

• The boiling point of a liquid is the temperature at which its vapor pressure equals the pressure of the gas above it.
• The normal boiling point is the temperature at which the vapor pressure equals one atmosphere (760 mm Hg/torr).
• The higher the vapor pressure of a liquid, the lower its boiling point.

Boiling Point, Evaporation, and Temperature

• At 25 °C, the vapor pressure is less than atmospheric pressure, so bubbles cannot form.
• At 70 °C, the vapor pressure increases, allowing bubbles to form and rise because the vapor pressure can overcome atmospheric pressure.
• At 100 °C, the vapor pressure further increases.

Relationship Between Vapor Pressure and Intermolecular Forces

• High vapor pressure indicates a high concentration of molecules escaping the liquid surface into the vapor phase.
• If molecules escape easily, intermolecular forces are relatively weak.
• A small amount of heat is required to break these weak forces and boil the liquid, resulting in a low boiling point.

Raoult’s Law

• The vapor pressure of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent at that temperature multiplied by its mole fraction.
• $P_0$ is the vapor pressure of the pure solvent at a particular temperature.
• $x$ is the mole fraction of the solvent, representing the fraction of the total number of moles of solvent present.

Ideal Mixtures

• An ideal mixture obeys Raoult's Law.
• Intermolecular forces before and after mixing are approximately the same.
• Examples of nearly ideal mixtures include:
  • Hexane and heptane
  • Benzene and methylbenzene
  • Propan-1-ol and propan-2-ol
• Note: No mixture is truly ideal.

Raoult’s Law and Binary Mixtures

• In a pure liquid, energetic molecules overcome intermolecular attractions and escape to form a vapor.
• The same principle applies to a second liquid in the mixture.
• At any temperature, a certain proportion of molecules will have enough energy to leave the surface.

Ideal Mixture Behavior

• In an ideal mixture, the tendency of different molecules to escape is unchanged.
• Mixtures like hexane and heptane exhibit close-to-ideal behavior due to similarly sized molecules and van der Waals attractions.

Raoult’s Law Applied to Binary Mixtures

• The partial vapor pressure of a component in a mixture equals the vapor pressure of the pure component at that temperature multiplied by its mole fraction in the mixture.
• Raoult's Law only works for ideal mixtures.

Equations for Total and Partial Vapor Pressures

• The total vapor pressure of the mixture is:
  $P<em>{total} = P</em>A + P<em>B$ * Where $P</em>A$ and $P_B$ are the partial vapor pressures of components A and B.
• The partial vapor pressures of the components A and B reads
  $P<em>A = x</em>A * P<em>{A,0}$; $P</em>B = x<em>B * P</em>{B,0}$.

Vapor Composition of a Binary Mixture

• When boiling a liquid mixture, the more volatile substance escapes more easily into the vapor phase.
• The vapor composition can be determined by condensing and analyzing the vapor.

Boiling Point Composition Diagrams

• The vapor above the boiling liquid is richer in the more volatile component (e.g., component B).

Deviations from Raoult’s Law in Non-ideal Mixtures

• Positive Deviation: The vapor pressure of the mixture is higher than expected.
• Negative Deviation: The vapor pressure is lower than expected.