Chemistry Chapter 12: Freezing Point Depression

Course Information

• The course is Physical Chemistry I (CHY2018).
• Course materials are available at utechonline.utech.edu.jm and on Scoology.com (access code: 4RDC-F4TD-C9475).
• Assessment includes:
  • Test 1 (Week 6): 15%
  • Test 2 (Week 12): 15%
  • Tutorial quizzes: 20%
  • Laboratory: 20%
  • Final examination: 30%

Unit 1: Phase Equilibria

• Students should be able to:
  • Review colligative properties of solutions
  • Understand the Theory of Ideal Solutions
  • Understand one-component systems (vapour pressure diagrams)
  • Understand the qualitative relationship between boiling point, latent heat of vaporisation and intermolecular forces.
  • Understand two-component systems (mixtures of two miscible liquids)
  • Apply Raoult's Law to the vapour pressures of miscible liquids
  • Understand phase diagrams, fractional distillation, azeotropic mixtures, and eutectic systems.
  • Understand partition coefficients
  • Understand immiscible solutions
• Recommended text: Elements of Physical Chemistry (5th) by Peter Atkins

What is Phase Equilibria?

• The study of equilibrium between or within different states of matter (solid, liquid, gas).

Colligative Properties of Solutions

• Properties that depend on the concentration of solute particles but not on their identity.
• In liquid solutions, solute molecules displace solvent molecules, reducing solvent concentration.
• Colligative properties depend only on the ratio of solute to solvent, not the properties of either.
• Colligative properties are independent of the nature of the solute.

Colligative Properties of Solutions (continued)

• 'Colligative' means 'depending on the collection'.
• The properties are associated with changes in the entropy or disorder of the solvent.
• The increase in disorder is independent of the identities of the species used.
• It is dependent on the number of solute particles, not their chemical identities.
• For example, a 0.01 mol kg-1 aqueous solution of any non-electrolyte will have the same boiling point, freezing point, and osmotic pressure.
• Molality (m) is defined as the number of moles of solute per kilogram of solvent.

Activity

• Calculate the molality of a solution containing 20.0 g of Br2 in 40.0 g of CH2Cl2.

Colligative Properties of Solutions (Characteristics)

• Ideal solute: has no effect on the enthalpy of the solution. 
• Ideal solute: impacts the entropy by introducing disorder.
• Entropy increases when components mix.
• Solute can modify solution properties.

Colligative Properties of Solutions (List)

• Vapor pressure depression
• Boiling point elevation
• Freezing point depression
• Osmotic pressure

Vapour Pressure Depression

• When a non-volatile solute is added to a solvent, the vapor pressure of the solvent above the solution is lower than the vapor pressure above the pure solvent.
• This is because solute molecules reduce the surface area available for solvent molecules to escape into the gas phase.
• The reduction in vapor pressure is proportional to the number of solute particles.

Vapor Pressure Depression (Raoult's Law)

• Raoult's Law states that the vapor pressure of the solvent is directly proportional to the mole fraction of the solvent in the solution.
  • P(solvent) = X(solvent) * P°(solvent)
  • Where P°(solvent) is the vapor pressure of the pure solvent

Vapor Pressure Depression (Important Points)

• The chemical nature of the solute does not affect vapor pressure depression, but the number of solute species does.
• The mole fraction of the solvent must include all the species in the solution.

Boiling Point Elevation

• The normal boiling point of a liquid is the point where its vapor pressure equals 1 atm.
• When a non-volatile solute is present, the solution has a lower vapor pressure.
• To reach 1 atm, the boiling point of the solution must be raised.
• Boiling point elevation is calculated using Raoult's Law, expressing the amount of solute particles as a molality instead of a mole fraction.

Normal Melting and Boiling Points

• Normal melting and boiling points occur when pressure = 1 atm.
• These points are found by a horizontal line drawn across the phase diagram at 1 atm pressure.

Boiling Point Elevation (Calculation)

• Molality is used to express solute concentration in boiling point elevation calculations because it is temperature-independent.
• The increase in boiling point is directly proportional to the solute concentration (in molality).
•  ΔT(solution) = K(b) m(solute)
  • K(b) is the boiling point elevation constant.

Freezing Point Depression

• The freezing point of a pure liquid is the temperature where molecules cluster to form a crystal lattice.
• At the freezing point, a dynamic equilibrium exists between the rate of freezing and melting.
• Adding a solute to a solution creates a higher concentration in the liquid phase.
• According to Le Chatelier's principle, the system shifts towards melting to correct the concentration gradient, causing a lower freezing point for the solution compared to the pure solvent.

Freezing Point Depression (Calculation)

• The freezing point depression of a solution is proportional to the solute's molality.
• ΔT(solution) = K(f) m(solute)
  • K(f) is the freezing point depression constant.

Freezing Point Depression (Applications)

• Used in everyday applications, such as salting roads to lower ice point.
• Used in antifreeze for cars to prevent water freezing in winter.
• Calcium chloride (CaCl2) can be used in colder temperatures.

Osmotic Pressure

• Osmosis is the movement of solvent across a semipermeable membrane from a region of low solute concentration to a region of high solute concentration.
• Applied pressure to prevent the flow of water is osmotic pressure.
• Osmotic pressure is the minimum pressure required to prevent the inward flow of water across a semipermeable membrane. 
• Osmotic pressure is a measure of the tendency of a solution to take in water by osmosis.

Osmotic Pressure (Calculation)

• The equation for calculating osmotic pressure is
  • Π = MRT
    • Π is osmotic pressure.
    • M is molar concentration
    • R is the ideal gas constant,
    • T is temperature in Kelvin.

Osmotic Pressure (Other important information)

• Measurements of freezing point depression and osmotic pressure are commonly used for determining the molar mass of solutes with low water solubility(e.g.large biomolecules).
• Vapor pressure depression and boiling point elevation are less sensitive to concentration changes

Activity

• Calculate the boiling point and freezing point for a 0.501 m glucose solution.

Phase Diagram

• Represents the phase changes of a substance as a function of temperature and pressure.
• Solid, liquid, and gas phases are shown.
• Important points, such as the triple point (where all three phases coexist) and the critical point (where the liquid and gas phases become indistinguishable)

Phase Diagram (Specific Points)

• Triple point: The temperature and pressure where all three classical phases (solid, liquid, gas) coexist simultaneously. .
• Critical point: The point where the liquid-gas phase boundary ends, and above which there is no liquid-gas phase boundary. At this point, the critical temperature (Tc) and critical pressure (Pc) are reached.

Phase Diagram (Specific Substances)

• Water and carbon dioxide phase diagrams have different shapes and are not ideal.

Phase Rule

• Degrees of freedom (F) refer to the variables (pressure, temperature, and composition) that can be changed independenly without changing the number of phases.
• Components (C) relate to the minimal amount of independent species needed to identify the composition of all existing phases within a system.
• The phase rule: F = C - P + 2 (where P is the number of phases)

Azeotropes

• Liquid mixtures having fixed boiling points when they are heated.
• They show a maximum/minimum in the boiling point curve.
• Azeotropes indicate differences in interactions between molecules.

Raoult's Law

• The partial vapor pressure of a substance in a liquid mixture is proportional to its mole fraction in the mixture and its vapor pressure when pure
• P(substance)=X(substance) P°(substance)
• Where;

Ideal Solutions

• Hypothetical solutions in which Raoult's law holds throughout their entire composition range.

Ideal Solutions (Important Factors)

• Components should have comparable molecular shapes and intermolecular forces.
• Benzene and toluene mixtures are good examples.

Limitations of Raoult's Law

• Ideal solutions are theoretical concepts, and all real solutions deviate from Raoult's law to some extent.

Limitations of Raoult's Law(Deviations from Ideality)

• Variations usually small for excess solvents; deviate more for concentrated solutes.
• Environment unlike that of pure solute; unlikely that vapor pressure is directly related.

Examples of Ideal Mixtures

• Mixtures of similar substances, such as hexane and heptane, benzene and methylbenzene, and propan-1-ol and propan-2-ol.

Vapour Pressure/Composition Diagrams

• Partial vapor pressure of each component is proportional to its mole fraction.

Boiling Point/Composition Diagrams

• Boiling point at which the vapour pressure equals the external pressure
• Liquid with higher vapor pressure boils at lower temperature
• Mixture boiling point curve will be a single line( ideal mixtures)

Problem

• Calculate the partial vapor pressure of A in a mixture
• Calculate the partial vapor pressure of B in a mixture
• Calculate the total vapor pressure of the liquid

Definitions

• Colligative properties: Solution properties depending on concentration, not identity.
• Phase diagram: Graphic representation of phase changes.
• Triple point: Temperature/pressure where all three phases coexist.
• Molarity: Moles of solute/litre of solution.
• Molality, Moles of solute/kg of solvent.
• A Azeotrope is a constant boiling point and composition mixture of two liquids
• Raoult's Law: Vapor pressure of solvent is proportional to its mole fraction.
• Immiscible mixtures: Components don't dissolve in each other
• Partition coefficent: Ration of solute concentration in two immiscible phases
• Solvent-solvent extraction: Separating immiscible mixtures by using different solvents
• Solid-phase extraction: Separating immiscible mixtures by using different solid phases
• Plasma: Ionized gas
• Supercritical fluid: Substance above its critical point.
• Superfluid: A state of matter with zero viscosity.