Concepts.doc (Word 97)

KEY CONCEPTS FOR EXAM #2

Note: This list is only a guide to help you study. It is NOT comprehensive, and the exam may cover any topics discussed in class.

Classifications of Phase Transitions

  • First Order Phase Transitions the first derivatives of the chemical potentials are discontinuous at the transition
  • Second Order the first derivatives of the chemical potentials are continuous, but the second derivatives are discontinuous
  • plots of relevant variables at the phase transition (e.g. Cp vs. Temp, etc)

Criteria for an Ideal Solution

  • all intermolecular interactions are identical
  • there is no change in volume upon mixing
  • there is random mixing of components

Thermodynamics of Mixing

For ideal gases

Raoult's Law

  • Ideal solution

or

  • Non-ideal solutions

or

where xi is mole fraction of i in solution, gi is the activity coefficient of i, Pi is the partial vapor pressure of i, and Pi* is the pressure of pure i.

  • In an ideal solution, all intermolecular interactions (i.e. solute-solvent, solute-solute, solvent-solvent) are identical
  • Positive deviations from Raoult's Law occur when the interactions between the solute and the solvent are weaker than solute-solute and solvent-solvent interactions. Typically, the solute molecules break up strong interactions of the solvent with itself.
  • Negative deviations from Raoult's Law occur when the interactions between the solute and the solvent are stronger than solute-solute and solvent-solvent interactions. The solvent and solute molecules decrease each other's escaping tendency.

Henry's Law (obeyed by solute in dilute solutions)

where ki is Henry's Law constant, xi is mole fraction of i in solution

  • Henry's Law approximation is most accurate for dilute solutions (i.e. when the substance is a solute in low concentrations). Raoult's Law is most accurate for concentrated solutions (i.e. when the substance is a solvent in high concentration)

Composition of the Vapor

where Yi is the mole fraction of component i in the vapor phase, and Ptotal is the total pressure of the vapor phase above the solution

Variations of Equilibrium Constants with Temperature (Van't Hoff Equation)

or

Chemical Equilibria

  • "extent of reaction" parameter,
  • corresponds to reaction advancement from reactant to products
  • For a substance with several phases in equilibrium, the chemical potentials of all present phases are equal (e.g. the chemical potentials of the vapor and the liquid are equal)
  • For ideal solutions every component has its chemical potential given by

Clapeyron Equation

Clausius-Clapeyron Equation

or

This can be rewritten as:

Maxwell Relations

Other Concepts

  • Definitions of chemical potential, activity, fugacity, activity coefficient
  • "Regular" solution model for non-electrolytes
  • Colligative properties
  • Variations of equilibrium constants with pressure
  • Gibbs phase rule
  • Phase equilibrium, constructions of phase diagrams for a single-component system
  • Triple points on a phase diagram points on phase diagrams where three phases are in equilibrium

Relevant pages in Mortimer are Chapters 6, 7, 8, and Chapter 5 (starting with Section 5.3).

Electrolyte chemistry will NOT be on Exam #2.

Note: This list is only a guide to help you study. It is NOT comprehensive, and the exam may cover any topics discussed in class. Please remember also that even though Exam #2 will cover primarily the material discussed after Exam #1, all exams are comprehensive and you may need to know some concepts covered on Exam #1, especially material that relates directly to current topics (e.g. calculations of DG, DS, DH, DA, heat capacities, etc).