Equilibria Involving Condensed Matter e.g. where but At equilibrium,  K depends only on the ______________ pressures of the gaseous reaction components. A special case is the ____________ of a liquid: Modified by Jed Macosko 12/3/2018

Modified by Jed Macosko Phase Equilibria Consider a closed system of a single component. The __________ ____________ determines which phase is stable at a particular T and P. µ tends to a ____________. At the melting point Tm, µ(s) = µ(l) At the boiling point Tb. µ(l) = µ(g) These points depend on ____________ and ___________. Tm µ gas liquid solid T Tb higher pressure µ phase 1 phase 2 Tx Tx' phase transition at higher T Modified by Jed Macosko 12/3/2018

The Clapeyron Equation Consider two phases a and b in equilibrium: If small changes in T and P are made such that a and b are still in equilibrium: Melting Integrating, and usually  Tm increases with pressure not for ___________! Modified by Jed Macosko 12/3/2018

The Clausius-Clapeyron Equation Vaporization Assuming the vapour is an ideal gas, Integrating, The normal boiling point is the temperature at which the vapour pressure becomes standard, i.e. ___________. ___________ solid  gas The liquid is not stable at any temperature. Triple Point: solid, liquid and gas are all in equilibrium This happens at the pressure where the sublimation temperature and the boiling temperature coincide. At the triple point, vapour pressure of liquid = vapour pressure of solid Ttriple and Ptriple are ___________. Modified by Jed Macosko 12/3/2018

Modified by Jed Macosko The Phase Rule How many intensive variables are needed to describe fully a system of C ___________and P ___________? Two for temperature and pressure. How many for the composition of each phase? Take mole fractions of each component in each phase C-1 because for each phase but since the phases are in equilibrium, (P – 1)C variables are redundant  Number of independent concentration variables  Total number of variables (___________of freedom) Phase: A state of matter that is uniform throughout, in both chemical composition and physical state. Component: The number of components is the minimum number of independent species necessary to define the composition of all phases in the system. Reactions and phase ___________must be taken into account. Modified by Jed Macosko 12/3/2018

Phase Diagrams of ___________Materials For single phase regions there are 2 degrees of freedom. For phase ___________there is 1 degree of freedom. At the triple point there is ___________freedom. e.g. CO2 Pressure Temperature P3 Triple point Critical point solid gas liquid __________fluid T3 Pc Tc Modified by Jed Macosko 12/3/2018

The Phase Diagram of ___________ Pressure / atm Temperature /°C 218 1.0 100 374 Triple point Critical point ICE VAPOUR STEAM LIQUID SUPERCRITICAL FLUID There are other solid phases at much higher ___________. Modified by Jed Macosko 12/3/2018

Modified by Jed Macosko 12/3/2018