CHEMISTRY E182019 Phase equilibria G=0 Clausius Clapeyron CH7 This course is approximately at this level Phase equilibria G=0 Clausius Clapeyron Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

T-S diagrams T-s diagrams Gas steam Liquid L+G CH7 p=1000 bar technically realizable maximum Saturated liquid curve Gas steam Saturated vapour curve Liquid L+G

T-S diagrams evaporation CH7 T-s diagrams Saturated liquid s’=2 kJ/kgK Saturated steam s’’=6 kJ/kgK Enthalpy of evaporation hLG=T(s’’-s’)=5004=2MJ/kg

Solid-Liquid-Gas Phase diagrams L-liquid G-gas L-liquid S-solid CH7 Phase diagrams G-gas L-liquid S-solid S+G L+G v p S-solid L-liquid G-gas T p The reason why the regions L+G, S+G appear in the p-v diagram is that the specific volume v (unlike T,p) varies during phase transformations.

liquid-like hydrogen-bonded clusters dispersed within a gas-like phase Solid-Liquid-Gas CH7 Phase diagram ice-water-steam TRIPLE POINT CRITICAL POINT liquid-like hydrogen-bonded clusters dispersed within a gas-like phase Cubic ice Hexagonal ice

Solid-Liquid-Gas L-liquid S-solid G-gas CH7 p T Melting hSL>0, sSL>0, GSL=0, dp=dT=0 S-solid L-liquid G-gas T p Evaporation hLG>0, sLG>0, GLG=0, dp=dT=0 Sublimation hSG>0, sSG>0, GSG=0, dp=dT=0 During phase transitions the pressure and temperature are constant. Also Gibbs energy remains constant as follows from its definition g=h-Ts=0. Only specific volume increases or decreases.

Clausius Clapeyron Solid-Liquid-Gas CH7 S-solid L-liquid G-gas T p Slopes dp/dT are given by Clausius Clapeyron equation Phase transition lines in the p-T diagram are described by the Clausius Clapeyron equation Enthalpy of phase changes, e.g. hLG Specific volume changes, e.g. vG-vL

Clausius Clapeyron Solid-Liquid-Gas CH7 S-solid L-liquid G-gas T p dp/dt>0 because hLG>0 vLG>0 (volume of steam is greater than volume of liquid) The slope dp/dT is negative because specific volume of ice is greater than volume of liquid Melting point temperature of ice decreases with pressure – therefore ice under skates melts and forms a liquid film

Closed loop (evaporation, expansion, condensation, compression) Clausius Clapeyron derivation CH7 T+dT T s=s’’-s’ Clausius Clapeyron equation can be derived from energy balance of a closed cycle in Ts diagram: Heat added-difference between evaporation enthalpy at T+dT and condensation enthalpy at temperature T Mechanical work-received in one cycle Closed loop (evaporation, expansion, condensation, compression)

Clausius Clapeyron and hLG CH7 Clausius Clapeyron equation is exact, because follows from thermodynamic principles. Individual terms (dp/dT,v’’) can be approximated by semiempirical equations (different state equations, Antoine’s equation) State equation Antoine’s equation Result can be improved when using Van der Waals Giving expression for ΔhLG or Redlich Kwong state equation

Multicomponent equilibrium CH7 HEAVY LIGHT A B xA= yA= Liquid phase Gaseous phase Question: Is there a relationship between composition of binary mixture in the liquid phase xA and gaseous phase yA? Binary mixture pA=pA"xA Answer: Yes, Raoult’s law applicable to ideal liquids

Raoult’s law CH7 HEAVY B Fact: It does not matter, how much liquid is in the vessel, pressure of vapours is the same, and given by Antoine’s equation Therefore also the molar volume nB/V is independent of amount of liquid.

Raoult’s law LIGHT HEAVY A B xA CH7 Volume xAV Volume V after expansion of nA molecules to volume V xA Volume V Volume xAV giving Raoult’s law …and also answer to the previous question

HEAVY LIGHT A B Raoult’s law CH7 xA Volume V Volume xAV 1-xA=xB

Distillation Liquid mixture enriched by heavy component Cooling condensing Liquid mixture enriched by heavy component Liquid mixture enriched by light component Initial composition of Liquid Mixture

Henry’s constant can be found in tables Liquid – noncondensable gas CH7 Given temperature T and molar fraction of dissolved CO2 H2O+CO2 yCO2 What to do if T > Tcrit = 31 oC ? Henry’s law H2O+CO2 xCO2 Henry’s constant can be found in tables

Tutorial LIGHT HEAVY A B CH7 Given total pressure p and molar fraction of liquid phase xA calculate Equilibrium temperature T Molar composition of vapours Nonlinear equation for T (Excel solution) p=const Repeated distillation yA 0 xA 1

Tutorial SYRINGE alcohol CH7 Initial state: Syringe filled by liquid mixture H2O (B) + CH3OH (A) (methylalcohol). Initial volume V0, molar fraction of methylalcohol xA, number of moles nA, nB are given (approximated from density). Final state: Volume is increased to V1. Temperature is constant (room temperature). Calculate pressure p, molar fraction of methylalcohol in liquid and vapour phase. V1 VL VG V0

Tutorial Syringe alcohol CH7 Unknown 9 variables xA=? yA=? p=? VL=? VG=? nAL=? nAG=? nBL=? nBG=? Equations LINEAR NONLINEAR