Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

1. This course is approximately at this level CHEMISTRYE182019 CH7 Phase equilibriaG=0Clausius Clapeyron Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

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

3. 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

4. L-liquid p G-gas S-solid p L+G L-liquid S-solid S+G G-gas v T Solid-Liquid-Gas CH7 Phase diagrams 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.

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

6. p L-liquid S-solid G-gas T Solid-Liquid-Gas CH7 MeltinghSL>0, sSL>0, GSL=0, dp=dT=0 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.

7. p L-liquid S-solid G-gas T Clausius Clapeyron Solid-Liquid-Gas CH7 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

8. p L-liquid S-solid G-gas T Clausius Clapeyron Solid-Liquid-Gas CH7 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

9. T+dT T s=s’’-s’ Clausius Clapeyronderivation CH7 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)

10. 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

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

12. HEAVY B Raoult’s law CH7 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.

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

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

15. Cooling condensing Liquid mixture enriched by heavy component Liquid mixture enriched by light component Distillation CH7 Initial composition of Liquid Mixture

16. 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

17. LIGHT A HEAVY B Tutorial 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

18. VG V1 V0 VL Tutorial SYRINGE alcohol CH7 Final state: Volume is increased to V1. Temperature is constant (room temperature). Calculate pressure p, molar fraction of methylalcohol in liquid and vapour phase. 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).

19. TutorialSyringe alcohol CH7 Unknown 9 variables xA=? yA=? p=? VL=? VG=? nAL=? nAG=? nBL=? nBG=? Equations LINEAR NONLINEAR