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CHEMISTRY E182019
CH7
Phase equilibria?G0Clausius Clapeyron
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
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T-S diagrams
CH7
T-s diagrams
p1000 bar technically realizable maximum
Saturated liquid curve
Gas steam
Saturated vapour curve
Liquid
LG
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T-S diagrams evaporation
CH7
T-s diagrams
Saturated liquid s2 kJ/kgK
Saturated steam s6 kJ/kgK
Enthalpy of evaporation ?hLGT(s-s)500?42MJ/k
g
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Solid-Liquid-Gas
CH7
Phase diagrams
The reason why the regions LG, SG appear in the
p-v diagram is that the specific volume v (unlike
T,p) varies during phase transformations.
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Solid-Liquid-Gas
CH7
Phase diagram ice-water-steam
liquid-like hydrogen-bonded clusters dispersed
within a gas-like phase
Cubic ice
Hexagonal ice
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Solid-Liquid-Gas
CH7
Melting ?hSLgt0, ?sSLgt0, ?GSL0, dpdT0
Evaporation ?hLGgt0, ?sLGgt0, ?GLG0, dpdT0
Sublimation ?hSGgt0, ?sSGgt0, ?GSG0, dpdT0
During phase transitions the pressure and
temperature are constant. Also Gibbs energy
remains constant as follows from its definition
?g?h-T?s0. Only specific volume increases or
decreases.
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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
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Clausius Clapeyron Solid-Liquid-Gas
CH7
dp/dtgt0 because ?hLGgt0 ?vLGgt0 (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
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Clausius Clapeyron derivation
CH7
Clausius Clapeyron equation can be derived from
energy balance of a closed cycle in Ts diagram
Heat added-difference between evaporation
enthalpy at TdT and condensation enthalpy at
temperature T
Mechanical work-received in one cycle
Closed loop (evaporation, expansion,
condensation, compression)
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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, Antoines equation)
State equation
Antoines equation
Result can be improved when using Van der Waals
Giving expression for ?hLG
or Redlich Kwong state equation
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Multicomponent equilibrium
CH7
pApA"xA
Answer Yes, Raoults law applicable to ideal
liquids
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Raoults law
CH7
Fact It does not matter, how much liquid is in
the vessel, pressure of vapours is the same, and
given by Antoines equation
Therefore also the molar volume nB/V is
independent of amount of liquid.
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Raoults law
CH7
after expansion of nA molecules to volume V
giving Raoults law
and also answer to the previous question
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Raoults law
CH7
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Distillation
CH7
Initial composition of Liquid Mixture
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Liquid noncondensable gas
CH7
Given temperature T and molar fraction of
dissolved CO2
H2OCO2 yCO2
What to do if T gt Tcrit 31 oC ?
Henrys law
H2OCO2 xCO2
Henrys constant can be found in tables
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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)
pconst
Repeated distillation
yA
0 xA 1
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Tutorial SYRINGE alcohol
CH7
Final state Volume is increased to V1.
Temperature is constant (room temperature). Calcul
ate 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).
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Tutorial Syringe alcohol
CH7
Unknown 9 variables xA? yA? p? VL? VG? nAL?
nAG? nBL? nBG?
Equations
LINEAR NONLINEAR