Chemical Thermodynamics 2013/2014 12 th Lecture: Mixtures of Volatile Liquids Valentim M B Nunes, UD de Engenharia.
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ChemicalChemical ThermodynamicsThermodynamics2013/20142013/2014
12th Lecture: Mixtures of Volatile LiquidsValentim M B Nunes, UD de Engenharia
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IntroductioIntroductionnThe concept of ideal solution cam now be extended to solutions of several volatile components. In an ideal solution of two volatile liquids we have:
** and BBBAAA pxppxp
The total vapor pressure of mixture is then:
ABAB
BBAABA
xpppp
pxpxppp
***
**
or
This clearly show that the total vapor pressure (at constant T) changes linearly with the composition of mixture.
Some mixtures with resemblance in molecular structure
4
The composition of vaporThe composition of vapor
The composition of liquid and vapor is not necessarily the same. It seems obvious that the vapor should be more richer in the more volatile component. Using Dalton`s law:
ppyp
py BB
AA and
It follows that: AB
ABAB
AAA yy
xppp
pxy
1 and
***
*
Inverting this expression we obtain: AABA
BAA yppp
pyx
***
*
Now, combining this two results:
AABA
BA
yppp
ppp
***
**
6
Total phase diagram Total phase diagram
Combining both diagrams into one plot allow us to see the composition of both liquid and gas phase:
Above the liquid line the liquid phase is more stable. Bellow the vapor line the gas phase is more stable. In the middle region of the diagram we have the liquid vapor equilibrium, with two phases coexisting. At a given pressure we have a liquid with composition a in equilibrium with vapor of composition b.
7
Interpretation of the diagram Interpretation of the diagram
If we know the composition of one phase at a given temperature we can determine the composition of another phase from the diagram.
The line a2a2’’a2’, for instance, is a “tie linetie line”. It describes a state at constant pressure, and since T is already fixed, the Gibbs phase rule allow us to conclude that the compositions of both phases are completely defined!
Remember: g+F = C+2
8
The lever ruleThe lever rule
To calculate the amounts of both phases in equlibria we use the lever rulelever rule: we measure the distances l and l’ along the horizontal tie line.
l
l
n
n
9
T-x DiagramsT-x Diagrams
Instead of T being fixed as in previous diagrams, we can keep constant pressure, and generate T-x diagrams. These diagrams have great importance in practical separation processes like distillationdistillation.
TB*
TA*
hea
t
vaporization
condensation
10
Real Real Solutions Solutions Some mixture behave almost ideally. But, in many other cases, real solutions display marked deviations. In some systems with strong non-ideality, the mixtures form an azeotropeazeotrope (coming from the Greek word for “boiling without changing”)
11
Azeotropic Azeotropic MixturesMixtures
Component A: tb/°C Component B: t/°C Azeotrope: %A and tb/°C
H2O 100 HCl -80 20.2 108.6
C6H5OH 182.2 C6H5NH2 184.3 42 186.2
CHCl3 61.2 CH3COCH3 56.1 78.5 64.4
H2O 100 C2H5OH 78.3 4.0 78.2
CCl4 76.8 CH3OH 64.7 79.4 55.7
CHCl3 61.2 CH3OH 64.7 87.4 53.4
Suppose we try to distillate an ethanol/water mixture in a fractionating column. The fractionation shifts the vapor towards the azeotropic composition and vapor emerges on the top of the column. Then it boils unchanged when water content is 4% and temperature around 78 °C (commercial ethanol)
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