1. Chapter 4 Vapor Pressure
pº = Pressure of a substance in equilibrium with its pure condensed (liquid or solid) phase
Why do we care?
-spills
-pesticide application
-will lead us to Henry’s law constant

2. Air Octanol Water KH = PoL/Csatw Kow = Csato/Csatw Koa = Csato/PoL
A gas is a gas is a gas
T, P
Koa KH
Octanol
PoL
Water
NOM, biological lipids, other solvents
T, chemical composition
Fresh, salt, ground, pore
T, salinity, cosolvents
Kow
Pure Phase
(l) or (s)
Csato
Csatw
Ideal behavior

3. Ranges of pº (atm)
PCBs – 10-5 to 10-9
n-alkanes – to 10-16
n-C10H22 ~
n-C20H42 ~ 10-9
Benzene ~
toluene ~
Ethylbenzene ~
propyl benzene ~
carbon tetrachloride ~
methane
Even though VP is “low”, gas phase may still be important.

4. Phase diagram
picture of three-phase diagram

5. Ideal Gas Law p = pressure V = volume n = moles of gas
R = gas constant
T = temperature (Kelvin)

6. Thermodynamic considerations (deriving the van’t Hoff equation)
consider a gas: if T or P is changed and equilibrium is re-established:
the change in chemical potential in the two systems is equal
where S = molar entropy
and V = molar volume

7. at equilibrium substituting:
for a liquid vaporizing, the volume change can be assumed to be equal to the volume of gas produced, since the volume of the solid or liquid is negligible
Q. where did the n go?
A. this is molar volume

8. where DH12 = DHvap (gas) or DHsub (solid)
recall (calculus!)
The van’t Hoff equation
where DH12 = DHvap (gas) or DHsub (solid)
= energy required to convert one mole of liquid (or solid) to gas without an increase in T.
DHvap is a function of T.
As T approaches the boiling point, DHvap increases rapidly
At T < boiling point, DHvap increases slowly
from 0-40ºC, DHvap can be assumed to be constant

9. integrate assuming
DHvap is constant:
Antoine equation
if DHvap is not constant:
another Antoine equation

10. Using DHvap to predict VP at other temperatures
As we saw in the thermodynamics lecture:
Specifically,

11. Note the change in slope when the substance is solid (sublimation)
DHsub = DHmelt (~25%) + DHvap (~75%)
still use liquid phase as reference:
Hypothetical subcooled liquid
= liquid cooled below melting point without crystallizing
compound
pºs <
pºL
1,4-dichlorobenzene
3.04
2.76
phenol
3.59
3.41
22’55’ PCB
7.60
6.64
22’455’ PCB
8.02
7.40
-log P
Becomes important later when we talk about solubility

12. Molecular interactions affecting vapor pressure
Molecule:molecule interactions in condensed phase (L or s) have greatest affect on VP
strong interactions lead to large DHvap, low VP
weak interactions lead to small DHvap, high VP
Intermolecular interactions can be classified into three types:
van der Waals forces (nonpolar)
Polar forces
Hydrogen bonding

13. van der Waals forces nonspecific
function of size (number of electrons)
consist of:
London dispersive energies
fleeting areas of charge
Induced dipoles
areas of charge arising from interactions with a polar molecule
“nonpolar”

14. Polar interactions: Hydrogen bonds dipole-dipole interactions Specific
permanent areas of charge on two molecules attract
Hydrogen bonds
Specific
donors and acceptors
table 4.3

15. Part of Table 4.3

16. Vapor Pressure Estimation Technique
based on regression of lots of VP data, best fit gives:
H-bonding ability
size
polarizability
pressure in Pa, where:
refractive index (response to light) is a function of polarizability.
see table 3.1, also might be available in the CRC

17. Refractive index
Difference between polarity and polarizability

18. Trouton’s rule
At their boiling points, most organic compounds have a similar entropy of vaporization:
DSvap (Tb) = 85 – 90 J/molK
We can be slightly more accurate with Kistiakowsky’s expression:
DSvap (Tb) = KF( ln(Tb)) J/molK Tb in K (eqn 4-20)
KF = 1 for most compounds
At the boiling point:
exception: strongly polar or H-bonding compounds
So if we know Tb, we can estimate DHvap (at the boiling point) fairly accurately

19. Table 4.2

20. Estimating VP at other T (need DHvap)
Recognize that DHvap is not constant.
Especially if Tb is high (> 100ºC), the estimate of DHvap from Trouton/Kistiakowsky may not be valid at the temperature of interest.
Empirically, DHvap is a function of the VP:

21. FIG 4.7
From a data set of many compounds, Goss and Schwarzenbach (1999) get:

22. Less empirically,
assume DHvap is linearly proportional to T (i.e. assume that the heat capacity, DCpvap is constant:
don’t let notation confuse you. (Tb) means at the boiling point. You do not multiply DHvap by the boiling point
substitute this expression into the Clausius-Clapeyron equation and integrate from Tb to T:

23. but we still need to know DCp(Tb)!
Recall:
substitute:
but we still need to know DCp(Tb)!
generally:
ranges from 1.0 to 0.6
and DSvap(Tb)~ 88 J/molK

24. finally!
KF is the Fishtine factor, usually 1, but sometimes as high as 1.3 (see p 113)
the old edition gave (where KF =1):
in atm
Eqn 4-33
in atm
OK for liquids with Tb < 100ºC
High MW compounds, need correction for intermolecular forces (but we don’t have their boiling points anyway!) (For refinements see equation 4-33)
Can estimate boiling points, see p. 120

25. solids?
those previous equations yielded the vapor pressure of the hypothetical subcooled liquid.
How can we correct this to give the true vapor pressure of a solid?
Prausnitz (1969):
Where DSfus(Tm) = entropy of fusion at melting point
unfortunately DSfus is much more variable than DSvap
J/molK
Where t = number of torsional bonds and s = rotational symmetry number (see p. 125)

27. the older edition of your book gave this simpler (but less accurate) equation:
DSfus(Tm) ~ (n-5) J/molK
Where n = number of flexing chain atoms.
if n<5, then ignore this term

28. Estimation of vapor pressures for polychlorinated biphenyls: a comparison of eleven predictive methods Lawrence P. Burkhard, Anders W. Andren, and David E. Armstrong Environmental Science and Technology 1985, 19,
conclusions:
non-correlative methods have poor predictive ability (error increases as VP decreases)
correlative methods requiring a set of compounds with known P are much better
best method: determine VP as function of GC retention times

29. Determination of vapor pressures for nonpolar and semipolar organic compounds from GC retention data (Hinckley et al, 1990)
Chromatographed 2 reference compounds (eicosane and p,p’DDT) having known VP and DHvap versus a host of unknowns (PAHs, organochlorines, etc)
Isothermal runs allow determination of RRT at several T
Comparison of RRT with reference compounds allows determination of VP at given T
Comparison of changes in RRT with T and knowledge of DHvap for reference compound allows calculation of DHvap for all unknowns

30. Problem 4.2
In a dump site, you find an old 3-liter pressure bottle containing FREON 12 with a pressure gauge that reads 2.7 bar. (First, you realize that this gauge was not manufactured in the US.) The temperature is 10ºC. What mass of FREON 12 is in the bottle?
Also estimate the free energy, enthalpy, and entropy of condensation of FREON 12.
You find the following info for FREON 12 in the CRC:

31. Problem 4.6
estimate VP at 0C based on VP at 25ºC or based solely on Tb and Tm
(hint s = 4)

32. Homework
Do problems 4.3 and 4.4
Due 2/2/10