Vapor Pressure

CEE-PUBH 5730-6730 Lecture 4

Vapor pressure (Pv)

•  Pressure exerted when a chemical is in equilibrium with its own vapor at a specified temperature.

•  Can be regarded as the maximum amount or solubility of the substance in the air phase.

•  Difference in Pv for different compounds is due to differences in molecular-molecular interactions.

Why is Pv important/how is it used?

•  Used with aqueous solubility to calculate Henry's Law Constants

•  Used to estimate how rapidly a chemical may evaporate in a spill situation.

•  Used to determine the speciation of the compound (gaseous vs. particulate) in the atmosphere

Units of Vapor pressure

1Torr = 1 mm Hg = 1.333 × 102 Pa 1 atmosphere = 1.013 × 105 Pa 1 bar = 105 Pa

Thermodynamic considerations

•  Simplified phase diagram •  Solid-vapor equilibrium •  Liquid-vapor equilibrium

Simplified phase diagram of organic liquids and solid

Liquid-vapor equilibrium (Clausius–Clapeyron)

•  ln P˚ = - ∆Hvap/RT + A = -B/T + A –  At temperatures well below the boiling point, Hvap is relatively

independent of temperature and ∆Hvap is assumed to be constant.

–  ∆Hvap: energy require to convert one mole of liquid to vapor without increasing the temperature.

–  This expression can be used to calculate vapor pressures (P˚) at any other temperature provided that no other phase change occurs within the temperature range considered.

Antoine equation

•  ln P˚ = -B/T+C + A •  where C is used to correct for the temperature

dependence of ∆Hvap. •  Values for A, B, and C are tabulated for a variety

of compounds. •  Used to describe the temperature dependence

of Pv

Supplemental Table: Properties of Pure Species

Vapor pressure (P sat) by the Antoine Equation: ln P sat/kPa = A ! Bt/"C+ C

Latent heat of vaporization at the normal boiling point (!Hn), and normal boiling point (tn)

Parameters for Antoine Eqn. Temp. Range !Hn tnName Formula A† B C "C kJ/mol "CAcetone C3H6O 14.3145 2756.22 228.060 !26 — 77 29.10 56.2Acetic acid C2H4O2 15.0717 3580.80 224.650 24 — 142 23.70 117.9Acetonitrile* C2H3N 14.8950 3413.10 250.523 !27 — 81 30.19 81.6Benzene C6H6 13.7819 2726.81 217.572 6 — 104 30.72 80.0iso-Butane C4H10 13.8254 2181.79 248.870 !83 — 7 21.30 !11.9n-Butane C4H10 13.6608 2154.70 238.789 !73 — 19 22.44 !0.51-Butanol C4H10O 15.3144 3212.43 182.739 37 — 138 43.29 117.62-Butanol* C4H10O 15.1989 3026.03 186.500 25 — 120 40.75 99.5iso-Butanol C4H10O 14.6047 2740.95 166.670 30 — 128 41.82 107.8tert-Butanol C4H10O 14.8445 2658.29 177.650 10 — 101 39.07 82.3Carbon tetrachloride CCl4 14.0572 2914.23 232.148 !14 — 101 29.82 76.6Chlorobenzene C6H5Cl 13.8635 3174.78 211.700 29 — 159 35.19 131.71-Chlorobutane C4H9Cl 13.7965 2723.73 218.265 !17 — 79 30.39 78.5Chloroform CHCl3 13.7324 2548.74 218.552 !23 — 84 29.24 61.1Cyclohexane C6H12 13.6568 2723.44 220.618 9 — 105 29.97 80.7Cyclopentane C5H10 13.9727 2653.90 234.510 !35 — 71 27.30 49.2n-Decane C10H22 13.9748 3442.76 193.858 65 — 203 38.75 174.1Dichloromethane CH2Cl2 13.9891 2463.93 223.240 !38 — 60 28.06 39.7Diethyl ether C4H10O 14.0735 2511.29 231.200 !43 — 55 26.52 34.41,4-Dioxane C4H8O2 15.0967 3579.78 240.337 20 — 105 34.16 101.3n-Eicosane C20H42 14.4575 4680.46 132.100 208 — 379 57.49 343.6Ethanol C2H6O 16.8958 3795.17 230.918 3 — 96 38.56 78.2Ethylbenzene C8H10 13.9726 3259.93 212.300 33 — 163 35.57 136.2Ethylene glycol* C2H6O2 15.7567 4187.46 178.650 100 — 222 50.73 197.3n-Heptane C7H16 13.8622 2910.26 216.432 4 — 123 31.77 98.4n-Hexane C6H14 13.8193 2696.04 224.317 !19 — 92 28.85 68.7Methanol CH4O 16.5785 3638.27 239.500 !11 — 83 35.21 64.7Methyl acetate C3H6O2 14.2456 2662.78 219.690 !23 — 78 30.32 56.9Methyl ethyl ketone C4H8O 14.1334 2838.24 218.690 !8 — 103 31.30 79.6Nitromethane* CH3NO2 14.7513 3331.70 227.600 56 — 146 33.99 101.2n-Nonane C9H20 13.9854 3311.19 202.694 46 — 178 36.91 150.8iso-Octane C8H18 13.6703 2896.31 220.767 2 — 125 30.79 99.2n-Octane C8H18 13.9346 3123.13 209.635 26 — 152 34.41 125.6n-Pentane C5H12 13.7667 2451.88 232.014 !45 — 58 25.79 36.0Phenol C6H6O 14.4387 3507.80 175.400 80 — 208 46.18 181.81-Propanol C3H8O 16.1154 3483.67 205.807 20 — 116 41.44 97.22-Propanol C3H8O 16.6796 3640.20 219.610 8 — 100 39.85 82.2Toluene C7H8 13.9320 3056.96 217.625 13 — 136 33.18 110.6Water H2O 16.3872 3885.70 230.170 0 — 200 40.66 100.0o-Xylene C8H10 14.0415 3358.79 212.041 40 — 172 36.24 144.4m-Xylene C8H10 14.1387 3381.81 216.120 35 — 166 35.66 139.1p-Xylene C8H10 14.0579 3331.45 214.627 35 — 166 35.67 138.3

Based primarily on data presented by B. E. Poling, J. M. Prausnitz, and J. P. O’Connell,The Properties of Gases and Liquids, 5th ed., App. A, McGraw-Hill, New York, 2001.

*Antoine parameters adapted from Gmehling et al. See footnote 2, p. 764.†Antoine parameters A are adjusted to reproduce the listed values of tn .

Temperature dependence of Pv

Solid-vapor equilibrium

•  Below the melting point a solid can vaporize without melting (sublimes)

•  ∆ Hsub = ∆ Hmelt + ∆Hvap (L) of the hypothetical subcooled liquid (imaginary liquid cooled below its melting pt without becoming solid)

•  For solids, the reference state fugacity is the vapor pressure of the subcooled liquid.

•  The Pv for a subcooled liquid is obtained by extrapolation of Pv data above the melting point.

Molecular interactions governing vapor pressure

•  The stronger the intermolecular attractions, the lower the vapor pressure.

•  Electron deficient molecular regions of one molecule drawn toward electron-rich regions of neighboring molecules.

•  Summation of intermolecular forces determines vapor pressure.

Intermolecular forces •  Van der Waals or dispersive attractions

– nonpolar molecules-greater the size, greater the attraction

•  Polar interactions – dipole:dipole – dipole: induced dipole attraction – hydrogen bonding (i.e. alcohols and amines)

•  Electronegativities H,C, S, I < N, Br < Cl < O < F

MW Solubility Vapor Press. Vapor Press. H Chemical g/mol mp, ˚C bp, ˚C (mg/L) Pa (atm) Log Kow (dimensionless)

Trichlorofluoromethane 137.4 -111 23.8 1100 9.04E-01 2.53 4.62E+00 n-Hexane 86.2 -95 68 9.5 1.99E-01 4.11 7.40E+01 1,1,1-Trichloroethane 133.4 -32 113 730 1.26E-01 2.47 9.44E-01 Benzene 78.1 5.53 80 1780 1.25E-01 2.13 2.25E-01 Cyclohexane 84.2 6.55 80.7 55 1.25E-01 3.44 7.85E+00 Trichloroethylene 131.4 -73 87 1100 9.74E-02 2.29 4.76E-01 Toluene 92.1 -95 111 515 3.75E-02 2.69 2.74E-01 Chlorobenzene 112.6 -46.5 132 472 1.56E-02 2.84 1.52E-01 p-Xylene 106.2 13.2 138 185 1.15E-02 3.15 2.71E-01 Quinoline 129.2 -15.6 237.7 60000 1.31E-03 2.03 1.16E-04 Phenol 94.1 40.9 181.75 82000 6.97E-04 1.46 3.27E-05 1,2,4-Trichlorobenzene 181.5 17 213.5 34.6 5.98E-04 4.00 1.28E-01 p-Cresol 108.1 34.8 201.9 16800 1.45E-04 1.95 3.81E-05 Naphthalene 128.2 80.2 218 31.7 1.03E-04 3.35 1.70E-02 2-Chlorobiphenyl 188.7 34 374 1.3 2.01E-05 4.54 1.20E-01 2,2'4,4'-Tetrachlorobiphenyl 291.9 83 0.068 1.97E-07 5.90 3.47E-02 Phenanthrene 178.2 101 339 1.29 1.59E-07 4.57 8.98E-04 Pentachlorophenol 266.4 190 310 14 1.45E-07 5.01 1.13E-04 Hexachlorobenzene 284.8 230 322 0.005 2.27E-08 5.50 5.29E-02 2,2',4,4',6,6'-Hexachlorobiphenyl 360.9 114 0.0007 1.58E-08 7.00 3.33E-01 Anthracene 178.2 216.2 340 0.041 7.90E-09 4.63 1.40E-03 Pyrene 202.3 156 360 0.135 5.92E-09 5.22 3.63E-04 2,4-D 221.0 138 215 890 5.53E-10 2.81 5.61E-09 DDT 354.5 108.5 0.0031 1.97E-10 6.19 9.23E-04 Benzo(a)pyrene 252.3 175 0.0038 6.91E-12 6.04 1.88E-05 2,3,7,8-TCDD 322.0 305 0.0193 9.87E-13 6.80 6.73E-07 Physical-Chemical Properties of Selected Organic Chemicals at 25˚C (Mackay, 1991)

Selected experimental Pv values

Method for Pv measurement

OECD GUIDELINES FOR THE TESTING OF CHEMICALS GUIDELINE 104 VAPOR PRESSURE

Exp. determination of Pv

•  Gas saturation or generator column method – Generate a saturated gas stream by flowing gas

through column containing the volatile solid or liquid solute coated on a inert packing. Column exit gas is analyzed for solute concentration.

•  Burkhard, L. P., D. E. Armstrong, et al. (1984). “Vapor Pressures for Biphenyl, 4-Chlorobiphenyl, 2,2',3,3',5,5',6,6'-Octachlorobiphenyl, and Decachlorobiphenyl.” J. Chem. Eng. Data 29: 248-250.

Databases of Pv values

•  Environmental Fate/Exposure Database – http://www.srcinc.com/what-we-do/efdb.aspx

•  CRC Handbook of Chemistry and Physics (Lide, 1995)

•  The Handbook of Physical Properties of Organic Chemicals (Howard & Meylan, 1997)

•  The Handbook of Vapor Pressure (Yaws, 1994) •  The Illustrated Handbook of Physical-Chemical

Properties and Environmental Fate for Organic Chemicals (Mackay et al., 1999)

Estimation of Pv

•  Review article: –  Dearden, J C. 2003. QUANTITATIVE STRUCTURE–

PROPERTY RELATIONSHIPS FOR PREDICTION OF BOILING POINT, VAPOR PRESSURE, AND MELTING POINT. Environmental Toxicology and Chemistry 22: 1696-1709

Estimation of Pv •  From TB and TM - Derivatives of the Clausius-Clapeyron equation

(Antoine equation, modified Watson Correlation) –  Assumptions: linear temperature dependence of ∆Hvap, ∆Svap is

the same for many organic compounds –  ln P = -(4.4 + ln TB) x {1.803(TB/T - 1) - 0.803 ln (TB/T)} - 6.8

(TM/T - 1) •  where P is vapor pressure in atm, TB is the boiling point (K), TM is the

melting point (K) and T is the temperature of interest (K). The last term is used to account for melting of subcooled liquid. This term, that includes the melting point, is ignored for liquids.

•  Mackay, D., A. Bobra, et al. (1982). “Vapor Pressure Correlations for Low Volatility Environmental Chemicals.” Environ. Sci. Technol. 16: 645-649.

Correlation with GC retention times

•  Westcott, J. W. and T. F. Bidleman (1981). “Determination of polychlorinated biphenyl vapor pressures by capillary gas chromatography.” J. Chromatogr. 210: 331-336.

Group Contribution method

•  Burkhard, L. P. (1985). “Estimation of Vapor Pressures for Halogenated Aromatic Hydrocarbons by a Group-Contribution Method.” Ind. Eng. Chem. Fundam. 24: 119-120.

UNIversal Functional Activity Coefficient (UNIFAC) derived variables

•  UNIFAC is a group contribution method for estimating activity coefficients

•  log Pv= 6.94 - (2.25 Vu + 4.23 log γC) -0.577 log γR) - 0.01(mp-25)

•  Banerjee, S., P. H. Howard, S.S. Lande. 1990. General structure-vapor pressure relationships for organics. Chemosphere 21(10-11): 1173-1180.

Computerized methods

•  MPBPVP from Syracuse Research Corp. – http://www.epa.gov/opptintr/exposure/pubs/

episuite.htm •  SPARC from the University of Georgia

– http://ibmlc2.chem.uga.edu/sparc/index.cfm •  ACD from Advanced Chemistry Development

Effect of environmental variables -temperature

•  Pv of any chemical increases with an increase in temperature. •  Pv for a compound may change by more than 10X over an

environmentally relevant temperature range. •  For biphenyl:

–  at T = 5.2 ˚C, Pv = 0.106 Pa –  at T = 24.7 ˚C, Pv = 1.15 Pa

•  The effect of temperature is often modeled by Antoine equation: ln Pv = A- B/T + C where A and C are empirical constants and B = ∆Hvap/R