Designation: E2071 − 00 (Reapproved 2015)Standard Practice forCalculating Heat of Vaporization or Sublimation from VaporPressure Data1This standard is issued under the fixed designation E2071; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes the calculation of the heat ofvaporization of a liquid or the heat of sublimation of a solidfrom measured vapor pressure data. It is applicable to pureliquids, azeotropes, pure solids, and homogenous solid solu-tions over the temperature range for which the vapor pressureequation fitted to the measured data is applicable.NOTE 1—This practice is generally not applicable to liquid mixtures.For a pure liquid or azeotrope, composition does not change uponvaporization so that the integral heat of vaporization is identical to thedifferential heat of vaporization. Non-azeotropic liquid mixtures changecomposition upon vaporizing. Heat of vaporization data computed fromthis practice for a liquid mixture are valid only as an approximation to themixture differential heat of vaporization; it is not a valid approximation tothe mixture integral heat of vaporization.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 There is no ISO standard equivalent to this practice.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D2879 Test Method for Vapor Pressure-Temperature Rela-tionship and Initial Decomposition Temperature of Liq-uids by IsoteniscopeE1142 Terminology Relating to Thermophysical PropertiesE1194 Test Method for Vapor Pressure (Withdrawn 2013)3E1719 Test Method for Vapor Pressure of Liquids by Ebul-liometryE1782 Test Method for Determining Vapor Pressure byThermal Analysis3. Terminology3.1 Symbols:3.1.1 A, B, C—Antoine vapor pressure equation constants(log10, kPa, K), Antoine vapor pressure equation:log10P 5 A 2 B/~T1C!3.1.2 P—vapor pressure, kPa.3.1.3 Pc—critical pressure, kPa.3.1.4 Pr—reduced pressure = P/Pc.3.1.5 T—absolute temperature, K.3.1.6 Tc—critical temperature, K.3.1.7 Tr—reduced temperature = T/Tc.3.1.8 V—molar volume, cm3/mol.3.1.9 R—gas constant, 8.31433 J/mol-K; 8314330 kPa-cm3/mol-K.3.1.10 ∆HV—heat of vaporization, J/mol.3.1.11 ∆ZV—difference in compressibility factor (Z = PV/RT) upon vaporization. Clapeyron equation:∆HV52R∆

[email protected]~lnP!/d~1/T!#3.1.11.1 Discussion—The subscript “V” will be usedthroughout this practice to designate the vaporization of aliquid. If the vapor pressure data were measured for a solid,substitute the subscript “S” for the sublimation of a solid.3.2 Definitions:3.2.1 Specialized terms used in this practice are defined inTerminology E1142.3.2.2 sublimation—transition from a solid phase to a gas-eous phase.3.2.3 vaporization—transition from a liquid phase to agaseous phase.1This practice is under the jurisdiction of Committee E37 on Thermal Measure-ments and is the direct responsibility of Subcommittee E37.10 on Fundamental,Statistical and Mechanical Properties.Current edition approved May 1, 2015. Published May 2015. Originallyapproved in 2000. Last previous edition approved in 2010 as E2071 – 00 (2010).DOI: 510.1520/E2071-00R15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14. Summary of Practice4.1 Vapor pressure data are measured by other referencedASTM standards and then correlated with the Antoine equa-tion. The heat of vaporization or sublimation is computed at thedesired temperature from the vapor-pressure temperature de-rivative from the fitted Antoine equation by use of theClapeyron equation (1).4In the Clapeyron equation, ∆ZVisdetermined by either the Clausius-Clapeyron(2) approxima-tion:~∆ZV5 1!or the Haggenmacher (3) approximation:S∆ZV5$1

[email protected]/~Tr!3#%12D4.2 An example calculation is given in Annex A1.5. Significance and Use5.1 If the heat of vaporization or sublimation is absorbed orliberated in a process at constant pressure, it is called enthalpyof vaporization or sublimation. Enthalpy of vaporization orsublimation is a fundamental thermodynamic property of aliquid or solid. It is an important quantity in the design of heatexchangers and other chemical process units. Enthalpy ofvaporization is also used to calculate solubility parameters (4).5.2 This practice may be used in research, regulatorycompliance, and quality assurance applications.6. Experimental Vapor Pressure Data6.1 Vapor pressure data are measured by Test MethodsD2879, E1194, E1719,orE1782. Note the safety precautionscontained in the test method used.6.1.1 Vapor pressure data from other reliable sources, forexample, peer-review technical journals, may be used. Thesource of the vapor pressure data must be noted.6.2 The measured vapor pressure data are fitted to anAntoine vapor pressure equation. See 10.3 in Test MethodE1719 for details on least-squares regression of vapor pressuredata.7. Calculation7.1 At each temperature of interest, calculate the vaporpressure from the Antoine equation and calculate the vapor-pressure temperature derivative from the fitted Antoine equa-tion constants from:@d~lnP!/d~1/T!#

[email protected]/~T1C!2#7.2 Calculate an approximation to ∆ZVat each temperature.7.2.1 The Clausius-Clapeyron approximation to ∆ ZVis:∆ZV[1.07.2.2 The Haggenmacher approximation to ∆ZVis:∆ZV5$1

[email protected]/~Tr!3#%12NOTE 2—The Clausius-Clapyeron approximation is generally used forsolids and for liquids at low Tr. The Haggenmacher approximation isgenerally used for liquids up to Tr≈ 0.75.7.2.3 If equation of state (Z) data are available for both thecondensed and gaseous phases, ∆ZVmay be calculated directlyfrom the equation of state data.7.3 Calculate the heat of vaporization or heat of sublimationat each temperature from the Clapeyron equation:∆HV52R∆

[email protected]~lnP!/d~1/T!#8. Report8.1 Report the following information:8.1.1 The test method and source of the vapor pressure dataused in the heat of vaporization or heat of sublimationcalculation. A vapor pressure data table shall also be reported.8.1.2 The Antoine equation constants fitted to the vaporpressure data.8.1.3 The approximation to ∆ZVused in the calculation.8.1.4 The values and source of the critical temperature andcritical pressure data if the Haggenmacher approximation wasused for ∆Z.8.1.5 A table that contains temperature, vapor pressure, thevapor pressure temperature derivative [d(lnP)/ d(1/T)], differ-ence in compressibility factor (∆ZV), and ∆HV, the heat ofvaporization or heat of sublimation.8.1.6 The specific dated version of this practice used.8.2 See the sample calculations and report in Annex A1.9. Keywords9.1 Antoine equation; Clausius-Clapeyron equation; en-thalpy of sublimation; enthalpy of vaporization; Haggen-macher equation; heat of sublimation; heat of vaporization;vapor pressure4The boldface numbers given in parentheses refer to a list of references at theend of the text.E2071 − 00 (2015)2ANNEX(Mandatory Information)A1. SAMPLE CALCULATIONS AND REPORTA1.1 Source of Sample Vapor Pressure DataA1.1.1 This sample calculation is performed on the samplevapor pressure data given for a toluene specimen in Annex A3of Test Method E1719. Heat of vaporization is calculated in10 K increments between 290 and 400 K. Calculations for boththe Clausius-Clapeyron and Haggenmacher approximations to∆ZVare listed.A1.2 Sample Experimental DataA1.2.1 These controlled pressure-boiling temperature datapairs were measured by Test Method E1719 ona75cm3specimen charged to a vapor-lift pump ebulliometer:P (kPa) T (K)10.0 318.420.0 335.430.0 345.850.0 360.770.0 371.285.0 377.9100.0 383.3A1.2.2 A non-linear least-squares fit of the Antoineequation, log10P = A - B/(T + C), produced these constants:A (fit) = 6.168057B (fit) = 1397.23C (fit) = –48.10A1.3 Sample CalculationA1.3.1 The critical temperature and pressure for toluene (5)are:Tc= 591.75 KPc= 4108.69 kPaAt 290 K:Tr= 0.490071821Pr= 0.000600191Vapor pressure 5 10 ˆ @6.168057 2 1397.23/~290 2 48.10!#5 2.465997

[email protected]~lnP!/d~1/T!# 522.3025851 @1397.23*2902/~290 2 48.10!2# 524623.8938 KA1.3.2 Haggenmacher approximation to ∆ZV:∆ZV5 $1 2 @0.000600191/~0.4900718121!3#%12 5 0.997447A1.3.3 ∆HVfrom Clausius-Clapeyron approximation:∆HV5 ~28.31433!*1.00*~24623.8938! 5 38444.6 J/molA1.3.4 ∆HVfrom Haggenmacher approximation:∆HV5 ~28.31433!*0.997447*~24623.8938! 5 38346.4 J/molA1.4 Sample Heat of Vaporization ReportA1.4.1 Clausius-Clapeyron Approximation Report:A1.4.1.1 Data are for a toluene specimen and are listed inAnnex A3 of Test Method E1719. These controlled pressure-boiling temperature data pairs were measured by Test MethodE1719 ona75cm3specimen charged to a vapor-lift pumpebulliometer:P (kPa) T (K)10.0 318.420.0 335.430.0 345.850.0 360.770.0 371.285.0 377.9100.0 383.3A1.4.1.2 A non-linear least-squares fit of the Antoine equa-tion:log10P 5 A 2 B/~T1C!produced these constants:A (fit) = 6.168057B (fit) = 1397.23C (fit) = –48.10A1.4.1.3 The Clausius Clapeyron approximation for ∆ ZVwas used.Temperature Pressure[d(lnP)/d(1/T)] ∆ZV∆HVK kPa K J/mol290 2.4659968 –4623.8938 1.00000000 38444.6300 4.1811179 –4563.2028 1.00000000 37940.0310 6.8089762 –4507.5026 1.00000000 37476.9320 10.697757 –4456.2047 1.00000000 37050.4330 16.277326 –4408.8094 1.00000000 36656.3340 24.064868 –4364.8893 1.00000000 36291.1350 34.668504 –4324.0774 1.00000000 35951.8360 48.788774 –4286.0560 1.00000000 35635.7370 67.217970 –4250.5496 1.00000000 35340.5380 90.837442 –4217.3173 1.00000000 35064.2390 120.61303 –4186.1482 1.00000000 34805.0400 157.58889 –4156.8566 1.00000000 34561.5A1.4.2 Haggenmacher Approximation Report:A1.4.2.1 Data are for a toluene specimen and are listed inAnnex A3 of Test Method E1719. These controlled pressure-boiling temperature data pairs were measured by Test MethodE1719 ona75cm3specimen charged to a vapor-lift pumpebulliometer:P (kPa) T (K)10.0 318.420.0 335.430.0 345.850.0 360.770.0 371.285.0 377.9100.0 383.3A1.4.2.2 A non-linear least-squares fit of the Antoine equa-tion:log10P 5 A 2 B/~T1C!produced these constants:A (fit) = 6.168057B (fit) = 1397.23C (fit) = –48.10E2071 − 00 (2015)3A1.4.2.3 The Haggenmacher approximation for ∆ ZVwasused. The critical temperature and pressure used for toluene (5)are:Tc= 591.75 KPc= 4108.69 kPaTemperature Pressure[d(lnP)/d(1/T)] ∆ZV∆HVK kPa K J/mol290 2.4659968 –4623.8938 0.99744709 38346.4300 4.1811179 –4563.2028 0.99608744 37791.5Temperature Pressure[d(lnP)/d(1/T)] ∆ZV∆HVK kPa K J/mol310 6.8089762 –4507.5026 0.99421990 37260.2320 10.697757 –4456.2047 0.99173347 36744.1330 16.277326 –4408.8094 0.98851253 36235.2340 24.064868 –4364.8893 0.98443961 35726.4350 34.668504 –4324.0774 0.97939800 35211.1360 48.788774 –4286.0560 0.97327384 34683.3370 67.217970 –4250.5496 0.96595780 34137.4380 90.837442 –4217.3173 0.95734617 33568.5390 120.61303 –4186.1482 0.94734133 32972.2400 157.58889 –4156.8566 0.93585171 32344.4REFERENCES(1) Van Ness, H. C., and Abbott, M. M., Classical Thermodynamics ofNonelectrolyte Solutions, McGraw-Hill, New York, NY, 1982, pp.96–100.(2) Van Ness, H. C., and Abbott, M. M., Classical Thermodynamics ofNonelectrolyte Solutions, McGraw-Hill, New York, NY, 1982, p. 100.(3) Haggenmacher, J. E., Journal of the American Chemical Society,Vol68, 1946.(4) Barton, A. F. M., CRC Handbook of Solubility Parameters and OtherCohesion Parameters, CRC Press, Boca Raton, FL, 1991.(5) Daubert, T. E., ed., The DIPPR Project 801 Data Compilation, DesignInstitute of Physical Property Data, AICHE, New York, NY, 1990,CAS#, 108–88–3.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or

[email protected] (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http://www.copyright.com/E2071 − 00 (2015)4