Phase Change Properties (chemicals.phase_change)

This module contains lookup functions for melting and boiling point, heat of fusion, various enthalpy of vaporization estimation routines, and dataframes of fit coefficients.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker.

Boiling Point

chemicals.phase_change.Tb(CASRN, method=None)[source]

This function handles the retrieval of a chemical’s normal boiling point. Lookup is based on CASRNs. Will automatically select a data source to use if no method is provided; returns None if the data is not available. Function has data for approximately 34000 chemicals.

Parameters
CASRNstr

CASRN [-]

Returns
Tbfloat

Boiling temperature, [K]

Other Parameters
methodstr, optional

A string for the method name to use, as defined in the variable, Tb_all_methods.

See also

Tb_methods

Notes

The available sources are as follows:

  • ‘CRC_ORG’, a compillation of data on organics as published in [1].

  • ‘CRC_INORG’, a compillation of data on inorganic as published in [1].

  • ‘WEBBOOK’, a NIST resource [6] containing mostly experimental and averaged values

  • ‘WIKIDATA’, data from the Wikidata project [3]

  • ‘COMMON_CHEMISTRY’, a project from the CAS [4]

  • ‘JOBACK’, an estimation method for organic substances in [5]

  • ‘YAWS’, a large compillation of data from a variety of sources both experimental and predicted; no data points are sourced in the work of [2].

  • ‘HEOS’, a series of values from the NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids (and other high-precision fundamental equations of state)

References

1(1,2)

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.

2

Yaws, Carl L. Thermophysical Properties of Chemicals and Hydrocarbons, Second Edition. Amsterdam Boston: Gulf Professional Publishing, 2014.

3

Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/

4

“CAS Common Chemistry”. https://commonchemistry.cas.org/.

5

Joback, K.G., and R.C. Reid. “Estimation of Pure-Component Properties from Group-Contributions.” Chemical Engineering Communications 57, no. 1-6 (July 1, 1987): 233-43. doi:10.1080/00986448708960487.

6

Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds., NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q

7

Huber, Marcia L., Eric W. Lemmon, Ian H. Bell, and Mark O. McLinden. “The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids.” Industrial & Engineering Chemistry Research 61, no. 42 (October 26, 2022): 15449-72. https://doi.org/10.1021/acs.iecr.2c01427.

Examples

>>> Tb('7732-18-5')
373.124
chemicals.phase_change.Tb_methods(CASRN)[source]

Return all methods available to obtain the normal boiling point for the desired chemical.

Parameters
CASRNstr

CASRN, [-]

Returns
methodslist[str]

Methods which can be used to obtain the Tb with the given inputs.

See also

Tb
chemicals.phase_change.Tb_all_methods = ('HEOS', 'CRC_INORG', 'CRC_ORG', 'COMMON_CHEMISTRY', 'WEBBOOK', 'YAWS', 'WIKIDATA', 'JOBACK')

Tuple of method name keys. See the Tbg for the actual references

Melting Point

chemicals.phase_change.Tm(CASRN, method=None)[source]

This function handles the retrieval of a chemical’s melting point. Lookup is based on CASRNs. Will automatically select a data source to use if no method is provided; returns None if the data is not available. Function has data for approximately 83000 chemicals.

Parameters
CASRNstr

CASRN [-]

Returns
Tmfloat

Melting temperature, [K]

Other Parameters
methodstr, optional

A string for the method name to use, as defined by the vairable Tm_all_methods.

See also

Tm_methods

Notes

The available sources are as follows:

  • ‘OPEN_NTBKM, a compillation of data on organics as published in [1] as Open Notebook Melting Points; Averaged (median) values were used when multiple points were available. For more information on this invaluable and excellent collection, see http://onswebservices.wikispaces.com/meltingpoint.

  • ‘CRC_ORG’, a compillation of data on organics as published in [2].

  • ‘CRC_INORG’, a compillation of data on inorganic as published in [2].

  • ‘WEBBOOK’, a NIST resource [6] containing mostly experimental and averaged values

  • ‘WIKIDATA’, data from the Wikidata project [3]

  • ‘COMMON_CHEMISTRY’, a project from the CAS [4]

  • ‘JOBACK’, an estimation method for organic substances in [5]

References

1

Bradley, Jean-Claude, Antony Williams, and Andrew Lang. “Jean-Claude Bradley Open Melting Point Dataset”, May 20, 2014. https://figshare.com/articles/Jean_Claude_Bradley_Open_Melting_Point_Datset/1031637.

2(1,2)

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.

3

Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/

4

“CAS Common Chemistry”. https://commonchemistry.cas.org/.

5

Joback, K.G., and R.C. Reid. “Estimation of Pure-Component Properties from Group-Contributions.” Chemical Engineering Communications 57, no. 1-6 (July 1, 1987): 233-43. doi:10.1080/00986448708960487.

6

Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds., NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q

Examples

>>> Tm(CASRN='7732-18-5')
273.15
chemicals.phase_change.Tm_methods(CASRN)[source]

Return all methods available to obtain the melting point for the desired chemical.

Parameters
CASRNstr

CASRN, [-]

Returns
methodslist[str]

Methods which can be used to obtain the Tm with the given inputs.

See also

Tm
chemicals.phase_change.Tm_all_methods = ('OPEN_NTBKM', 'CRC_INORG', 'CRC_ORG', 'COMMON_CHEMISTRY', 'WEBBOOK', 'WIKIDATA', 'JOBACK')

Tuple of method name keys. See the Tm for the actual references

Heat of Fusion

Heat of fusion does not strongly depend on temperature or pressure. This is the standard value, at 1 atm and the normal melting point.

chemicals.phase_change.Hfus(CASRN, method=None)[source]

This function handles the retrieval of a chemical’s heat of fusion. Lookup is based on CASRNs. Will automatically select a data source to use if no method is provided; returns None if the data is not available.

Function has data for approximately 22000 chemicals.

Parameters
CASRNstr

CASRN [-]

Returns
Hfusfloat

Molar enthalpy of fusion at normal melting point, [J/mol]

Other Parameters
methodstr, optional

A string for the method name to use, as defined by the variable, Hfus_all_methods.

See also

Hfus_methods

Notes

The available sources are as follows:

  • ‘CRC’, a compillation of data on organics and inorganics as published in [1].

  • ‘WEBBOOK’, a NIST resource [4] containing mostly experimental and averaged values

  • ‘WIKIDATA’, data from the Wikidata project [2]

  • ‘JOBACK’, an estimation method for organic substances in [3]

References

1

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.

2

Wikidata. Wikidata. Accessed via API. https://www.wikidata.org/

3

Joback, K.G., and R.C. Reid. “Estimation of Pure-Component Properties from Group-Contributions.” Chemical Engineering Communications 57, no. 1-6 (July 1, 1987): 233-43. doi:10.1080/00986448708960487.

4

Shen, V.K., Siderius, D.W., Krekelberg, W.P., and Hatch, H.W., Eds., NIST WebBook, NIST, http://doi.org/10.18434/T4M88Q

Examples

>>> Hfus('7732-18-5')
6010.0
chemicals.phase_change.Hfus_methods(CASRN)[source]

Return all methods available to obtain the heat of fusion for the desired chemical.

Parameters
CASRNstr

CASRN, [-]

Returns
methodslist[str]

Methods which can be used to obtain the Hfus with the given inputs.

See also

Hfus
chemicals.phase_change.Hfus_all_methods = ('CRC', 'WEBBOOK', 'WIKIDATA', 'JOBACK')

Tuple of method name keys. See the Hfus for the actual references

Heat of Vaporization at Tb Correlations

chemicals.phase_change.Riedel(Tb, Tc, Pc)[source]

Calculates enthalpy of vaporization at the boiling point, using the Ridel [1] CSP method. Required information are critical temperature and pressure, and boiling point. Equation taken from [2] and [3].

The enthalpy of vaporization is given by:

ΔvapH=1.093TbRln⁡Pc−1.0130.930−Tbr\Delta_{vap} H=1.093 T_b R\frac{\ln P_c-1.013}{0.930-T_{br}}
Parameters
Tbfloat

Boiling temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

Returns
Hvapfloat

Enthalpy of vaporization at the normal boiling point, [J/mol]

Notes

This equation has no example calculation in any source. The source has not been verified. It is equation 4-144 in Perry’s. Perry’s also claims that errors seldom surpass 5%.

[2] is the source of example work here, showing a calculation at 0.0% error.

Internal units of pressure are bar.

References

1

Riedel, L. “Eine Neue Universelle Dampfdruckformel Untersuchungen Uber Eine Erweiterung Des Theorems Der Ubereinstimmenden Zustande. Teil I.” Chemie Ingenieur Technik 26, no. 2 (February 1, 1954): 83-89. doi:10.1002/cite.330260206.

2(1,2,3)

Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.

3

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

Pyridine, 0.0% err vs. exp: 35090 J/mol; from Poling [2].

>>> Riedel(388.4, 620.0, 56.3E5)
35089.80179000598
chemicals.phase_change.Chen(Tb, Tc, Pc)[source]

Calculates enthalpy of vaporization using the Chen [1] correlation and a chemical’s critical temperature, pressure and boiling point.

The enthalpy of vaporization is given by:

ΔHvb=RTb3.978Tr−3.958+1.555ln⁡Pc1.07−Tr\Delta H_{vb} = RT_b \frac{3.978 T_r - 3.958 + 1.555 \ln P_c}{1.07 - T_r}
Parameters
Tbfloat

Boiling temperature of the fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

The formulation presented in the original article is similar, but uses units of atm and calorie instead. The form in [2] has adjusted for this. A method for estimating enthalpy of vaporization at other conditions has also been developed, but the article is unclear on its implementation. Based on the Pitzer correlation.

Internal units: bar and K

References

1

Chen, N. H. “Generalized Correlation for Latent Heat of Vaporization.” Journal of Chemical & Engineering Data 10, no. 2 (April 1, 1965): 207-10. doi:10.1021/je60025a047

2

Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.

Examples

Same problem as in Perry’s examples.

>>> Chen(294.0, 466.0, 5.55E6)
26705.902558030946
chemicals.phase_change.Liu(Tb, Tc, Pc)[source]

Calculates enthalpy of vaporization at the normal boiling point using the Liu [1] correlation, and a chemical’s critical temperature, pressure and boiling point.

The enthalpy of vaporization is given by:

ΔHvap=RTb[Tb220]0.0627(1−Tbr)0.38ln⁡(Pc/PA)1−Tbr+0.38Tbrln⁡Tbr\Delta H_{vap} = RT_b \left[ \frac{T_b}{220}\right]^{0.0627} \frac{ (1-T_{br})^{0.38} \ln(P_c/P_A)}{1-T_{br} + 0.38 T_{br} \ln T_{br}}
Parameters
Tbfloat

Boiling temperature of the fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

This formulation can be adjusted for lower boiling points, due to the use of a rationalized pressure relationship. The formulation is taken from the original article.

A correction for alcohols and organic acids based on carbon number, which only modifies the boiling point, is available but not implemented.

No sample calculations are available in the article.

Internal units: Pa and K

References

1

LIU, ZHI-YONG. “Estimation of Heat of Vaporization of Pure Liquid at Its Normal Boiling Temperature.” Chemical Engineering Communications 184, no. 1 (February 1, 2001): 221-28. doi:10.1080/00986440108912849.

Examples

Same problem as in Perry’s examples

>>> Liu(294.0, 466.0, 5.55E6)
26378.575260517395
chemicals.phase_change.Vetere(Tb, Tc, Pc, F=1.0)[source]

Calculates enthalpy of vaporization at the boiling point, using the Vetere [1] CSP method. Required information are critical temperature and pressure, and boiling point. Equation taken from [2].

The enthalpy of vaporization is given by:

ΔHvapRTb=τb0.38[ln⁡Pc−0.513+0.5066PcTbr2]τb+F(1−τb0.38)ln⁡Tbr\frac {\Delta H_{vap}}{RT_b} = \frac{\tau_b^{0.38} \left[ \ln P_c - 0.513 + \frac{0.5066}{P_cT_{br}^2}\right]} {\tau_b + F(1-\tau_b^{0.38})\ln T_{br}}
Parameters
Tbfloat

Boiling temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

Ffloat, optional

Constant for a fluid, [-]

Returns
Hvapfloat

Enthalpy of vaporization at the boiling point, [J/mol]

Notes

The equation cannot be found in the original source. It is believed that a second article is its source, or that DIPPR staff have altered the formulation.

Internal units of pressure are bar.

References

1

Vetere, Alessandro. “Methods to Predict the Vaporization Enthalpies at the Normal Boiling Temperature of Pure Compounds Revisited.” Fluid Phase Equilibria 106, no. 1-2 (May 1, 1995): 1-10. doi:10.1016/0378-3812(94)02627-D.

2(1,2)

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

Example as in [2], p2-487; exp: 25.73

>>> Vetere(294.0, 466.0, 5.55E6)
26363.43895706672

Heat of Vaporization at T Correlations

chemicals.phase_change.Pitzer(T, Tc, omega)[source]

Calculates enthalpy of vaporization at arbitrary temperatures using a fit by [2] to the work of Pitzer [1]; requires a chemical’s critical temperature and acentric factor.

The enthalpy of vaporization is given by:

ΔvapHRTc=7.08(1−Tr)0.354+10.95ω(1−Tr)0.456\frac{\Delta_{vap} H}{RT_c}=7.08(1-T_r)^{0.354}+10.95\omega(1-T_r)^{0.456}
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

omegafloat

Acentric factor [-]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

This equation is listed in [3], page 2-487 as method #2 for estimating Hvap. This cites [2].

The recommended range is 0.6 to 1 Tr. Users should expect up to 5% error. This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.

The original article has been reviewed and found to have a set of tabulated values which could be used instead of the fit function to provide additional accuracy.

References

1

Pitzer, Kenneth S. “The Volumetric and Thermodynamic Properties of Fluids. I. Theoretical Basis and Virial Coefficients.” Journal of the American Chemical Society 77, no. 13 (July 1, 1955): 3427-33. doi:10.1021/ja01618a001

2(1,2)

Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.

3(1,2)

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, Eighth Edition. McGraw-Hill Professional, 2007.

Examples

Example as in [3], p2-487; exp: 37.51 kJ/mol

>>> Pitzer(452, 645.6, 0.35017)
36696.749078320056
chemicals.phase_change.SMK(T, Tc, omega)[source]

Calculates enthalpy of vaporization at arbitrary temperatures using a the work of [1]; requires a chemical’s critical temperature and acentric factor.

The enthalpy of vaporization is given by:

ΔHvapRTc=(ΔHvapRTc)(R1)+(ω−ω(R1)ω(R2)−ω(R1))[(ΔHvapRTc)(R2)−(ΔHvapRTc)(R1)]\frac{\Delta H_{vap}} {RT_c} = \left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} + \left( \frac{\omega - \omega^{(R1)}} {\omega^{(R2)} - \omega^{(R1)}} \right) \left[\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R2)} - \left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} \right]
(ΔHvapRTc)(R1)=6.537τ1/3−2.467τ5/6−77.251τ1.208+59.634τ+36.009τ2−14.606τ3\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} = 6.537 \tau^{1/3} - 2.467 \tau^{5/6} - 77.251 \tau^{1.208} + 59.634 \tau + 36.009 \tau^2 - 14.606 \tau^3
(ΔHvapRTc)(R2)−(ΔHvapRTc)(R1)=−0.133τ1/3−28.215τ5/6−82.958τ1.208+99.00τ+19.105τ2−2.796τ3\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R2)} - \left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)}=-0.133 \tau^{1/3} - 28.215 \tau^{5/6} - 82.958 \tau^{1.208} + 99.00 \tau + 19.105 \tau^2 -2.796 \tau^3
τ=1−T/Tc\tau = 1-T/T_c
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

omegafloat

Acentric factor [-]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

The original article has been reviewed and found to have coefficients with slightly more precision. Additionally, the form of the equation is slightly different, but numerically equivalent.

The refence fluids are:

ω0\omega_0 = benzene = 0.212

ω1\omega_1 = carbazole = 0.461

A sample problem in the article has been verified. The numerical result presented by the author requires high numerical accuracy to obtain.

This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.

References

1(1,2)

Sivaraman, Alwarappa, Joe W. Magee, and Riki Kobayashi. “Generalized Correlation of Latent Heats of Vaporization of Coal-Liquid Model Compounds between Their Freezing Points and Critical Points.” Industrial & Engineering Chemistry Fundamentals 23, no. 1 (February 1, 1984): 97-100. doi:10.1021/i100013a017.

Examples

Problem in [1]:

>>> SMK(553.15, 751.35, 0.302)
39866.18999046229
chemicals.phase_change.MK(T, Tc, omega)[source]

Calculates enthalpy of vaporization at arbitrary temperatures using a the work of [1]; requires a chemical’s critical temperature and acentric factor.

The enthalpy of vaporization is given by:

ΔHvap=ΔHvap(0)+ωΔHvap(1)+ω2ΔHvap(2)\Delta H_{vap} = \Delta H_{vap}^{(0)} + \omega \Delta H_{vap}^{(1)} + \omega^2 \Delta H_{vap}^{(2)}
ΔHvap(i)RTc=b(j)τ1/3+b2(j)τ5/6+b3(j)τ1.2083+b4(j)τ+b5(j)τ2+b6(j)τ3\frac{\Delta H_{vap}^{(i)}}{RT_c} = b^{(j)} \tau^{1/3} + b_2^{(j)} \tau^{5/6} + b_3^{(j)} \tau^{1.2083} + b_4^{(j)}\tau + b_5^{(j)} \tau^2 + b_6^{(j)} \tau^3
τ=1−T/Tc\tau = 1-T/T_c
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

omegafloat

Acentric factor [-]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

The original article has been reviewed. A total of 18 coefficients are used:

WARNING: The correlation has been implemented as described in the article, but its results seem different and with some error. Its results match with other functions however.

Has poor behavior for low-temperature use. This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.

References

1

Morgan, David L., and Riki Kobayashi. “Extension of Pitzer CSP Models for Vapor Pressures and Heats of Vaporization to Long-Chain Hydrocarbons.” Fluid Phase Equilibria 94 (March 15, 1994): 51-87. doi:10.1016/0378-3812(94)87051-9.

Examples

Problem in article for SMK function.

>>> MK(553.15, 751.35, 0.302)
38728.00667307733
chemicals.phase_change.Velasco(T, Tc, omega)[source]

Calculates enthalpy of vaporization at arbitrary temperatures using a the work of [1]; requires a chemical’s critical temperature and acentric factor.

The enthalpy of vaporization is given by:

ΔvapH=RTc(7.2729+10.4962ω+0.6061ω2)(1−Tr)0.38\Delta_{vap} H = RT_c(7.2729 + 10.4962\omega + 0.6061\omega^2)(1-T_r)^{0.38}
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

omegafloat

Acentric factor [-]

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

The original article has been reviewed. It is regressed from enthalpy of vaporization values at 0.7Tr, from 121 fluids in REFPROP 9.1. A value in the article was read to be similar, but slightly too low from that calculated here. This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.

References

1(1,2)

Velasco, S., M. J. Santos, and J. A. White. “Extended Corresponding States Expressions for the Changes in Enthalpy, Compressibility Factor and Constant-Volume Heat Capacity at Vaporization.” The Journal of Chemical Thermodynamics 85 (June 2015): 68-76. doi:10.1016/j.jct.2015.01.011.

Examples

From graph, in [1] for perfluoro-n-heptane.

>>> Velasco(333.2, 476.0, 0.5559)
33299.428636069264
chemicals.phase_change.Clapeyron(T, Tc, Pc, dZ=1, Psat=101325)[source]

Calculates enthalpy of vaporization at arbitrary temperatures using the Clapeyron equation.

The enthalpy of vaporization is given by:

ΔHvap=RTΔZln⁡(Pc/Psat)(1−Tr)\Delta H_{vap} = RT \Delta Z \frac{\ln (P_c/Psat)}{(1-T_{r})}
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

dZfloat

Change in compressibility factor between liquid and gas, []

Psatfloat

Saturation pressure of fluid [Pa], optional

Returns
Hvapfloat

Enthalpy of vaporization, [J/mol]

Notes

No original source is available for this equation. [1] claims this equation overpredicts enthalpy by several percent. Under Tr = 0.8, dZ = 1 is a reasonable assumption. This equation is most accurate at the normal boiling point.

Internal units are bar.

WARNING: I believe it possible that the adjustment for pressure may be incorrect

References

1

Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.

Examples

Problem from Perry’s examples.

>>> Clapeyron(T=294.0, Tc=466.0, Pc=5.55E6)
26512.36357131963
chemicals.phase_change.Watson(T, Hvap_ref, T_ref, Tc, exponent=0.38)[source]

Calculates enthalpy of vaporization of a chemical at a temperature using the known heat of vaporization at another temperature according to the Watson [1] [2] correlation. This is an application of the corresponding-states principle, with an emperical temperature dependence.

ΔHvapT1ΔHvapT2=(1−Tr,11−Tr,2)0.38\frac{\Delta H_{vap}^{T1}}{\Delta H_{vap}^{T2}} = \left( \frac{1-T_{r,1}}{1-T_{r,2}} \right)^{0.38}
Parameters
Tfloat

Temperature for which to calculate heat of vaporization, [K]

Hvap_reffloat

Enthalpy of vaporization at the known temperature point, [J/mol]

T_reffloat

Reference temperature; ideally as close to T as posible, [K]

Tcfloat

Critical temperature of fluid [K]

exponentfloat, optional

A fit exponent can optionally be used instead of the Watson 0.38 exponent, [-]

Returns
Hvapfloat

Enthalpy of vaporization at T, [J/mol]

References

1

Watson, KM. “Thermodynamics of the Liquid State.” Industrial & Engineering Chemistry 35, no. 4 (1943): 398-406.

2

Martin, Joseph J., and John B. Edwards. “Correlation of Latent Heats of Vaporization.” AIChE Journal 11, no. 2 (1965): 331-33. https://doi.org/10.1002/aic.690110226.

Examples

Predict the enthalpy of vaporization of water at 320 K from a point at 300 K:

>>> Watson(T=320, Hvap_ref=43908, T_ref=300.0, Tc=647.14)
42928.990094915454

The error is 0.38% compared to the correct value of 43048 J/mol.

If the provided temperature is above the critical point, zero is returned.

chemicals.phase_change.Watson_n(T1, T2, Hvap1, Hvap2, Tc)[source]

Calculates the Watson heat of vaporizaton extrapolation exponent given two known heats of vaporization.

n=[ln⁡(Hvap1Hvap2)ln⁡(T1−TcT2−Tc)]n = \left[ \frac{\ln{\left(\frac{Hvap_{1}}{Hvap_{2}} \right)}} {\ln{\left(\frac{T_{1} - T_{c}}{T_{2} - T_{c}} \right)}}\right]
Parameters
T1float

Temperature of first heat of vaporization point, [K]

T2float

Temperature of second heat of vaporization point, [K]

Hvap1float

Enthalpy of vaporization at the first known temperature point, [J/mol]

Hvap2float

Enthalpy of vaporization at the second known temperature point, [J/mol]

Tcfloat

Critical temperature of fluid [K]

Returns
exponentfloat

A fit exponent that can be used instead of the Watson 0.38 exponent, [-]

Notes

This can be useful for extrapolating when a correlation does not reach the critical point.

Examples

>>> Watson_n(T1=320, T2=300, Hvap1=42928.990094915454, Hvap2=43908, Tc=647.14)
0.380000000000

Heat of Vaporization at T Model Equations

chemicals.phase_change.Alibakhshi(T, Tc, C)[source]

Calculates enthalpy of vaporization of a chemical at a temperature using a theoretically-derived single-coefficient fit equation developed in [1]. This model falls apart at ~0.8 Tc.

ΔHvap=(4.5πNA)1/3.4.2×10−7(Tc−6)−0.5RTln⁡(T)+CT\Delta H_{vap} = \left(4.5\pi N_A\right)^{1/3.}4.2\times 10^{-7} (T_c - 6) - 0.5RT\ln(T) + CT
Parameters
Tfloat

Temperature for which to calculate heat of vaporization, [K]

Tcfloat

Critical temperature of fluid [K]

Cfloat

Alibakhshi fit coefficient, [J/mol/K]

Returns
Hvapfloat

Enthalpy of vaporization at T, [J/mol]

Notes

The authors of [1] evaluated their model on 1890 compounds for a temperature range of 50 K under Tb to 100 K below Tc, and obtained an average absolute relative error of 4.5%.

References

1(1,2)

Alibakhshi, Amin. “Enthalpy of Vaporization, Its Temperature Dependence and Correlation with Surface Tension: A Theoretical Approach.” Fluid Phase Equilibria 432 (January 25, 2017): 62-69. https://doi.org/10.1016/j.fluid.2016.10.013.

Examples

Predict the enthalpy of vaporization of water at 320 K:

>>> Alibakhshi(T=320.0, Tc=647.14, C=-16.7171)
41961.30490225752

The error is 2.5% compared to the correct value of 43048 J/mol.

chemicals.phase_change.PPDS12(T, Tc, A, B, C, D, E)[source]

Calculate the enthalpy of vaporization of a fluid using the 5-term power fit developed by the PPDS and named PPDS equation 12.

Hvap=RTc(Aτ1/3+Bτ2/3+Cτ+Dτ2+Eτ6)H_{vap} = RT_c \left(A\tau^{1/3} + B\tau^{2/3} + C\tau + D\tau^2 + E\tau^6\right)
τ=1−TTc\tau = 1 - \frac{T}{T_c}
Parameters
Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Afloat

Coefficient, [-]

Bfloat

Coefficient, [-]

Cfloat

Coefficient, [-]

Dfloat

Coefficient, [-]

Efloat

Coefficient, [-]

Returns
Hvapfloat

Enthalpy of vaporization at T, [J/mol]

Notes

Coefficients can be found in [1], but no other source for these coefficients has been found.

References

1(1,2)

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

2(1,2)

“Enthalpy of Vaporization: PPDS12.” https://trc.nist.gov/TDE/TDE_Help/Eqns-Pure-Hvap/PPDS12.htm.

Examples

Example from [1]:

>>> PPDS12(300.0, 591.75, 4.60584, 13.97224, -10.592315, 2.120205, 4.277128)
37948.76862035925

Example from [2] for benzene; note the coefficients from [2] predict enthalpy of vaporization in kJ/mol, so the output must be adjusted. The same effect can be obtained by multiplying each of the coefficients by 1000.

>>> 1000.0*PPDS12(300.0, 562.05, 0.00171484, 0.0258604, -0.0243564, 0.00740881, 0.00680068)
33662.4258030

Heat of Sublimation

No specific correlation is provided. This value is fairly strongly temperature dependent; the dependency comes almost entirely from the vaporization enthalpy’s dependence. To calculate heat of sublimation at any temperature, use the equation Hsub=Hfus+HvapH_{sub} = H_{fus} + H_{vap}.

Fit Coefficients

All of these coefficients are lazy-loaded, so they must be accessed as an attribute of this module.

chemicals.phase_change.phase_change_data_Perrys2_150

A collection of 344 coefficient sets from the DIPPR database published openly in [1]. Provides temperature limits for all its fluids. See chemicals.dippr.EQ106 for the model equation.

chemicals.phase_change.phase_change_data_VDI_PPDS_4

Coefficients for a equation form developed by the PPDS, published openly in [2]. Extrapolates poorly at low temperatures. See PPDS12 for the model equation.

chemicals.phase_change.phase_change_data_Alibakhshi_Cs

One-constant limited temperature range regression coefficients presented in [3], with constants for ~2000 chemicals from the DIPPR database. Valid up to 100 K below the critical point, and 50 K under the boiling point. See Alibakhshi for the model equation.

1

Green, Don, and Robert Perry. Perry’s Chemical Engineers’ Handbook, 8E. McGraw-Hill Professional, 2007.

2

Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.

3

Alibakhshi, Amin. “Enthalpy of Vaporization, Its Temperature Dependence and Correlation with Surface Tension: A Theoretical Approach.” Fluid Phase Equilibria 432 (January 25, 2017): 62-69. https://doi.org/10.1016/j.fluid.2016.10.013.

The structure of each dataframe is shown below:

In [1]: import chemicals

In [2]: chemicals.phase_change.phase_change_data_Perrys2_150
Out[2]: 
                           Chemical      Tc       C1  ...       C4    Tmin    Tmax
CAS                                                   ...                         
50-00-0              Formaldehyde    408.00  30760.0  ...  0.00000  181.15  408.00
55-21-0                 Benzamide    824.00  87809.0  ... -0.14162  403.00  824.00
56-23-5      Carbon tetrachloride    556.35  43252.0  ...  0.00000  250.33  556.35
57-55-6      1,2-Propylene glycol    626.00  80700.0  ...  0.00000  213.15  626.00
60-29-7             Diethyl ether    466.70  40600.0  ...  0.00000  156.85  466.70
...                             ...     ...      ...  ...      ...     ...     ...
10028-15-6                  Ozone    261.00  18587.0  ...  0.00000   80.15  261.00
10035-10-6       Hydrogen bromide    363.15  24850.0  ...  0.00000  185.15  363.15
10102-43-9           Nitric oxide    180.15  21310.0  ...  0.00000  109.50  180.15
13511-13-2    Propenylcyclohexene    636.00  58866.0  ...  0.00000  199.00  636.00
132259-10-0                   Air    132.45   8474.0  ...  0.00000   59.15  132.45

[344 rows x 8 columns]

In [3]: chemicals.phase_change.phase_change_data_VDI_PPDS_4
Out[3]: 
                         Chemical      MW  ...          D           E
CAS                                        ...                       
50-00-0              Formaldehyde   30.03  ...  -4.856937   11.036836
56-23-5      Carbon tetrachloride  153.82  ...  -0.172679    3.053272
56-81-5                  Glycerol   92.09  ...   2.052518  -13.771300
60-29-7             Diethyl ether   74.12  ...  -0.175016    3.557340
62-53-3                   Aniline   93.13  ...  -1.656520    3.263408
...                           ...     ...  ...        ...         ...
10097-32-2                Bromine  159.82  ...  -0.025698   -0.197360
10102-43-9           Nitric oxide   30.01  ...  -5.159373   97.203137
10102-44-0       Nitrogen dioxide   46.01  ...  10.653997   68.680656
10544-72-6    Dinitrogentetroxide   92.01  ...  -1.535179  102.679020
132259-10-0                   Air   28.96  ...  -8.064787   14.645081

[272 rows x 8 columns]

In [4]: chemicals.phase_change.phase_change_data_Alibakhshi_Cs
Out[4]: 
                         Chemical         C
CAS                                        
50-00-0              formaldehyde  -26.7916
50-21-5               lactic acid   30.5238
50-70-4                  sorbitol   89.1371
50-78-2      acetylsalicylic acid   15.9121
50-81-7             ascorbic acid  102.2858
...                           ...       ...
7642-10-6           cis-3-heptene  -17.8032
7719-09-7        thionyl chloride  -31.2745
7719-12-2  phosphorus trichloride  -27.0024
7783-06-4        hydrogen sulfide  -37.3259
7783-07-5       hydrogen selenide  -38.5320

[1890 rows x 2 columns]