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
- CASRN
str
CASRN [-]
- CASRN
- Returns
- Tb
float
Boiling temperature, [K]
- Tb
- Other Parameters
- method
str
,optional
A string for the method name to use, as defined in the variable, Tb_all_methods.
- method
See also
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
- CASRN
str
CASRN, [-]
- CASRN
- Returns
See also
- 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
- CASRN
str
CASRN [-]
- CASRN
- Returns
- Tm
float
Melting temperature, [K]
- Tm
- Other Parameters
- method
str
,optional
A string for the method name to use, as defined by the vairable Tm_all_methods.
- method
See also
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
- CASRN
str
CASRN, [-]
- CASRN
- Returns
See also
- 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
- CASRN
str
CASRN [-]
- CASRN
- Returns
- Hfus
float
Molar enthalpy of fusion at normal melting point, [J/mol]
- Hfus
- Other Parameters
- method
str
,optional
A string for the method name to use, as defined by the variable, Hfus_all_methods.
- method
See also
Notes
The available sources are as follows:
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
- CASRN
str
CASRN, [-]
- CASRN
- Returns
See also
- 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:
$\Delta_{vap} H=1.093 T_b R\frac{\ln P_c-1.013}{0.930-T_{br}}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization at the normal boiling point, [J/mol]
- Hvap
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:
$\Delta H_{vb} = RT_b \frac{3.978 T_r - 3.958 + 1.555 \ln P_c}{1.07 - T_r}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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:
$\Delta H_{vap} = RT_b \left[ \frac{T_b}{220}\right]^{0.0627} \frac{ (1-T_{br})^{0.38} \ln(P_c/P_A)}{1-T_{br} + 0.38 T_{br} \ln T_{br}}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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:
$\frac {\Delta H_{vap}}{RT_b} = \frac{\tau_b^{0.38} \left[ \ln P_c - 0.513 + \frac{0.5066}{P_cT_{br}^2}\right]} {\tau_b + F(1-\tau_b^{0.38})\ln T_{br}}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization at the boiling point, [J/mol]
- Hvap
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:
$\frac{\Delta_{vap} H}{RT_c}=7.08(1-T_r)^{0.354}+10.95\omega(1-T_r)^{0.456}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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:
$\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]$$\left( \frac{\Delta H_{vap}} {RT_c} \right)^{(R1)} = 6.537 \tau^{1/3} - 2.467 \tau^{5/6} - 77.251 \tau^{1.208} + 59.634 \tau + 36.009 \tau^2 - 14.606 \tau^3$$\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$$\tau = 1-T/T_c$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
Notes
The original article has been reviewed and found to have coefficients with slightly more precision. Additionally, the form of the equation is slightly different, but numerically equivalent.
The refence fluids are:
$\omega_0$ = benzene = 0.212
$\omega_1$ = carbazole = 0.461
A sample problem in the article has been verified. The numerical result presented by the author requires high numerical accuracy to obtain.
This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1(1,2)
Sivaraman, Alwarappa, Joe W. Magee, and Riki Kobayashi. “Generalized Correlation of Latent Heats of Vaporization of Coal-Liquid Model Compounds between Their Freezing Points and Critical Points.” Industrial & Engineering Chemistry Fundamentals 23, no. 1 (February 1, 1984): 97-100. doi:10.1021/i100013a017.
Examples
Problem in [1]:
>>> SMK(553.15, 751.35, 0.302) 39866.18999046229
- chemicals.phase_change.MK(T, Tc, omega)[source]¶
Calculates enthalpy of vaporization at arbitrary temperatures using a the work of [1]; requires a chemical’s critical temperature and acentric factor.
The enthalpy of vaporization is given by:
$\Delta H_{vap} = \Delta H_{vap}^{(0)} + \omega \Delta H_{vap}^{(1)} + \omega^2 \Delta H_{vap}^{(2)}$$\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$$\tau = 1-T/T_c$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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:
$\Delta_{vap} H = RT_c(7.2729 + 10.4962\omega + 0.6061\omega^2)(1-T_r)^{0.38}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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:
$\Delta H_{vap} = RT \Delta Z \frac{\ln (P_c/Psat)}{(1-T_{r})}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization, [J/mol]
- Hvap
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.
$\frac{\Delta H_{vap}^{T1}}{\Delta H_{vap}^{T2}} = \left( \frac{1-T_{r,1}}{1-T_{r,2}} \right)^{0.38}$- Parameters
- T
float
Temperature for which to calculate heat of vaporization, [K]
- Hvap_ref
float
Enthalpy of vaporization at the known temperature point, [J/mol]
- T_ref
float
Reference temperature; ideally as close to T as posible, [K]
- Tc
float
Critical temperature of fluid [K]
- exponent
float
,optional
A fit exponent can optionally be used instead of the Watson 0.38 exponent, [-]
- T
- Returns
- Hvap
float
Enthalpy of vaporization at T, [J/mol]
- Hvap
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 = \left[ \frac{\ln{\left(\frac{Hvap_{1}}{Hvap_{2}} \right)}} {\ln{\left(\frac{T_{1} - T_{c}}{T_{2} - T_{c}} \right)}}\right]$- Parameters
- T1
float
Temperature of first heat of vaporization point, [K]
- T2
float
Temperature of second heat of vaporization point, [K]
- Hvap1
float
Enthalpy of vaporization at the first known temperature point, [J/mol]
- Hvap2
float
Enthalpy of vaporization at the second known temperature point, [J/mol]
- Tc
float
Critical temperature of fluid [K]
- T1
- Returns
- exponent
float
A fit exponent that can be used instead of the Watson 0.38 exponent, [-]
- 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.
$\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
- Returns
- Hvap
float
Enthalpy of vaporization at T, [J/mol]
- Hvap
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.
$H_{vap} = RT_c \left(A\tau^{1/3} + B\tau^{2/3} + C\tau + D\tau^2 + E\tau^6\right)$$\tau = 1 - \frac{T}{T_c}$- Parameters
- Returns
- Hvap
float
Enthalpy of vaporization at T, [J/mol]
- Hvap
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 $H_{sub} = H_{fus} + H_{vap}$.
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]