Vapor Pressure (chemicals.vapor_pressure)

This module contains various vapor pressure estimation routines, dataframes of fit coefficients, some compound-specific equations, some analytical fitting routines, and sublimation pressure routines.

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

Fit Correlations

chemicals.vapor_pressure.Antoine(T, A, B, C, base=10.0)

Calculates vapor pressure of a chemical using the Antoine equation. Parameters A, B, and C are chemical-dependent. Parameters can be found in numerous sources; however units of the coefficients used vary. Originally proposed by Antoine (1888) [2].

$$\log_{\text{base}} P^{\text{sat}} = A - \frac{B}{T+C}$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

basefloat, optional

Optional base of logarithm; 10 by default

Returns

Psatfloat

Vapor pressure calculated with coefficients [Pa]

Notes

Assumes coefficients are for calculating vapor pressure in Pascal. Coefficients should be consistent with input temperatures in Kelvin; however, if both the given temperature and units are specific to degrees Celcius, the result will still be correct.

Converting units in input coefficients:

• ln to log10: Divide A and B by ln(10)=2.302585 to change parameters for a ln equation to a log10 equation.

• log10 to ln: Multiply A and B by ln(10)=2.302585 to change parameters for a log equation to a ln equation.

• mmHg to Pa: Add log10(101325/760)= 2.1249 to A.

• kPa to Pa: Add log_{base}(1000)= 6.908 to A for log(base)

• bar to Pa: Add log_{base}(100000)= 11.5129254 to A for log(base)

• °C to K: Subtract 273.15 from C only!

Note that if C is negative and T is less than C, the predicted vapor pressure would be high and positive at those temperatures under C; and a singularity would occur at T == C. This implementation is corrected to return zero for the case of T + C < 0.0, which matches the intention of the Antoine equation.

References

1(1,2)

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

2

Antoine, C. 1888. Tensions des Vapeurs: Nouvelle Relation Entre les Tensions et les Tempé. Compt.Rend. 107:681-684.

3

Yaws, Carl L. The Yaws Handbook of Vapor Pressure: Antoine Coefficients. 1 edition. Houston, Tex: Gulf Publishing Company, 2007.

Examples

Methane, coefficients from [1], at 100 K:

>>> Antoine(100.0, 8.7687, 395.744, -6.469)
34478.367349639906

Tetrafluoromethane, coefficients from [1], at 180 K

>>> Antoine(180, A=8.95894, B=510.595, C=-15.95)
702271.0518579542

Oxygen at 94.91 K, with coefficients from [3] in units of °C, mmHg, log10, showing the conversion of coefficients A (mmHg to Pa) and C (°C to K)

>>> Antoine(94.91, 6.83706+2.1249, 339.2095, 268.70-273.15)
162978.88655572367

n-hexane with Antoine coefficients from the NIST webbook in units of K and bar, calculating the vapor pressure in Pa at 200 K:

>>> Antoine(T=200, A=3.45604+5, B=1044.038, C=-53.893)
20.4329803671

chemicals.vapor_pressure.Wagner(T, Tc, Pc, a, b, c, d)

Calculates vapor pressure using the Wagner equation (2.5, 5 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\ln P^{sat}= \ln P_c + \frac{a\tau + b \tau^{1.5} + c\tau^{2.5} + d\tau^5} {T_r}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

Warning: Pc is often treated as adjustable constant. This is also called the PPDS16 equation [3].

References

1

Wagner, W. “New Vapour Pressure Measurements for Argon and Nitrogen and a New Method for Establishing Rational Vapour Pressure Equations.” Cryogenics 13, no. 8 (August 1973): 470-82. doi:10.1016/0011-2275(73)90003-9

2

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

3

PPDS2 Temperature-Dependent Equation Forms. National Engineering Laboratory, 2004 https://web.archive.org/web/20050510061545/http://www.ppds.co.uk/library/pdf/PPDS_EquationForms.pdf

Examples

Methane, coefficients from [2], at 100 K.

>>> Wagner(100., 190.551, 4599200, -6.02242, 1.26652, -0.5707, -1.366)
34415.004762637

chemicals.vapor_pressure.Wagner_original(T, Tc, Pc, a, b, c, d)

Calculates vapor pressure using the Wagner equation (3, 6 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\ln P^{sat}= \ln P_c + \frac{a\tau + b \tau^{1.5} + c\tau^3 + d\tau^6} {T_r}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

Warning: Pc is often treated as adjustable constant. This is also called the PPDS1 equation [3].

References

1

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

2

McGarry, Jack. “Correlation and Prediction of the Vapor Pressures of Pure Liquids over Large Pressure Ranges.” Industrial & Engineering Chemistry Process Design and Development 22, no. 2 (April 1, 1983): 313-22. doi:10.1021/i200021a023.

3

PPDS2 Temperature-Dependent Equation Forms. National Engineering Laboratory, 2004 https://web.archive.org/web/20050510061545/http://www.ppds.co.uk/library/pdf/PPDS_EquationForms.pdf

Examples

Methane, coefficients from [2], at 100 K.

>>> Wagner_original(100.0, 190.53, 4596420., a=-6.00435, b=1.1885,
... c=-0.834082, d=-1.22833)
34520.44601450499

chemicals.vapor_pressure.TRC_Antoine_extended(T, Tc, to, A, B, C, n, E, F)

Calculates vapor pressure of a chemical using the TRC Extended Antoine equation. Parameters are chemical dependent, and said to be from the Thermodynamics Research Center (TRC) at Texas A&M. Coefficients for various chemicals can be found in [1].

$$\log_{10} P^{sat} = A - \frac{B}{T + C} + 0.43429x^n + Ex^8 + Fx^{12}$$

$$x = \max \left(\frac{T-t_o-273.15}{T_c}, 0 \right)$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature of fluid, [K]

tofloat

Fit temperature-transition parameter, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

nfloat

Fit parameter, [-]

Efloat

Fit parameter, [-]

Ffloat

Fit parameter, [-]

Returns

Psatfloat

Vapor pressure calculated with coefficients [Pa]

Notes

Assumes coefficients are for calculating vapor pressure in Pascal. Coefficients should be consistent with input temperatures in Kelvin;

References

1(1,2)

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

Examples

Tetrafluoromethane, coefficients from [1], at 180 K:

>>> TRC_Antoine_extended(T=180.0, Tc=227.51, to=-120., A=8.95894,
... B=510.595, C=-15.95, n=2.41377, E=-93.74, F=7425.9)
706317.0898414153

chemicals.vapor_pressure.Yaws_Psat(T, A, B, C, D, E)

Calculates vapor pressure of a chemical using the Yaws equation for vapor pressure. Parameters A, B, C, D, and E are chemical-dependent. Parameters can be found in numerous sources; however units of the coefficients used vary.

$$\log_{10} P^{\text{sat}} = A + \frac{B}{T} + C\log_{10}(T) + DT + ET^2$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

A parameter, [-]

Bfloat

B parameter, [K]

Cfloat

C parameter, [-]

Dfloat

D parameter, [1/K]

Efloat

E parameter, [1/K^2]

Returns

Psatfloat

Vapor pressure calculated with coefficients [Pa]

Notes

Assumes coefficients are for calculating vapor pressure in Pascal. Coefficients should be consistent with input temperatures in Kelvin;

Converting units in input coefficients:

• mmHg to Pa: Add log10(101325/760)= 2.1249 to A.

• kPa to Pa: Add log_{10}(1000)= 3 to A

• bar to Pa: Add log_{10}(100000)= 5 to A

References

1

Yaws, Carl L. Chemical Properties Handbook: Physical, Thermodynamic, Environmental, Transport, Safety, and Health Related Properties for Organic and Inorganic Chemicals. McGraw-Hill, 2001.

2

“ThermoData Engine (TDE103a V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103a/Eqns-Pure-PhaseBoundaryLG/Yaws-VaporPressure.htm.

Examples

Acetone, coefficients from [1], at 400 K and with the conversion of A to obtain a result in Pa:

>>> Yaws_Psat(T=400.0, A=28.588 + log10(101325/760), B=-2469, C=-7.351, D=2.8025E-10, E=2.7361E-6)
708657.089106

Coefficients for benzene from [2] at 400 K; that source outputs vapor pressure in kPa. That style of coefficients can be converted to Pa by adding 3 to A.

>>> Yaws_Psat(T=400.0, A=39.7918+3, B=-2965.83, C=-12.073, D=0.0033269, E=1.58609e-6)
352443.191026

chemicals.vapor_pressure.TDE_PVExpansion(T, a1, a2, a3, a4=0.0, a5=0.0, a6=0.0, a7=0.0, a8=0.0)

Calculates vapor pressure or sublimation pressure of a chemical using the PVExpansion equation for vapor pressure or sublimation pressure. Parameters a1, a2, a3, a4, a5, a6, a7, and a8 are chemical-dependent. Parameters can be found in various sources; however units of the coefficients used vary.

$$\log P^{\text{sat}} = a_1 + \frac{a_2}{T} + a_3\ln(T) + a_4T + a_5T^2 + \frac{a_6}{T^2} + a_7 T^6 + \frac{a_8}{T^4}$$

Parameters

Tfloat

Temperature of fluid, [K]

a1float

Regression parameter, [-]

a2float

Regression parameter, [-]

a3float

Regression parameter, [-]

a4float

Regression parameter, [-]

a5float

Regression parameter, [-]

a6float

Regression parameter, [-]

a7float

Regression parameter, [-]

a8float

Regression parameter, [-]

Returns

Psatfloat

Vapor pressure calculated with coefficients [Pa]

Notes

Coefficients in [1] produce a vapor pressure in kPa; add log(1000) to a1 to make them produce vapor pressure in Pa.

References

1(1,2)

“ThermoData Engine (TDE103a V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-PhaseBoundaryLG/PVExpansion.htm

Examples

Coefficients for sublimation pressure from [1]:

>>> TDE_PVExpansion(T=273.16, a1=23.7969+log(1000), a2=-11422, a3=0.177978)
4.06220657398e-05

Fit Correlation Derivatives

chemicals.vapor_pressure.dAntoine_dT(T, A, B, C, base=10.0)

Calculates the first temperature derivative of vapor pressure of a chemical using the Antoine equation. Parameters A, B, and C are chemical-dependent.

$$\frac{\partial P^{\text{sat}} }{\partial T} = \frac{B \text{base}^{A - \frac{B}{C + T}} \log{\left(\text{base} \right)}} {\left(C + T\right)^{2}}$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

basefloat, optional

Optional base of logarithm; 10 by default

Returns

dPsat_dTfloat

First temperature derivative of vapor pressure calculated with coefficients [Pa/K]

Examples

Methane at 100 K:

>>> dAntoine_dT(100.0, 8.7687, 395.744, -6.469)
3591.4147747481

chemicals.vapor_pressure.d2Antoine_dT2(T, A, B, C, base=10.0)

Calculates the second temperature derivative of vapor pressure of a chemical using the Antoine equation. Parameters A, B, and C are chemical-dependent.

$$\frac{\partial^2 P^{\text{sat}} }{\partial T^2} = \frac{B \text{base}^{A - \frac{B}{C + T}} \left(\frac{B \log{\left( \text{base} \right)}}{C + T} - 2\right) \log{\left(\text{base} \right)}}{\left(C + T\right)^{3}}$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

basefloat, optional

Optional base of logarithm; 10 by default

Returns

d2Psat_dT2float

Second temperature derivative of vapor pressure calculated with coefficients [Pa/K^2]

Examples

Methane at 100 K:

>>> d2Antoine_dT2(100.0, 8.7687, 395.744, -6.469)
297.30093799054

chemicals.vapor_pressure.dWagner_dT(T, Tc, Pc, a, b, c, d)

Calculates the first temperature derivative of vapor pressure using the Wagner equation (2.5, 5 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\frac{\partial P^{\text{sat}} }{\partial T} = P_{c} \left(\frac{T_{c} \left(- \frac{a}{T_{c}} - \frac{1.5 b \tau^{0.5}}{T_{c}} - \frac{2.5 c \tau^{1.5}}{T_{c}} - \frac{5 d \tau^{4}}{T_{c}}\right)}{T} - \frac{T_{c} \left(a \tau + b \tau^{1.5} + c \tau^{2.5} + d \tau^{5}\right)}{T^{2}}\right) e^{\frac{T_{c} \left(a \tau + b \tau^{1.5} + c \tau^{2.5} + d \tau^{5}\right)}{T}}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

dPsat_dTfloat

First temperature derivative of vapor pressure at T [Pa/K]

Examples

Methane at 100 K.

>>> dWagner_dT(100., 190.551, 4599200, -6.02242, 1.26652, -0.5707, -1.366)
3587.2910498076

chemicals.vapor_pressure.d2Wagner_dT2(T, Tc, Pc, a, b, c, d)

Calculates the second temperature derivative of vapor pressure using the Wagner equation (2.5, 5 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\frac{\partial^2 P^{\text{sat}} }{\partial T^2} = \frac{P_{c} \left(\frac{\frac{0.75 b}{\tau^{0.5}} + 3.75 c \tau^{0.5} + 20 d \tau^{3}}{T_{c}} + \frac{2 \left(a + 1.5 b \tau^{0.5} + 2.5 c \tau^{1.5} + 5 d \tau^{4}\right)}{T} + \frac{25 \left( \frac{a}{5} + 0.3 b \tau^{0.5} + 0.5 c \tau^{1.5} + d \tau^{4} - \frac{T_{c} \left(- a \tau - b \tau^{1.5} - c \tau^{2.5} - d \tau^{5}\right)}{5 T}\right)^{2}}{T} - \frac{2 T_{c} \left(- a \tau - b \tau^{1.5} - c \tau^{2.5} - d \tau^{5}\right)}{T^{2}}\right) e^{- \frac{T_{c} \left(- a \tau - b \tau^{1.5} - c \tau^{2.5} - d \tau^{5}\right)}{T}}}{T}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

d2Psat_dT2float

Second temperature derivative of vapor pressure at T [Pa/K^2]

Notes

This second derivative is infinity at T == Tc.

Examples

Methane at 100 K.

>>> d2Wagner_dT2(100., 190.551, 4599200, -6.02242, 1.26652, -0.5707, -1.366)
296.7091513877

chemicals.vapor_pressure.dWagner_original_dT(T, Tc, Pc, a, b, c, d)

Calculates first temperature derivative of vapor pressure using the Wagner equation (3, 6 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\frac{\partial P^{\text{sat}} }{\partial T} = P_{c} \left(\frac{T_{c} \left(- \frac{a}{T_{c}} - \frac{1.5 b \tau^{0.5}}{T_{c}} - \frac{3 c \tau^{2}}{T_{c}} - \frac{6 d \tau^{5}} {T_{c}}\right)}{T} - \frac{T_{c} \left(a \tau + b \tau^{1.5} + c \tau^{3} + d \tau^{6}\right)}{T^{2}}\right) e^{\frac{T_{c} \left(a \tau + b \tau^{1.5} + c \tau^{3} + d \tau^{6}\right)}{T}}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

dPsat_dTfloat

First temperature derivative of vapor pressure at T [Pa/K]

Examples

Methane at 100 K.

>>> dWagner_original_dT(100.0, 190.53, 4596420., a=-6.00435, b=1.1885,
... c=-0.834082, d=-1.22833)
3593.70783283

chemicals.vapor_pressure.d2Wagner_original_dT2(T, Tc, Pc, a, b, c, d)

Calculates second temperature derivative of vapor pressure using the Wagner equation (3, 6 form).

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

$$\frac{\partial^2 P^{\text{sat}} }{\partial T^2} = \frac{P_{c} \left(\frac{\frac{0.75 b}{\tau^{0.5}} + 6 c \tau + 30 d \tau^{4}}{T_{c}} + \frac{2 \left(a + 1.5 b \tau^{0.5} + 3 c \tau^{2} + 6 d \tau^{5}\right)}{T} + \frac{36 \left(\frac{a}{6} + 0.25 b \tau^{0.5} + \frac{c \tau^{2}}{2} + d \tau^{5} - \frac{T_{c} \left( - a \tau - b \tau^{1.5} - c \tau^{3} - d \tau^{6}\right)}{6 T} \right)^{2}}{T} - \frac{2 T_{c} \left(- a \tau - b \tau^{1.5} - c \tau^{3} - d \tau^{6}\right)}{T^{2}}\right) e^{- \frac{T_{c} \left(- a \tau - b \tau^{1.5} - c \tau^{3} - d \tau^{6}\right)}{T}}}{T}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

d2Psat_dT2float

Second temperature derivative of vapor pressure at T [Pa/K^2]

Notes

This second derivative is infinity at T == Tc.

Examples

Methane at 100 K.

>>> d2Wagner_original_dT2(100.0, 190.53, 4596420., a=-6.00435, b=1.1885,
... c=-0.834082, d=-1.22833)
296.87593368224

chemicals.vapor_pressure.dTRC_Antoine_extended_dT(T, Tc, to, A, B, C, n, E, F)

Calculates the first temperature derivative of vapor pressure of a chemical using the TRC Extended Antoine equation.

$$\frac{\partial P^{\text{sat}} }{\partial T} = 10^{A - \frac{B}{C + T} + \frac{E \left(T - T_{ref} - to\right)^{8}} {T_{c}^{8}} + \frac{F \left(T - T_{ref} - to\right)^{12}}{T_{c}^{12}} + f \left(\frac{T - T_{ref} - to}{T_{c}}\right)^{n}} \left(\frac{B}{\left(C + T\right)^{2}} + \frac{8 E \left(T - T_{ref} - to\right)^{7}}{T_{c}^{8}} + \frac{12 F \left(T - T_{ref} - to \right)^{11}}{T_{c}^{12}} + \frac{f n \left(\frac{T - T_{ref} - to} {T_{c}}\right)^{n}}{T - T_{ref} - to}\right) \log{\left(10 \right)}$$

$$x = \max \left(\frac{T-t_o-273.15}{T_c}, 0 \right)$$

$$T_{ref} = 273.15 \text{ K}$$

$$f = 0.43429$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature of fluid, [K]

tofloat

Fit temperature-transition parameter, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

nfloat

Fit parameter, [-]

Efloat

Fit parameter, [-]

Ffloat

Fit parameter, [-]

Returns

dPsat_dTfloat

First temperature derivative of vapor pressure calculated with coefficients [Pa/K]

Examples

Tetrafluoromethane at 180 K:

>>> dTRC_Antoine_extended_dT(T=180.0, Tc=227.51, to=-120., A=8.95894,
... B=510.595, C=-15.95, n=2.41377, E=-93.74, F=7425.9)
31219.6061263

chemicals.vapor_pressure.d2TRC_Antoine_extended_dT2(T, Tc, to, A, B, C, n, E, F)

Calculates the second temperature derivative of vapor pressure of a chemical using the TRC Extended Antoine equation.

$$\frac{\partial^2 P^{\text{sat}} }{\partial T^2} = 10^{A - \frac{B}{C + T} + \frac{E \left(- T + T_{ref} + to\right)^{8}} {T_{c}^{8}} + \frac{F \left(- T + T_{ref} + to\right)^{12}}{T_{c}^{12}} + f \left(- \frac{- T + T_{ref} + to}{T_{c}}\right)^{n}} \left( - \frac{2 B}{\left(C + T\right)^{3}} + \frac{56 E \left(- T + T_{ref} + to\right)^{6}}{T_{c}^{8}} + \frac{132 F \left(- T + T_{ref} + to\right)^{10}}{T_{c}^{12}} + \frac{f n^{2} \left(- \frac{- T + T_{ref} + to}{T_{c}}\right)^{n}}{\left(- T + T_{ref} + to\right)^{2}} - \frac{f n \left(- \frac{- T + T_{ref} + to}{T_{c}}\right)^{n}} {\left(- T + T_{ref} + to\right)^{2}} + \left(- \frac{B}{\left(C + T\right)^{2}} + \frac{8 E \left(- T + T_{ref} + to\right)^{7}} {T_{c}^{8}} + \frac{12 F \left(- T + T_{ref} + to\right)^{11}} {T_{c}^{12}} + \frac{f n \left(- \frac{- T + T_{ref} + to} {T_{c}}\right)^{n}}{- T + T_{ref} + to}\right)^{2} \log{\left(10 \right)}\right) \log{\left(10 \right)}$$

$$x = \max \left(\frac{T-t_o-273.15}{T_c}, 0 \right)$$

$$T_{ref} = 273.15 \text{ K}$$

$$f = 0.43429$$

Parameters

Tfloat

Temperature of fluid, [K]

Tcfloat

Critical temperature of fluid, [K]

tofloat

Fit temperature-transition parameter, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

nfloat

Fit parameter, [-]

Efloat

Fit parameter, [-]

Ffloat

Fit parameter, [-]

Returns

d2Psat_dT2float

Second temperature derivative of vapor pressure calculated with coefficients [Pa/K]

Examples

Tetrafluoromethane at 180 K:

>>> d2TRC_Antoine_extended_dT2(T=180.0, Tc=227.51, to=-120., A=8.95894,
... B=510.595, C=-15.95, n=2.41377, E=-93.74, F=7425.9)
1022.550368944

chemicals.vapor_pressure.dYaws_Psat_dT(T, A, B, C, D, E)

Calculates the first temperature derivative of vapor pressure of a chemical using the Yaws equation for vapor pressure. Parameters A, B, C, D, and E are chemical-dependent. Parameters can be found in numerous sources; however units of the coefficients used vary.

$$\frac{\partial P^{\text{sat}} }{\partial T} = 10^{A + \frac{B}{T} + \frac{C \log{\left(T \right)}}{\log{\left(10 \right)}} + D T + E T^{2}} \left(- \frac{B}{T^{2}} + \frac{C}{T \log{\left(10 \right)}} + D + 2 E T\right) \log{\left(10 \right)}$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

A parameter, [-]

Bfloat

B parameter, [K]

Cfloat

C parameter, [-]

Dfloat

D parameter, [1/K]

Efloat

E parameter, [1/K^2]

Returns

dPsat_dTfloat

First temperature derivative of vapor pressure calculated with coefficients [Pa/K]

Examples

Benzene:

>>> dYaws_Psat_dT(T=400.0, A=42.7918, B=-2965.83, C=-12.073, D=0.0033269, E=1.58609e-6)
8134.87548930

chemicals.vapor_pressure.d2Yaws_Psat_dT2(T, A, B, C, D, E)

Calculates the second temperature derivative of vapor pressure of a chemical using the Yaws equation for vapor pressure. Parameters A, B, C, D, and E are chemical-dependent. Parameters can be found in numerous sources; however units of the coefficients used vary.

$$\frac{\partial^2 P^{\text{sat}} }{\partial T^2} = 10^{A + \frac{B}{T} + \frac{C \log{\left(T \right)}}{\log{\left(10 \right)}} + D T + E T^{2}} \left(\frac{2 B}{T^{3}} - \frac{C}{T^{2} \log{\left(10 \right)}} + 2 E + \left(- \frac{B}{T^{2}} + \frac{C}{T \log{\left(10 \right)}} + D + 2 E T\right)^{2} \log{\left(10 \right)}\right) \log{\left(10 \right)}$$

Parameters

Tfloat

Temperature of fluid, [K]

Afloat

A parameter, [-]

Bfloat

B parameter, [K]

Cfloat

C parameter, [-]

Dfloat

D parameter, [1/K]

Efloat

E parameter, [1/K^2]

Returns

d2Psat_dT2float

Second temperature derivative of vapor pressure calculated with coefficients [Pa/K^2]

Examples

Benzene:

>>> d2Yaws_Psat_dT2(T=400.0, A=42.7918, B=-2965.83, C=-12.073, D=0.0033269, E=1.58609e-6)
141.7181045862

Jacobians (for fitting)

chemicals.vapor_pressure.Wagner_fitting_jacobian(Ts, Tc, Pc, a, b, c, d)

Calculates the jacobian of the Wagner (2.5, 5) vapor pressure equation for use in fitting these parameters when experimental values are known.

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

Parameters

Tslist[float]

Temperatures of fluid data points, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

jaclist[list[float, 4], len(Ts)]

Matrix of derivatives of the equation with respect to the fitting parameters, [various]

chemicals.vapor_pressure.Wagner_original_fitting_jacobian(Ts, Tc, Pc, a, b, c, d)

Calculates the jacobian of the Wagner (3, 6) vapor pressure equation for use in fitting these parameters when experimental values are known.

Requires critical temperature and pressure as well as four coefficients specific to each chemical.

Parameters

Tslist[float]

Temperatures of fluid data points, [K]

Tcfloat

Critical temperature, [K]

Pcfloat

Critical pressure, [Pa]

a, b, c, dfloats

Parameters for wagner equation. Specific to each chemical. [-]

Returns

jaclist[list[float, 4], len(Ts)]

Matrix of derivatives of the equation with respect to the fitting parameters, [various]

chemicals.vapor_pressure.Antoine_fitting_jacobian(Ts, A, B, C, base=10.0)

Calculates the jacobian of the Antoine vapor pressure equation for use in fitting these parameters when experimental values are known.

Requires three coefficients specific to each chemical.

Parameters

Tslist[float]

Temperatures of fluid data points, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

basefloat, optional

Optional base of logarithm; 10 by default, [-]

Returns

jaclist[list[float, 3], len(Ts)]

Matrix of derivatives of the equation with respect to the fitting parameters, [various]

chemicals.vapor_pressure.Yaws_Psat_fitting_jacobian(Ts, A, B, C, D, E)

Compute and return the Jacobian of the property predicted by the Yaws vapor pressure equation with respect to all the coefficients. This is used in fitting parameters for chemicals.

Parameters

Tslist[float]

Temperatures of the experimental data points, [K]

Afloat

A parameter, [-]

Bfloat

B parameter, [K]

Cfloat

C parameter, [-]

Dfloat

D parameter, [1/K]

Efloat

E parameter, [1/K^2]

Returns

jaclist[list[float, 5], len(Ts)]

Matrix of derivatives of the equation with respect to the fitting parameters, [various]

chemicals.vapor_pressure.TRC_Antoine_extended_fitting_jacobian(Ts, Tc, to, A, B, C, n, E, F)

Calculates the jacobian of the TRC Antoine extended vapor pressure equation for use in fitting these parameters when experimental values are known.

Requires 7 coefficients specific to each chemical.

Parameters

Tslist[float]

Temperatures of fluid data points, [K]

Tcfloat

Critical temperature of fluid, [K]

tofloat

Fit temperature-transition parameter, [K]

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

nfloat

Fit parameter, [-]

Efloat

Fit parameter, [-]

Ffloat

Fit parameter, [-]

Returns

jaclist[list[float, 7], len(Ts)]

Matrix of derivatives of the equation with respect to the fitting parameters, [various]

Vapor Pressure Estimation Correlations

chemicals.vapor_pressure.Lee_Kesler(T, Tc, Pc, omega)

Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [1]; requires a chemical’s critical temperature and acentric factor.

The vapor pressure is given by:

$$\ln P^{sat}_r = f^{(0)} + \omega f^{(1)}$$

$$f^{(0)} = 5.92714-\frac{6.09648}{T_r}-1.28862\ln T_r + 0.169347T_r^6$$

$$f^{(1)} = 15.2518-\frac{15.6875}{T_r} - 13.4721 \ln T_r + 0.43577T_r^6$$

Parameters

Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

omegafloat

Acentric factor [-]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

This equation appears in [1] in expanded form. The reduced pressure form of the equation ensures predicted vapor pressure cannot surpass the critical pressure.

References

1(1,2)

Lee, Byung Ik, and Michael G. Kesler. “A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States.” AIChE Journal 21, no. 3 (1975): 510-527. doi:10.1002/aic.690210313.

2

Reid, Robert C..; Prausnitz, John M.;; Poling, Bruce E. The Properties of Gases and Liquids. McGraw-Hill Companies, 1987.

Examples

Example from [2]; ethylbenzene at 347.2 K.

>>> Lee_Kesler(347.2, 617.1, 36E5, 0.299)
13078.694162949312

chemicals.vapor_pressure.Ambrose_Walton(T, Tc, Pc, omega)

Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [1]; requires a chemical’s critical temperature and acentric factor.

The vapor pressure is given by:

$$\ln P_r=f^{(0)}+\omega f^{(1)}+\omega^2f^{(2)}$$

$$f^{(0)}=\frac{-5.97616\tau + 1.29874\tau^{1.5}- 0.60394\tau^{2.5} -1.06841\tau^5}{T_r}$$

$$f^{(1)}=\frac{-5.03365\tau + 1.11505\tau^{1.5}- 5.41217\tau^{2.5} -7.46628\tau^5}{T_r}$$

$$f^{(2)}=\frac{-0.64771\tau + 2.41539\tau^{1.5}- 4.26979\tau^{2.5} +3.25259\tau^5}{T_r}$$

$$\tau = 1-T_{r}$$

Parameters

Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

omegafloat

Acentric factor [-]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

Somewhat more accurate than the Lee_Kesler formulation.

References

1

Ambrose, D., and J. Walton. “Vapour Pressures up to Their Critical Temperatures of Normal Alkanes and 1-Alkanols.” Pure and Applied Chemistry 61, no. 8 (1989): 1395-1403. doi:10.1351/pac198961081395.

2

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

Examples

Example from [2]; ethylbenzene at 347.25 K.

>>> Ambrose_Walton(347.25, 617.15, 36.09E5, 0.304)
13278.878504306222

chemicals.vapor_pressure.boiling_critical_relation(T, Tb, Tc, Pc)

Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship as in [1]; requires a chemical’s critical temperature and pressure as well as boiling point.

The vapor pressure is given by:

$$\ln P^{sat}_r = h\left( 1 - \frac{1}{T_r}\right)$$

$$h = T_{br} \frac{\ln(P_c/101325)}{1-T_{br}}$$

Parameters

Tfloat

Temperature of fluid [K]

Tbfloat

Boiling temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

Units are Pa. Formulation makes intuitive sense; a logarithmic form of interpolation.

References

1(1,2)

Reid, Robert C..; Prausnitz, John M.;; Poling, Bruce E. The Properties of Gases and Liquids. McGraw-Hill Companies, 1987.

Examples

Example as in [1] for ethylbenzene

>>> boiling_critical_relation(347.2, 409.3, 617.1, 36E5)
15209.467273093938

chemicals.vapor_pressure.Sanjari(T, Tc, Pc, omega)

Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [1]. Requires a chemical’s critical temperature, pressure, and acentric factor. Although developed for refrigerants, this model should have some general predictive ability.

The vapor pressure of a chemical at T is given by:

$$P^{sat} = P_c\exp(f^{(0)} + \omega f^{(1)} + \omega^2 f^{(2)})$$

$$f^{(0)} = a_1 + \frac{a_2}{T_r} + a_3\ln T_r + a_4 T_r^{1.9}$$

$$f^{(1)} = a_5 + \frac{a_6}{T_r} + a_7\ln T_r + a_8 T_r^{1.9}$$

$$f^{(2)} = a_9 + \frac{a_{10}}{T_r} + a_{11}\ln T_r + a_{12} T_r^{1.9}$$

Parameters

Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

omegafloat

Acentric factor [-]

Returns

Psatfloat

Vapor pressure, [Pa]

Notes

a[1-12] are as follows: 6.83377, -5.76051, 0.90654, -1.16906, 5.32034, -28.1460, -58.0352, 23.57466, 18.19967, 16.33839, 65.6995, -35.9739.

For a claimed fluid not included in the regression, R128, the claimed AARD was 0.428%. A re-calculation using 200 data points from 125.45 K to 343.90225 K evenly spaced by 1.09775 K as generated by NIST Webbook April 2016 produced an AARD of 0.644%. It is likely that the author’s regression used more precision in its coefficients than was shown here. Nevertheless, the function is reproduced as shown in [1].

For Tc=808 K, Pc=1100000 Pa, omega=1.1571, this function actually declines after 770 K.

References

1(1,2)

Sanjari, Ehsan, Mehrdad Honarmand, Hamidreza Badihi, and Ali Ghaheri. “An Accurate Generalized Model for Predict Vapor Pressure of Refrigerants.” International Journal of Refrigeration 36, no. 4 (June 2013): 1327-32. doi:10.1016/j.ijrefrig.2013.01.007.

Examples

>>> Sanjari(347.2, 617.1, 36E5, 0.299)
13651.916109552523

chemicals.vapor_pressure.Edalat(T, Tc, Pc, omega)

Calculates vapor pressure of a fluid at arbitrary temperatures using a CSP relationship by [1]. Requires a chemical’s critical temperature, pressure, and acentric factor. Claimed to have a higher accuracy than the Lee-Kesler CSP relationship.

The vapor pressure of a chemical at T is given by:

$$\ln(P^{sat}/P_c) = \frac{a\tau + b\tau^{1.5} + c\tau^3 + d\tau^6} {1-\tau}$$

$$a = -6.1559 - 4.0855\omega$$

$$b = 1.5737 - 1.0540\omega - 4.4365\times 10^{-3} d$$

$$c = -0.8747 - 7.8874\omega$$

$$d = \frac{1}{-0.4893 - 0.9912\omega + 3.1551\omega^2}$$

$$\tau = 1 - \frac{T}{T_c}$$

Parameters

Tfloat

Temperature of fluid [K]

Tcfloat

Critical temperature of fluid [K]

Pcfloat

Critical pressure of fluid [Pa]

omegafloat

Acentric factor [-]

Returns

Psatfloat

Vapor pressure, [Pa]

Notes

[1] found an average error of 6.06% on 94 compounds and 1106 data points.

References

1(1,2)

Edalat, M., R. B. Bozar-Jomehri, and G. A. Mansoori. “Generalized Equation Predicts Vapor Pressure of Hydrocarbons.” Oil and Gas Journal; 91:5 (February 1, 1993).

Examples

>>> Edalat(347.2, 617.1, 36E5, 0.299)
13461.273080743307

Sublimation Pressure Estimation Correlations

chemicals.vapor_pressure.Psub_Clapeyron(T, Tt, Pt, Hsub_t)

Calculates sublimation pressure of a solid at arbitrary temperatures using an approximate themodynamic identity - the Clapeyron equation as described in [1] and [2]. Requires a chemical’s triple temperature, triple pressure, and triple enthalpy of sublimation.

The sublimation pressure of a chemical at T is given by:

$$\ln \frac{P}{P_{tp}} = -\frac{\Delta H_{sub}}{R} \left(\frac{1}{T}-\frac{1}{T_{tp}} \right)$$

Parameters

Tfloat

Temperature of solid [K]

Ttfloat

Triple temperature of solid [K]

Ptfloat

Truple pressure of solid [Pa]

Hsub_tfloat

Enthalpy of fusion at the triple point of the chemical, [J/mol]

Returns

Psubfloat

Sublimation pressure, [Pa]

Notes

Does not seem to capture the decrease in sublimation pressure quickly enough.

References

1

Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley. “Use of the DIPPR Database for the Development of QSPR Correlations: Solid Vapor Pressure and Heat of Sublimation of Organic Compounds.” International Journal of Thermophysics 25, no. 2 (March 1, 2004): 337-50. https://doi.org/10.1023/B:IJOT.0000028471.77933.80.

2

Feistel, Rainer, and Wolfgang Wagner. “Sublimation Pressure and Sublimation Enthalpy of H2O Ice Ih between 0 and 273.16K.” Geochimica et Cosmochimica Acta 71, no. 1 (January 1, 2007): 36-45. https://doi.org/10.1016/j.gca.2006.08.034.

Examples

>>> Psub_Clapeyron(250, Tt=273.15, Pt=611.0, Hsub_t=51100.0)
76.06457150831804
>>> Psub_Clapeyron(300, Tt=273.15, Pt=611.0, Hsub_t=51100.0)
4577.282832876156

Correlations for Specific Substances

chemicals.vapor_pressure.Psat_IAPWS(T)

Calculates vapor pressure of water using the IAPWS explicit equation.

$$P^{sat} = 10^6 \left[ \frac{2C}{-B + \sqrt{B^2 - 4AC}} \right]^4$$

$$A = \nu^2 + n_1 \nu + n_2$$

$$B = n_3 \nu^2 + n_4\nu + n_5$$

$$C = n_6\nu^2 + n_7\nu + n_8$$

$$\nu = T + \frac{n_9}{T - n_{10}}$$

Parameters

Tfloat

Temperature of water, [K]

Returns

Psatfloat

Vapor pressure at T [Pa]

Notes

This formulation is quite efficient, and can also be solved backward. The range of validity of this equation is 273.15 K < T < 647.096 K, the IAPWS critical point.

Extrapolation to lower temperatures is very poor. The function continues to decrease until a pressure of 5.7 mPa is reached at 159.77353993926621 K; under that pressure the vapor pressure increases, which is obviously wrong.

References

1

Kretzschmar, Hans-Joachim, and Wolfgang Wagner. International Steam Tables: Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Springer, 2019.

Examples

>>> Psat_IAPWS(300.)
3536.58941301301

chemicals.vapor_pressure.dPsat_IAPWS_dT(T)

Calculates the first temperature dervative of vapor pressure of water using the IAPWS explicit equation. This was derived with SymPy, using the CSE method.

Parameters

Tfloat

Temperature of water, [K]

Returns

dPsat_dTfloat

Temperature dervative of vapor pressure at T [Pa/K]

Notes

The derivative of this is useful when solving for water dew point.

References

1

Kretzschmar, Hans-Joachim, and Wolfgang Wagner. International Steam Tables: Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Springer, 2019.

Examples

>>> dPsat_IAPWS_dT(300.)
207.88388134164282

chemicals.vapor_pressure.Tsat_IAPWS(P)

Calculates the saturation temperature of water using the IAPWS explicit equation.

$$T_s = \frac{n_{10} + D - \left[(n_{10}+D)^2 - 4(n_9 + n_{10}D) \right]^{0.5}}{2}$$

$$E = \beta^2 + n_3 \beta + n_6$$

$$F = n_1 \beta^2 + n_4\beta + n_7$$

$$G = n_2\beta^2 + n_5\beta + n_8$$

$$\beta = \left(P_{sat} \right)^{0.25}$$

Parameters

Psatfloat

Vapor pressure at T [Pa]

Returns

Tfloat

Temperature of water along the saturation curve at Psat, [K]

Notes

The range of validity of this equation is 273.15 K < T < 647.096 K, the IAPWS critical point.

The coefficients n1 to n10 are (0.11670521452767E4, -0.72421316703206E6, -0.17073846940092E2, 0.12020824702470E5, -0.32325550322333E7, 0.14915108613530E2, -0.48232657361591E4, 0.40511340542057E6, -0.23855557567849, 0.65017534844798E3)

References

1

Kretzschmar, Hans-Joachim, and Wolfgang Wagner. International Steam Tables: Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Springer, 2019.

Examples

>>> Tsat_IAPWS(1E5)
372.75591861133773

Analytical Fit Equations

chemicals.vapor_pressure.Antoine_coeffs_from_point(T, Psat, dPsat_dT, d2Psat_dT2, base=10.0)

Calculates the antoine coefficients A, B, and C from a known vapor pressure and its first and second temperature derivative.

Parameters

Tfloat

Temperature of fluid, [K]

Psatfloat

Vapor pressure at specified T [Pa]

dPsat_dTfloat

First temperature derivative of vapor pressure at specified T [Pa/K]

d2Psat_dT2float

Second temperature derivative of vapor pressure at specified T [Pa/K^2]

Basefloat, optional

Base of logarithm; 10 by default

Returns

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Cfloat

Antoine C parameter, [K]

Notes

Coefficients are for calculating vapor pressure in Pascal. This is primarily useful for interconverting vapor pressure models, not fitting experimental data.

Derived with SymPy as follows:

>>> from sympy import * 
>>> base, A, B, C, T = symbols('base, A, B, C, T') 
>>> v = base**(A - B/(T + C)) 
>>> d1, d2 = diff(v, T), diff(v, T, 2) 
>>> vk, d1k, d2k = symbols('vk, d1k, d2k') 
>>> solve([Eq(v, vk), Eq(d1, d1k), Eq(d2, d2k)], [A, B, C]) 

References

1

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

Examples

Recalculate some coefficients from a calcualted value and its derivative:

>>> T = 178.01
>>> A, B, C = (24.0989474955895, 4346.793091137991, -18.96968471040141)
>>> Psat = Antoine(T, A, B, C, base=exp(1))
>>> dPsat_dT, d2Psat_dT2 = (0.006781441203850251, 0.0010801244983894853) # precomputed
>>> Antoine_coeffs_from_point(T, Psat, dPsat_dT, d2Psat_dT2, base=exp(1))
(24.098947495155, 4346.793090994, -18.969684713118)

chemicals.vapor_pressure.Antoine_AB_coeffs_from_point(T, Psat, dPsat_dT, base=10.0)

Calculates the antoine coefficients A, B, with C set to zero to improve low-temperature or high-temperature extrapolation, from a known vapor pressure and its first temperature derivative.

Parameters

Tfloat

Temperature of fluid, [K]

Psatfloat

Vapor pressure at specified T [Pa]

dPsat_dTfloat

First temperature derivative of vapor pressure at specified T [Pa/K]

Basefloat, optional

Base of logarithm; 10 by default

Returns

Afloat

Antoine A parameter, [-]

Bfloat

Antoine B parameter, [K]

Notes

Coefficients are for calculating vapor pressure in Pascal. This is primarily useful for interconverting vapor pressure models, not fitting experimental data.

Derived with SymPy as follows:

>>> from sympy import * 
>>> base, A, B, T = symbols('base, A, B, T') 
>>> v = base**(A - B/T) 
>>> d1, d2 = diff(v, T), diff(v, T, 2) 
>>> vk, d1k = symbols('vk, d1k') 
>>> solve([Eq(v, vk), Eq(d1, d1k)], [A, B]) 

References

1

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

Examples

Recalculate some coefficients from a calcualted value and its derivative:

>>> T = 178.01
>>> A, B = (27.358925161569008, 5445.569591293226)
>>> Psat = Antoine(T, A, B, C=0, base=exp(1))
>>> dPsat_dT = B*exp(1)**(A - B/T)*log(exp(1))/T**2
>>> Antoine_AB_coeffs_from_point(T, Psat, dPsat_dT, base=exp(1))
(27.35892516156901, 5445.569591293226)

chemicals.vapor_pressure.DIPPR101_ABC_coeffs_from_point(T, Psat, dPsat_dT, d2Psat_dT2)

Calculates the first three DIPPR101 coefficients A, B, and C from a known vapor pressure and its first and second temperature derivative.

If the second derivative is infinity as is the case in some vapor pressure models at the critical point, only the A and C coefficients are fit, using the first derivative an the actual value of vapor pressure.

Parameters

Tfloat

Temperature of fluid, [K]

Psatfloat

Vapor pressure at specified T [Pa]

dPsat_dTfloat

First temperature derivative of vapor pressure at specified T [Pa/K]

d2Psat_dT2float

Second temperature derivative of vapor pressure at specified T [Pa/K^2]

Returns

Afloat

DIPPR101 A parameter (same as Antoine A), [-]

Bfloat

DIPPR101 B parameter (same as Antoine B), [K]

C: float

DIPPR101 C parameter (NOT same as Antoine C, multiplied by log(T)), [-]

Notes

Coefficients are for calculating vapor pressure in Pascal. This is primarily useful for interconverting vapor pressure models, not fitting experimental data.

Derived with SymPy as follows:

>>> from sympy import * 
>>> base, A, B, C, T = symbols('base, A, B, C, T') 
>>> v = exp(A + B/T + C*log(T)) 
>>> d1, d2 = diff(v, T), diff(v, T, 2) 
>>> vk, d1k, d2k = symbols('vk, d1k, d2k') 
>>> solve([Eq(v, vk), Eq(d1, d1k), Eq(d2, d2k)], [A, B, C]) 

Examples

Calculate the coefficients:

>>> T = 178.01
>>> Psat, dPsat_dT, d2Psat_dT2 = (0.03946094565666715, 0.006781441203850251, 0.0010801244983894853)
>>> DIPPR101_ABC_coeffs_from_point(T, Psat, dPsat_dT, d2Psat_dT2)
(72.47169926642, -6744.620564969, -7.2976291987890)

Fit Coefficients

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

chemicals.vapor_pressure.Psat_data_WagnerMcGarry

Coefficients for the Wagner 3,6 original model equation documented in Wagner_original with data for 245 chemicals, from [1].

chemicals.vapor_pressure.Psat_data_WagnerPoling

Coefficients for the Wagner 2.5, 5 model equation documented in Wagner in [2], with data for 104 chemicals.

chemicals.vapor_pressure.Psat_data_AntoinePoling

Standard Antoine equation coefficients, as documented in the function Antoine and with data for 325 fluids from [2]. Coefficients were altered to be in units of Pa and Celcius.

chemicals.vapor_pressure.Psat_data_AntoineExtended

Data for 97 chemicals in [2] for the TRC extended Antoine model TRC_Antoine_extended.

chemicals.vapor_pressure.Psat_data_Perrys2_8

A collection of 341 coefficient sets for thermo.dippr.EQ101 from the DIPPR database published openly in [4].

chemicals.vapor_pressure.Psat_data_VDI_PPDS_3

Coefficients for the Wagner equation Wagner, published openly in [3].

chemicals.vapor_pressure.Psat_data_Alcock_elements

Coefficients for the DIPPR 101 equation chemicals.dippr.EQ101, published in [5] and converted to provide base SI units (and use the natural logarithm).

chemicals.vapor_pressure.Psub_data_Alcock_elements

Coefficients for the DIPPR 101 equation chemicals.dippr.EQ101, published in [5] and converted to provide base SI units (and use the natural logarithm). Note this is a sublimation pressure data set.

chemicals.vapor_pressure.Psub_data_Landolt_Antoine

Standard Antoine equation coefficients for sublimation pressure, as documented in the function Antoine and with data for ~1000 solids from [6], [7], and [8]. Coefficients were altered to be in units of Pa and Kelvin with the exponential instead of base-10 power.

chemicals.vapor_pressure.Psat_data_Landolt_Antoine

Standard Antoine equation coefficients for vapor pressure, as documented in the function Antoine and with data for ~6000 liquids from [6], [7], and [8]. Coefficients were altered to be in units of Pa and Kelvin with the exponential instead of base-10 power.

1

McGarry, Jack. “Correlation and Prediction of the Vapor Pressures of Pure Liquids over Large Pressure Ranges.” Industrial & Engineering Chemistry Process Design and Development 22, no. 2 (April 1, 1983): 313-22. doi:10.1021/i200021a023.

2(1,2,3)

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

3

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

4

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

5(1,2)

Alcock, C. B., V. P. Itkin, and M. K. Horrigan. “Vapour Pressure Equations for the Metallic Elements: 298-2500K.” Canadian Metallurgical Quarterly 23, no. 3 (July 1, 1984): 309-13. https://doi.org/10.1179/cmq.1984.23.3.309.

6(1,2)

Hall, K. R. Vapor Pressure and Antoine Constants for Hydrocarbons, and S, Se, Te, and Halogen Containing Organic Compounds. Springer, 1999.

7(1,2)

Dykyj, J., and K. R. Hall. “Vapor Pressure and Antoine Constants for Oxygen Containing Organic Compounds”. 2000.

8(1,2)

Hall, K. R. Vapor Pressure and Antoine Constants for Nitrogen Containing Organic Compounds. Springer, 2001.

The structure of each dataframe is shown below:

In [1]: import chemicals

In [2]: chemicals.vapor_pressure.Psat_data_WagnerMcGarry
Out[2]: 
                                    Name        A  ...      Tc   Tmin
CAS                                                ...               
50-00-0                     formaldehyde -7.29343  ...  408.00  184.0
56-23-5             carbon tetrachloride -7.07139  ...  556.40  250.0
60-29-7                     diethylether -7.29916  ...  466.74  250.0
62-53-3                          aniline -7.65517  ...  699.00  376.0
64-17-5                          ethanol -8.51838  ...  513.92  293.0
...                                  ...      ...  ...     ...    ...
7732-18-5                          water -7.76451  ...  647.35  275.0
7782-41-4                       fluorine -6.18224  ...  144.31   64.0
7782-44-7                         oxygen -6.28275  ...  154.70   54.0
16747-38-9    2,3,3,4-tetramethylpentane -7.65000  ...  607.60  332.0
16747-50-5  l-methyl-l-ethylcyclopentane -7.09092  ...  592.00  316.0

[245 rows x 8 columns]

In [3]: chemicals.vapor_pressure.Psat_data_WagnerPoling
Out[3]: 
                                                         Name  ...    Tmax
CAS                                                            ...        
60-29-7                                        diethyl ether   ...  466.74
64-17-5                                              ethanol   ...  513.92
64-18-6                                       methanoic acid   ...  588.00
64-19-7                                        ethanoic acid   ...  592.71
67-56-1                                             methanol   ...  512.64
...                                                       ...  ...     ...
7727-37-9                                           nitrogen   ...  126.20
7783-81-5                               uranium hexafluoride   ...  503.35
13838-16-9  2-chloro-1,1,2-trifluoroethyl difluoromethyl e...  ...  475.03
26171-83-5                                     1,2-butandiol   ...  506.40
26675-46-7  1-chloro-2,2,2-trifluoroethyl difluoromethyl e...  ...  467.80

[104 rows x 9 columns]

In [4]: chemicals.vapor_pressure.Psat_data_AntoinePoling
Out[4]: 
                                Chemical         A  ...    Tmin    Tmax
CAS                                                 ...                
56-23-5              tetrachloromethane    9.10445  ...  259.00  373.76
60-29-7                   diethyl ether    9.10962  ...  229.71  328.31
62-53-3                    benzeneamine    9.40870  ...  349.86  484.81
64-17-5                         ethanol   10.33675  ...  276.50  369.54
64-19-7                   ethanoic acid    9.54456  ...  297.58  414.97
...                                  ...       ...  ...     ...     ...
14762-55-1                     helium-3    6.39750  ...    1.12    4.41
16747-38-9   2,3,3,4-tetramethylpentane    8.99105  ...  307.81  443.27
20291-95-6       2,2,5-trimethylheptane    9.00345  ...  318.00  452.00
800000-51-5            hydrogen, normal    7.94928  ...   13.33   22.94
800000-54-8           deuterium, normal    8.25315  ...   17.57   26.23

[325 rows x 6 columns]

In [5]: chemicals.vapor_pressure.Psat_data_AntoineExtended
Out[5]: 
                                      Chemical        A  ...    Tmin    Tmax
CAS                                                      ...                
62-53-3                          benzeneamine   9.40870  ...  488.15  673.15
74-85-1                                ethene   8.91382  ...  188.15  273.15
74-89-5                           methanamine   9.21300  ...  288.15  423.15
75-04-7                            ethanamine   8.88560  ...  308.15  443.15
75-10-5                       difluoromethane   9.29712  ...  238.15  338.15
...                                        ...      ...  ...     ...     ...
1067-08-9             3-ethyl-3-methylpentane   8.98950  ...  408.15  543.15
1511-62-2                bromodifluoromethane   8.40030  ...  273.15  403.15
1640-89-7                   ethylcyclopentane   9.00408  ...  408.15  569.52
1717-00-6         1,1-dichloro-1-fluoroethane   9.03117  ...  333.15  473.15
2837-89-0  1-chloro-1,2,2,2-tetrafluoroethane   8.98581  ...  283.15  383.15

[97 rows x 11 columns]

In [6]: chemicals.vapor_pressure.Psat_data_Perrys2_8
Out[6]: 
                           Chemical       C1        C2  ...   C5    Tmin    Tmax
CAS                                                     ...                     
50-00-0               Formaldehyde   101.510  -4917.20  ...  1.0  181.15  408.00
55-21-0                 Benzamide     85.474 -11932.00  ...  6.0  403.00  824.00
56-23-5       Carbon tetrachloride    78.441  -6128.10  ...  2.0  250.33  556.35
57-55-6      1,2-Propylene glycol    212.800 -15420.00  ...  2.0  213.15  626.00
60-29-7             Diethyl ether    136.900  -6954.30  ...  1.0  156.85  466.70
...                             ...      ...       ...  ...  ...     ...     ...
10028-15-6                  Ozone     40.067  -2204.80  ...  6.0   80.15  261.00
10035-10-6       Hydrogen bromide     29.315  -2424.50  ...  6.0  185.15  363.15
10102-43-9           Nitric oxide     72.974  -2650.00  ...  6.0  109.50  180.15
13511-13-2    Propenylcyclohexene     64.268  -7298.90  ...  6.0  199.00  636.00
132259-10-0                   Air     21.662   -692.39  ...  1.0   59.15  132.45

[340 rows x 8 columns]

In [7]: chemicals.vapor_pressure.Psat_data_VDI_PPDS_3
Out[7]: 
                         Chemical      Tm      Tc  ...        B        C        D
CAS                                                ...                           
50-00-0              Formaldehyde  181.15  408.05  ...  1.28290 -0.50464 -4.29089
56-23-5      Carbon tetrachloride  250.25  556.35  ...  1.96174 -2.05900 -3.26771
56-81-5                  Glycerol  291.45  850.05  ... -0.33345 -5.98569 -1.33011
60-29-7             Diethyl ether  156.75  466.63  ...  2.15613 -3.02766 -2.37858
62-53-3                   Aniline  267.15  699.05  ...  1.96206 -3.65571 -2.00622
...                           ...     ...     ...  ...      ...      ...      ...
10097-32-2                Bromine  265.85  584.15  ...  1.50339 -0.64097 -3.62166
10102-43-9           Nitric oxide  112.15  180.15  ...  0.85755 -3.11447 -8.98765
10102-44-0       Nitrogen dioxide  261.85  431.15  ...  2.37620  0.67820 -2.53997
10544-72-6    Dinitrogentetroxide  261.85  431.10  ...  3.10196  0.59704 -5.33648
132259-10-0                   Air   63.05  132.53  ... -0.21537  0.93623 -3.02641

[275 rows x 8 columns]

In [8]: chemicals.vapor_pressure.Psat_data_Alcock_elements
Out[8]: 
                   name           A             B  ...    E       Tmin    Tmax
CAS                                                ...                        
7439-93-2       lithium   30.888526 -19157.507974  ... -3.0   453.6500  1000.0
7440-23-5        sodium   30.867803 -12972.764414  ... -3.0   370.9440   700.0
7440-09-7     potassium   30.483272 -10806.031841  ... -3.0   336.6500   600.0
7440-17-7      Rubidium   30.674386  -9843.551273  ... -3.0   312.4500   550.0
7440-46-2       Caesium   30.480969  -9353.100648  ... -3.0   301.6500   550.0
7429-90-5     Aluminium   35.882834 -39019.606986  ... -3.0   933.4730  1800.0
7440-55-3       gallium   19.870657 -31842.449251  ... -3.0   302.9146  1600.0
7440-74-6        Indium   34.365430 -28938.889449  ... -3.0   429.7500  1500.0
7440-28-0      Thallium   31.392793 -21605.155928  ... -3.0   577.1500  1100.0
7440-31-5           Tin   17.786817 -34785.153000  ... -3.0   505.0780  1850.0
7439-92-1          Lead   31.171744 -23239.991344  ... -3.0   600.6120  1200.0
7440-65-5       Yttrium   43.175121 -51151.927841  ... -3.0  1795.1500  2300.0
7439-91-0     Lanthanum   26.548154 -50603.912589  ... -3.0  1193.1500  2450.0
7440-32-6      Titanium   49.219406 -58091.919311  ... -3.0  1943.1500  2400.0
7440-67-7     Zirconium   15.173383 -66231.557615  ... -3.0  2127.1500  2500.0
7440-06-4      Platinum   60.472140 -71198.233660  ... -3.0  2041.3500  2500.0
7440-50-8        Copper   37.335765 -40127.150416  ... -3.0  1357.7700  1850.0
7440-57-5          Gold   35.238110 -43514.253087  ... -3.0  1337.3300  2050.0
7440-45-1        Cerium   25.394558 -48994.405609  ... -3.0  1072.1500  2450.0
7440-10-0  Praseodymium   38.965995 -43042.223143  ... -3.0  1204.1500  2200.0
7440-00-8     Neodymium   40.068933 -39717.290269  ... -3.0  1289.1500  2000.0
7440-54-2    Gadolinium   35.947306 -47214.507332  ... -3.0  1586.1500  2250.0
7440-27-9       Terbium   38.703500 -46171.436285  ... -3.0  1632.1500  2200.0
7439-94-3      Lutetium   54.932120 -54202.853089  ... -3.0  1936.1500  2350.0
7440-29-1       Thorium  148.700293 -85151.899324  ... -3.0  2023.1500  2500.0
7440-13-3  Protactinium   35.081534 -78331.642279  ... -3.0  1845.1500  2500.0
7439-99-8     Neptunium   48.979938 -55303.488764  ... -3.0   917.1500  2500.0
7440-07-5     Plutonium   41.441274 -40495.564030  ... -3.0   913.1500  2450.0
7440-51-9        Curium   56.511693 -49353.608883  ... -3.0  1618.1500  2200.0
7440-41-7     Beryllium   24.848846 -36221.966098  ... -3.0  1560.1500  1800.0
7440-39-3        Barium   20.752547 -18796.002114  ... -3.0  1000.1500  1200.0
7440-20-2      Scandium   24.869569 -40712.007029  ... -3.0  1814.1500  2000.0
7440-62-2      Vanadium   27.480701 -57589.955761  ... -3.0  2183.1500  2500.0
7439-89-6          Iron   26.140596 -45070.800610  ... -3.0  1811.1500  2100.0
7440-48-4        Cobalt   26.465261 -47382.596044  ... -3.0  1768.1500  2150.0
7440-02-0        Nickel   26.875121 -47813.179456  ... -3.0  1728.1500  2150.0
7440-05-3     Palladium   24.019915 -41213.970580  ... -3.0  1827.9500  2100.0
7440-22-4        Silver   24.770558 -31837.844081  ... -3.0  1234.9300  1600.0
7440-66-6          Zinc   23.909391 -14474.049895  ... -3.0   692.6770   750.0
7440-43-9       Cadmium   23.596240 -12415.538821  ... -3.0   594.2190   650.0
7439-97-6       Mercury   23.306114  -7345.246447  ... -3.0   298.0000   400.0
7440-52-0        Erbium   22.320607 -33111.173637  ... -3.0  1802.1500  1900.0
7440-61-1       Uranium   59.270190 -66259.188636  ... -3.0  1408.1500  2500.0

[43 rows x 8 columns]

In [9]: chemicals.vapor_pressure.Psub_data_Alcock_elements
Out[9]: 
          Name           A             B        C         D   Tmin      Tmax
CAS                                                                         
7440-22-4   Ag   29.290532 -34389.108364  -0.2779 -0.000392  298.0  1234.930
7429-90-5   Al   27.929705 -39710.382514   0.0639 -0.000776  298.0   933.473
7440-35-9   Am   27.591225 -34202.598971   0.1914 -0.001082  298.0  1449.150
7440-57-5   Au   30.027360 -44419.169029  -0.3496 -0.000294  298.0  1337.330
7440-39-3   Ba   30.874711 -21929.820426  -0.8280 -0.001278  298.0  1000.150
7440-41-7   Be   22.884741 -38842.307934   0.6521 -0.000739  298.0  1560.150
7440-70-2   Ca   22.465670 -21363.384493   0.5348 -0.001558  298.0  1115.150
7440-43-9   Cd   30.879316 -13686.565793  -0.8052  0.000000  298.0   594.219
7440-45-1   Ce   28.427063 -50274.642920  -0.3851  0.000061  298.0  1072.150
7440-51-9   Cm   19.748620 -46346.432752   1.1098 -0.001112  298.0  1618.150
7440-48-4   Co   26.345526 -51458.171658   0.5578 -0.000994  298.0  1768.150
7440-50-8   Cu   29.509278 -40725.822540  -0.2638 -0.000342  298.0  1357.770
7429-91-6   Dy   28.067860 -35038.437360  -0.2717 -0.000542  298.0  1685.150
7440-52-0   Er   29.184614 -38059.429002  -0.4312 -0.000487  298.0  1802.150
7440-53-1   Eu   26.444537 -21506.144769  -0.1659 -0.000829  298.0  1095.150
7440-54-2   Gd   23.402822 -47677.326936   0.5450 -0.000752  298.0  1586.150
7440-58-6   Hf   32.101989 -74716.583683  -0.5041 -0.000076  298.0  2506.150
7440-60-0   Ho   26.497497 -36228.873853  -0.0278 -0.000724  298.0  1745.150
7440-74-6   In   31.171744 -29196.778979  -0.8495  0.000000  298.0   429.750
7439-88-5   Ir   33.812810 -80687.186829  -0.4773 -0.000114  298.0  2500.000
7439-91-0   La   28.827713 -51930.201602  -0.3323  0.000014  298.0  1193.150
7439-93-2   Li   29.463226 -19394.674238  -0.7074  0.000000  298.0   453.650
7439-94-3   Lu   28.443181 -51455.869073  -0.1187 -0.000297  298.0  1936.150
7439-96-5   Mn   26.502102 -34064.443866   0.4354 -0.001522  298.0  1519.150
7439-98-7   Mo   30.375050 -79178.993593  -0.0374 -0.000441  298.0  2500.000
7440-03-1   Nb   29.016525 -86874.232974   0.1441 -0.000163  298.0  2500.000
7440-00-8   Nd   21.984430 -39284.404272   0.6421 -0.001205  298.0  1289.150
7440-02-0   Ni   33.163481 -51916.386092  -0.4663 -0.000257  298.0  1728.150
7439-99-8   Np   38.201537 -56556.095054  -1.0343 -0.002741  298.0   917.150
7440-04-2   Os   35.371660 -95034.594543  -0.6908  0.000106  298.0  2500.000
7440-13-3   Pa   22.120282 -79441.488293   1.0093 -0.001063  298.0  1845.150
7439-92-1   Pb   30.720438 -23723.534213  -0.8782  0.000000  298.0   600.612
7440-05-3   Pd   29.541514 -45425.398715  -0.3414 -0.000359  298.0  1827.950
7440-10-0   Pr   23.423546 -42726.768986   0.3775 -0.001047  298.0  1204.150
7440-07-5   Pu   55.178497 -40546.220903  10.5178 -0.020075  298.0   600.000
7440-15-5   Re   33.096706 -93369.825521  -0.4647 -0.000242  298.0  2500.000
7440-16-6   Rh   31.606933 -66597.668645  -0.2168 -0.000248  298.0  2236.150
7440-18-8   Ru   25.212654 -78046.121727   0.7895 -0.000548  298.0  2606.150
7440-19-9   Sm   20.462421 -24759.697505   0.8499 -0.001609  298.0  1345.150
7440-31-5   Sn   30.577678 -36459.132362  -0.7398  0.000000  298.0   505.078
7440-24-6   Sr   22.599220 -19307.176005   0.4150 -0.001375  298.0  1050.150
7440-27-9   Tb   26.400788 -46758.595483   0.1472 -0.000706  298.0  1632.150
7440-29-1   Th   39.051191 -72950.500916  -1.6430  0.000580  298.0  2023.150
7440-28-0   Tl   32.235539 -22160.078935  -0.9887  0.000000  298.0   577.150
7440-32-6   Ti   29.265204 -57039.637924   0.1252 -0.000864  298.0  1943.150
7440-30-4   Tm   27.786944 -28056.999358  -0.3098 -0.000465  298.0  1400.000
7440-62-2    V   28.917514 -62188.218192   0.1970 -0.000394  298.0  2183.150
7440-33-7    W -242.181947 -65425.652832  35.4537 -0.008302  220.0  2500.000
7440-65-5    Y   26.310987 -50974.628789   0.2848 -0.000714  298.0  1795.150
7440-66-6   Zn   30.948394 -15940.796599  -0.7523  0.000000  298.0   692.677
7440-67-7   Zr   29.437898 -72245.909878  -0.0354 -0.000382  298.0  2127.150

In [10]: chemicals.vapor_pressure.Psub_data_Landolt_Antoine
Out[10]: 
                                                          Name  ...   Tmax
CAS                                                             ...       
50-29-3      2,2-Bis(4-chlorophenyl)-1,1,1-trichloroethane,...  ...  354.0
50-32-8                                         Benzo[a]pyrene  ...  431.0
50-36-2                                                Cocaine  ...  314.0
51-17-2                                          Benzimidazole  ...  340.0
51-28-5                                      2,4-Dinitrophenol  ...  333.0
...                                                        ...  ...    ...
900000-38-6  Hexamethylbenzene-1-chloro-2,4,6-trinitrobenze...  ...  631.0
900000-42-2               Hydrido-hexacarbonyl-rhenium complex  ...  369.0
900001-70-9        Bis(chloroethylene)(2,4-pentandione)iridium  ...  298.0
900001-71-0       Bis(chloroethylene)(2,4-pentandione)-rhodium  ...  288.0
900002-52-0                 2,4-Dimethyl-1,3,5-trinitrobenzene  ...  412.0

[1084 rows x 6 columns]

In [11]: chemicals.vapor_pressure.Psat_data_Landolt_Antoine
Out[11]: 
                                                          Name  ...   Tmax
CAS                                                             ...       
50-00-0                                               Methanal  ...  271.0
51-66-1                                  p-Methoxy-acetanilide  ...  533.0
51-75-2                        N-Methylbis(2-chloroethyl)amine  ...  333.0
51-79-6                                               Urethane  ...  457.0
51-80-9                  N,N,N’,N’-Tetramethyl-methane diamine  ...  348.0
...                                                        ...  ...    ...
900002-32-6  (+,-)-1-Cyclohexyl-6-cyclopentyl-3-phenethylhe...  ...  525.0
900002-51-9                           3-Chloro-2-buten-1-thiol  ...  397.0
900002-53-1                              2,4-Dinitro-thiophene  ...  566.0
900002-55-3  2,5-Dichloro-1-methyl-4-(1,1-dimethylethyl)ben...  ...  538.0
900002-56-4  Oxobis(trifluoro-methyl) bis[[2,2,2-trifluoro-...  ...  333.0

[6346 rows x 6 columns]