Local thermodynamic consistency of vapor‐liquid equilibrium data for binary and multicomponent systems

Stevenson, F. D.; Sater, V. E.

doi:10.1002/aic.690120335

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…The physical meaning of the derivation in our work is clear and its assumptions are accessible. This is because

is usually considered as a negligible factor in many studies, and Equation (5) is a common formula that can be used to examine activity coefficient experimental data for thermodynamic consistency [ 26 , 27 , 28 ].…”

Section: Theorymentioning

confidence: 99%

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

Zheng

Chen

Wang

et al. 2022

IJMS

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In this work, we propose the idea of considering \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) as an infinite dilution thermodynamic function. Our research shows that \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: \({\ln \left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}=\frac{A}{T}+B}\). Then, we use this equation to correlate the isothermal vapor–liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs–Duhem equation to re-derive the relationship between \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) and the infinite dilution activity coefficient (\({\gamma^{\infty}}\)) at low pressure. Based on the definition of partial molar volume, an equation for \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky–Kasarnovsky equation, the developed model provides more reliable results.

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“…The physical meaning of the derivation in our work is clear and its assumptions are accessible. This is because

Section: Theorymentioning

confidence: 99%

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

Zheng

Chen

Wang

et al. 2022

IJMS

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“…The thermodynamic consistency test discussed here is based on the Gibbs-Duhem equation integrated over an interval from data point a to an adjacent data point b. The utility of such a test has been illustrated by Stevenson and Sater (1966), who wrote the test equation as Consider a function (zi, z2, z3,----zk) where each of the Zt, i = 1 to k, are independent and contain normally distributed random error with a known standard deviation sZi. The standard deviation for the error in H at any fixed point is then given approximately by (3) Ind.…”

Section: Thermodynamic Consistency Testmentioning

confidence: 99%

Effects of Experimental Errors on Thermodynamic Consistency and on Representation of Vapor-Liquid Equilibrium Data

Ulrichson¹,

Stevenson²

1972

Ind. Eng. Chem. Fund.

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A thermodynamic consistency test based on the "local area" test is developed which permits analysis of vapor-liquid equilibrium data in terms of measurement uncertainties in the independent variables. The effect of random measurement errors on the consistency test and on the uncertainty in the activity coefficients is illustrated. Uncertainty in the measurement of liquid composition may cause large uncertainty in the activity coefficients but be difficult to detect by means of consistency test. Comparing the test results to the null value is shown to be of less value than comparison with the bounds of a confidence region.

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“…Consistency Tests Numerous forms of consistency tests exist (38)(39)(40)(41)(42)(43), most of which are based directly on the Gibbs-Duhem equation. When the thermodynamic data satisfy the Gibbs-Duhem equation, it is likely, but by no means certain, that they are correct but, if they do not satisfy this equation, it is certain that they are incorrect.…”

Section: Thermodynamic Analysismentioning

confidence: 99%

Phase Equilibria in the Systems Acetone–Methanol, Acetone–Cyclohexane, Methanol–Cyclohexane, and Acetone–Methanol–Cyclohexane

Campbell¹,

Anand²

1972

Can. J. Chem.

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The vapor pressure and vapor composition of the methanol-cyclohexane system were investigated at temperatures ranging from 25 to 50' . The same properties of the binary systems: acetone-methanol and acetone-cyclohexane, as well as those of the ternary system : methanol-cyclohexane-acetone, were determined experimentally at 25'. The total pressures and compositions of the vapor for solutions lying close to the critical solution temperature of the binary system or close to the plait point of the ternary system are constant within the range of experimental accuracy. All these systems show azeotropic behavior. The methanol-cyclohexane system has an equimolar excess Gibbs free energy, GE, at 25' of 384.7 cal/mol, while the corresponding equimolar value of GE for the acetone-methanol system at 25' is 102.6 and for the acetone-cyclohexane system, at 25", it is 274.5 cal/mol. La pression de vapeur et la composition de vapeur du systeme methanol-cyclohexane ont Cte ttudites sur une echelle de temperature allant de 25 A 50". Les m&mes proprietes des systtmes binaires: acetone-methanol et acetone-cyclohexane, ainsi que celles des systemes ternaires: methanol-cyclohexane-acetone, ont ete determinees experimentalement a 25". Les pressions totales et les compositions de la vapeur pour des solutions proches de la temperature critique de la solution du systtme binaire ou proches du point de plissement du systeme ternaire, sont constantes dans I'intervalle d'exactitude experimental. Tous ces systemes montrent un comportement azeotropique. Le systeme methanol-cyclohexane a un excts d'energie libre tquimolaire de Gibbs, GE, de 384.7 cal/mol a 25", alors que les valeurs tquimolaires correspondantes de GE pour le systtme acetone-methanol est de 102.6 a 25" et pour le systeme acetone-cyclohexane de 274.5 cal/mol a 25".

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Local thermodynamic consistency of vapor‐liquid equilibrium data for binary and multicomponent systems

Abstract: Y = viscosity vw LITERATURE CITED = viscosity, defined by Equation (2)

Cited by 8 publications

References 13 publications

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

Effects of Experimental Errors on Thermodynamic Consistency and on Representation of Vapor-Liquid Equilibrium Data

Phase Equilibria in the Systems Acetone–Methanol, Acetone–Cyclohexane, Methanol–Cyclohexane, and Acetone–Methanol–Cyclohexane

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