One-Parameter Equation for Excess Gibbs Energy of Strongly Nonideal Liquid Mixtures

Bruin, S.; Prausnitz, John M.

doi:10.1021/i260040a024

Cited by 30 publications

(18 citation statements)

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“…NRTL was proposed by Ranon and Prausnitz [15][16][17] and is based on the assumption that the local concentration around a molecule is different from Tetramethylthiourea Electrosorption Data the bulk concentration (non-randomness is caused by energetic differences). The authors developed a new equation for the excess Gibbs energy by introducing a constant characteristic of the non-randomness of the mixture into the expression for the local mole fractions.…”

Section: Theorymentioning

confidence: 99%

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The correct interpretation of tetramethylthiourea electrosorption data in 3 M NaClO4 solution

Nieszporek

2011

Collect. Czech. Chem. Commun.

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Tetramethylthiourea (TMTU) electrosorption behaviour at the mercury electrode in 3 M NaClO 4 has been examined. Using a new concept of adsorption isotherm, new theoretical expressions have been proposed. The application of these equations shows evident influence of the electrode charge on the TMTU adsorption. It can be concluded that TMTU molecules are largely specifically bonded and at zero electrode charge the change of adsorbed TMTU molecules orientation is observed. Keywords: Tetramethylthiourea; Standard free energy of adsorption; Flory-Huggins isotherm; Non-random two liquid model.The addition of organic compounds to aqueous solutions with a polarizable surface makes it possible to easily control the electrical variables. For example, thiourea, tertbutanol or tetramethylthiourea (TMTU) 1-5 can significantly affect the kinetics of ions electroreduction at the mercury electrode. Small additions of those substances can increase or decrease the rate of electrode processes. Such behaviour is commonly explained by the adsorption of organics at the electrode surface. In the chemical structure of thiourea and its derivatives a double bond is preesent between carbon and sulfur atoms. They adsorb at the mercury electrode through covalent bond formation. Earlier studies 6,7 showed that the standard free energy of adsorption ∆G 0 of TMTU is evidently larger than for thiourea. Undoubtedly, four -CH 3 groups which are typically hydrophobic significantly affect TMTU adsorption. Its molecular structure also suggests the possibility of an insignificant change of vertical orientation at the electrode surface.The investigation of organic compounds adsorption can provide a lot of important information helpful to understand the phenomena which occur during ion electroreduction at the electrode 8-14 . For example, the adsorp-

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Section: Theorymentioning

confidence: 99%

“…However, it seems that during the process of adsorption the adsorbed molecules sometimes form clusters [15][16][17] . In such a case another isotherm expression must be used that would better correspond to the investigated adsorption system.…”

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confidence: 99%

The correct interpretation of tetramethylthiourea electrosorption data in 3 M NaClO4 solution

Nieszporek

2011

Collect. Czech. Chem. Commun.

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“…One of the main disadvantages of the NRTL model is the strong correlation between the two energy interaction parameters ( and ). A number of researchers [9][10][11][12][13] have attempted to modify the original NRTL model to eliminate or reduce the correlation. Many of the modified models presented in the literature, however, were not successful in decoupling the energy interaction parameters between like and unlike molecules.…”

Section: Introductionmentioning

confidence: 99%

One-parameter modified nonrandom two-liquid (NRTL) activity coefficient model

Gebreyohannes

Neely

Gasem

2014

Fluid Phase Equilibria

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The nonrandom two-liquid (NRTL) model is utilized widely in phase equilibria calculations and employs three adjustable parameters (two interaction parameters and the non-randomness factor) that are determined through regression of experimental data for a specific binary vaporliquid equilibrium (VLE) system. The two interaction parameters (and) account for the difference between the pure-component liquid interactions (11 g and 22 g) and mixed-component liquid interactions (12 g and 21 g). The main disadvantage of the NRTL model is the strong correlation between the two parameters of the model. In this work, we propose a new modification to the NRTL model which addresses the limitation of the original model. The newly modified model recasts the formulation of the NRTL model parameters in such a way that the new parameters reflect two different characteristics. It also allows one of the two new model parameters to be generalized in terms of pure-component properties, which reduces the NRTL model to a one-parameter model. The original and modified NRTL models yield comparable precision in representing experimental equilibrium properties. Some of the benefits of our modification include easy generalizability of the parameters, ability to classify VLE behaviors based on a single model parameter and fewer convergence problems in parameter regressions.

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“…An important feature of Wilson's and the NRTL equations is that they use only parameters which can be obtained from binary mixture data (Van Laar's equation requires in addition a ternary interaction parameter). Many modifications of these two equations have been suggested [8][9][10][11][12][13] in order to minimize the number of parameters (at least two) to be determined from each binary system. Indeed, the determination of these parameters by best fit procedures is very time consuming and gives rise to different solutions [14][15][16] depending upon the initial guess when a search method is used.…”

Section: Introductionmentioning

confidence: 99%

A stochastic theory of non-ideal behaviour

Termonia

1979

Molecular Physics

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The stochastic theory described in Part I is extended here to the case of a ternary system [A, B, C] at equilibrium. Using the microenvironment and the quasi-chemical (QC) approximations, we derive equations to estimate the differences in chemical potentials in terms of the three pair interaction parameters O)AB , mAC and OgBc. Alternative equations for calculating these differences have been derived by Bell, using the QC approximation alone. We show that, within the framework of the QC approximation, these estimations are essentially unaffected by our additional microenvironment approximation. Furthermore, the results are in excellent agreement with values obtained with the help of exact equations using computer simulation of ternary lattices at equilibrium.The capability of the theory to predict liquid-liquid equilibria in real ternary systems is examined. Experimental data on binary systems permit us to evaluate the values of the pair interaction parameters 09Aa, mAC and O)Bc. The theory is capable of describing a variety of phenomena encountered in the experiment. The eruption of an island curve with a two-phase region is accounted for by the theory without requiring the addition of a ternary interaction parameter. In all the cases reported, our results are in better agreement with experiment than those obtained from the widely used Van Laar or NRTL equations, which have moreover the weakness of dealing with a relatively large number of parameters. In this connection, it is worth stressing that the three pair interaction parameters o9, used in our theory, represent the reduced interaction energies between molecules of different type. Therefore, if experiments could provide a complete set of values for these interaction energies, our description of a ternary system would constitute a ' zero parameter ' theory.

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One-Parameter Equation for Excess Gibbs Energy of Strongly Nonideal Liquid Mixtures

Cited by 30 publications

References 14 publications

The correct interpretation of tetramethylthiourea electrosorption data in 3 M NaClO4 solution

The correct interpretation of tetramethylthiourea electrosorption data in 3 M NaClO4 solution

One-parameter modified nonrandom two-liquid (NRTL) activity coefficient model

A stochastic theory of non-ideal behaviour

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