Concentration dependence of the boiling point of binary equidistant solutions

Marinichev, A. N.

doi:10.1134/s1070427207020085

Cited by 4 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the first target analyte C 11 , the accuracy of the extrapolation with 'classical' Equation (8) can be considered appropriate [the error, Dt R ¼ t R (calculated) À t R (experimental) equals À0.22 min], but for more 'remote' compounds C 12 and C 13 errors reach À0.59 and À1.88 min, correspondingly, that is absolutely unacceptable. These errors are observed in spite of high value (r ¼ 0.9999) of correlation coefficient of regression (8). Hence, we can conclude, that this 'classical' equation well interpolates experimental data, but cannot be recognized satisfactory for extrapolation of retention parameters.…”

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 82%

“…þ c was used to approximate the concentration dependence of the boiling points of binary solutions (x ¼ C, Y ¼ T) of equidistant compositions [8].…”

Section: Research Articlementioning

confidence: 99%

“…Before calculations by Equation (8), we must find t 0 by Equation (4), which gives 6.11 min. The parameters of linear regression (8) and the estimated retention times of n-alkanes C 11 -C 13 are listed in Tables I and II. For the first target analyte C 11 , the accuracy of the extrapolation with 'classical' Equation (8) can be considered appropriate [the error, Dt R ¼ t R (calculated) À t R (experimental) equals À0.22 min], but for more 'remote' compounds C 12 and C 13 errors reach À0.59 and À1.88 min, correspondingly, that is absolutely unacceptable.…”

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 99%

“…Parameters of 'classical' Equation (8) and alternative recurrent relation (9) for estimation of gas chromatographic retention times of n-alkanes C 11 -C 13 from the data on n-alkanes C 5 -C 10 Parameter Equation (8) Equation (9) t 0 6.11 [estimated by Equation ( Tables I and II. Graphic illustration of the linearity of the recurrent dependence for retention times of n-alkanes C 5 -C 10 is given in Figure 1.…”

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 99%

See 3 more Smart Citations

Application of recurrent relationships in chromatography

Зенкевич

2009

Journal of Chemometrics

View full text Add to dashboard Cite

Recurrent relationships of general form A(x R k) ¼ aA(x) R b were shown to be applicable to the approximation not only of values of most physicochemical constants of organic compounds (A) indicating monotonous or oscillating variations within different homologous series (x ¼ n C , k ¼ 1 or 2), but also of the dependences of chromatographic retention parameters on the number of carbon atoms in homologue molecules (A ¼ t R , x ¼ n C ) in gas and high performance liquid chromatography (HPLC). In these cases the values of argument (the number of carbon atoms in the molecule) are integer by definition, while the functions are discrete. Besides that, the same recurrent equations describe the temperature dependence of retention times of analytes under isothermal separation conditions in gas chromatography (A ¼ t R , x ¼ T, k ¼ DT ¼ const) and the dependences of retention times on the concentrations of an organic solvent as an eluent component (A ¼ t R , x ¼ C, k ¼ DC ¼ const) under isocratic separation conditions in HPLC, which are the examples of the functions of continuous arguments. Key mathematical properties of recurrences explaining us their promising applications in chemistry and chromatography are discussed. The method to apply recurrent equations to arbitrary, not necessary equidistant, values of continuous arguments is considered.

show abstract

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 82%

“…þ c was used to approximate the concentration dependence of the boiling points of binary solutions (x ¼ C, Y ¼ T) of equidistant compositions [8].…”

Section: Research Articlementioning

confidence: 99%

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 99%

Section: Recurrent Approximation Of the Dependence Of Chromatographicmentioning

confidence: 99%

See 2 more Smart Citations

Application of recurrent relationships in chromatography

Зенкевич

2009

Journal of Chemometrics

View full text Add to dashboard Cite

show abstract

“…in the approximation of the concentration dependence of boiling points of binary solutions (x ¼ C) of equidistant compositions (Dx ¼ const) [21] and second-or third-order homologous dependences of the temperatures of nematic-isotropic transitions in homologous liquid crystals [22].…”

Section: Processing the Numbers Of This Sequence (10 Points) With Firmentioning

confidence: 99%

Application of recurrent relations in chemistry

Зенкевич

2010

Journal of Chemometrics

View full text Add to dashboard Cite

As it was previously demonstrated, mathematical properties of simplest first-order recurrent relations A(n R 1) ¼ aA(n) R b provide important advantages at their applications in chemistry, namely in the approximation of monotonous variations of different physicochemical properties of homologues of various series of organic compounds. Besides that it was empirically revealed the unique 'chemical' property of recurrences that is the application of single equations of this kind to constants of different series. To explain this high 'approximating ability' of recurrences it was proved first time that numerical sequences that obey high-order recurrence in a limiting case can be approximated by first-order recurrence. Consequently, this fact explains us the existence of close analogy between first-order recurrent approximation of recursive numerical sequences (Fibonacci, Padovan, Lucas and Perrin sequences are considered as examples) and physicochemical constants of homologues. This analogy is considered as not 'chemically' correct proof, but reasonable explanation of the applicability of single recurrent equations to constants of different homologous series. The mentioned properties of recurrences seem to be the reason of their high approximating ability in relation to different chemical variables. Recurrent relations can be recommended as universal approach in processing of not only various sets of physicochemical constants of homologues, but also properties or processes characterized by equidistant values of arguments.

show abstract

Clapeyron.jl: An Extensible, Open-Source Fluid Thermodynamics Toolkit

Walker

Yew

Riedemann

2022

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Thermodynamic models are often vital when characterizing complex systems, particularly natural gas, electrolyte, polymer, pharmaceutical, and biological systems. However, their implementations have historically been abstruse and cumbersome, and as such, the only options available were black box commercial tools. In this article, we present : a pioneering attempt at an open-source fluid thermodynamics toolkit to build and make use of thermodynamic models. This toolkit is built using Julia, a modern language for scientific computing known for its ease of use, extensibility, and first-class support for differentiable programming. We currently support more models than any package available, including standard cubic (SRK, PR, PSRK, etc.), activity coefficient (NRTL, UNIFAC, etc.), COSMO-based, and the venerable SAFT equations. The property estimation methods supported are extensive, including bulk, VLE, LLE, VLLE, and critical properties. With , researchers and enthusiasts alike will be able to focus on the application and worry less about the implementation.

show abstract

Concentration dependence of the boiling point of binary equidistant solutions

Cited by 4 publications

References 2 publications

Application of recurrent relationships in chromatography

Application of recurrent relationships in chromatography

Application of recurrent relations in chemistry

Clapeyron.jl: An Extensible, Open-Source Fluid Thermodynamics Toolkit

Contact Info

Product

Resources

About