RESUMEN
Studies of protein adsorption on reversed-phase and ion exchange stationary phases demonstrated an increase in retention with increasing pressure, which is interpreted as a standard partial molar volume decrease during the transition of the protein from a mobile to a stationary phase. Investigation of the pressure effect on the retention of lysozyme and IgG on a cation exchange column surprisingly revealed a negative retention trend with the increase of pressure. Further investigation of this phenomenon was performed with ß-lactoglobulin, which enabled adsorption to be studied on both cation and anion exchange columns using the same mobile phase with a pH of 5.2. The same surface charge and standard partial molar volume in the mobile phase allowed us to examine only the effect of adsorption. Interestingly, a negative retention trend with a pressure increase occurred on an anion exchange column while a positive trend was present on a cation exchange column. This indicates that the interaction type governs the change in the standard partial molar volume during adsorption, which is independent of the applied pressure. Increasing the protein charge by decreasing the pH of the mobile phase to 4 reversed the retention trend (into a negative) with a pressure increase on the cation exchange column. A further decrease of the pH value resulted in an even more pronounced negative trend. This counterintuitive behavior indicates an increase in the standard partial molar volume during adsorption with the protein charge, possibly due to intermolecular repulsion of adsorbed protein molecules. While a detailed mechanism remains to be elucidated, presented results demonstrate the complexity of ion exchange interactions that can be investigated simply by changing the column pressure.
Asunto(s)
Lactoglobulinas , Muramidasa , Adsorción , Aniones , Cationes/química , Cromatografía por Intercambio Iónico/métodos , Inmunoglobulina G , Indicadores y ReactivosRESUMEN
In this study, comparative analyses were carried out with ion chromatography mass-spectrometry (IC-MS/MS) which has no derivatization step, high-performance liquid chromatography (HPLC) technique, as well as two quantitative and two semi-quantitative immunoassays. The results demonstrated that HPLC and quantitative immunoassay methods were well-correlated with IC-MS/MS in determining histamine in various types of fish products. The best correlation was observed with the HistaSure ELISA Fast Track kit (R2 = 0.9903). More than half of the values (68%) obtained by two methods were also statistically similar. The results of semi-quantitative test kits also supported histamine values estimated by quantitative methods, with some exceptions. The best results were found for HistaSure Lateral Flow in supporting the quantitative techniques. Therefore, these methods are found suitable for monitoring histamine in fish products in terms of food safety. Good correlations were also observed HPLC and IC-MS/MS in determining cadaverine, putrescine, and tyramine with the highest value observed for tyramine as R2 = 0.9785. However, no correlation was observed for other biogenic amines, and the majority of the results were significantly different from each other for these amines (p < 0.05). The differences may be caused by the drawbacks reported previously for HPLC. However, further studies are required to confirm the possible effects. This study provides a comparative evaluation of several methods in terms of their suitability in determining biogenic amines in fish products for both monitoring and regulatory purposes.
Asunto(s)
Aminas Biogénicas/análisis , Productos Pesqueros/análisis , Cromatografía Líquida de Alta Presión/métodos , Cromatografía por Intercambio Iónico/métodos , Histamina/análisis , Inmunoensayo/métodos , Espectrometría de Masas en Tándem/métodosRESUMEN
A new method was proposed for the determination of underivatized biogenic amines based on ion-exchange chromatography coupled with mass spectrometry detection. The method was applied to the analysis of 10 biogenic amines in fresh and processed fish products. The amines were extracted from muscle tissue with water without any additional derivative step or sample clean-up. Separation of biogenic amines was done by the IonPac (4 × 50 mm) column, applying a gradient eluent by mixing formic acid (2 mol L-1) and Milli-Q water (formic acid concentration from 400 mM to 2 M). The results demonstrated a linear response in the range of 0.01 to 10 mg L-1. The detection limits for the fish products ranged from 20 ng/g up to around 400 ng/g for histamine and putrescine, respectively. Spermidine and spermine showed significantly higher detection limits. This current method can be used for the determination of biogenic amines in both fresh and processed fish products for regulatory purposes and monitoring food-safety issues relating to these amines, particularly histamine. It is also a useful method for evaluation of other commercial analytical test kits and commonly used methods that are possibly affected by the food matrix due to processing or other drawbacks arising from the derivatization process.
RESUMEN
Human insulin and six most used therapeutic analogues are very similar in terms of retention on a reversed-phase column. Thus, the LC methods prescribed in the European Pharmacopoeia monographs for insulin and insulin analogues include many similar separation methods, which tend to be time consuming when separating individual products of insulins or are inadequate when handling a mixture. In this study, we present a simple, robust, versatile and accessible HPLC-UV separation method for identification and quantification of human insulin and its analogues in one run. The simultaneous separation and detection is possible by fine-tuning the mobile phase properties that affect the separation mechanism on a mixed mode column combining anion exchange and reversed-phase characteristics. Also developed was a simple and effective SPE sample cleaning procedure with insulin recoveries ranging from 80 to 100% for all analogues. On the other hand, the concentration of major excipients such as phenol and m-cresol fall below 1%. The two developed and validated separation methods differ in their compatibility with the use of a quaternary or binary pump, thus enabling sample characterisation independent of the HPLC solvent delivery system. The methods are compatible with the use of a mass spectrometric detector for an indisputable identification.
Asunto(s)
Cromatografía Líquida de Alta Presión/métodos , Insulina , Insulina/análogos & derivados , Insulina/análisis , Insulina/aislamiento & purificación , Modelos Lineales , Reproducibilidad de los Resultados , Sensibilidad y Especificidad , Espectrofotometría UltravioletaRESUMEN
In this study a new method for evaluating the pressure effect on separations of oligonucleotides and proteins on an anion exchange column was developed. The pressure rise of up to 500 bar was attained by coupling restriction capillaries to the column outlet to minimize differences in pressure over the column. Using pH transient measurements it was demonstrated that no shift in ion exchange equilibria occurs due to a pressure increase. Results from isocratic and gradient separations of oligonucleotides (model compounds) were evaluated by stoichiometric displacement and linear gradient elution model, respectively. Both elution modes demonstrated that for smaller oligonucleotides the number of binding sites remained unchanged with pressure rise while an increase for large oligonucleotides was observed, indicating their alignment over the stationary phase. From the obtained model parameters and their pressure dependencies, a thermodynamic description was made and compared between the elution modes. A complementary pattern of a linear increase of partial molar volume change with a pressure rise was established. Furthermore, estimation of the pressure effect was performed for bovine serum albumin and thyroglobulin that required gradient separations. Again, a raise in binding site number was found with pressure increase. The partial molar volume changes of BSA and Tg at the maximal investigated pressure and minimal salt concentration were -31.6 and -34.4 cm3/mol, respectively, indicating a higher rigidity of Tg. The proposed approach provides an insight into the molecule deformation over a surface at high pressures under nondenaturing conditions. The information enables a more comprehensive UHPLC method development.
Asunto(s)
Oligonucleótidos/aislamiento & purificación , Albúmina Sérica Bovina/aislamiento & purificación , Tiroglobulina/aislamiento & purificación , Adsorción , Animales , Bovinos , Cromatografía por Intercambio Iónico , Sustancias Macromoleculares/química , Sustancias Macromoleculares/aislamiento & purificación , Oligonucleótidos/química , Tamaño de la Partícula , Presión , Albúmina Sérica Bovina/química , Propiedades de Superficie , Termodinámica , Tiroglobulina/químicaRESUMEN
Shorter analysis times and greater resolving power are contributing factors for transfer of separation methods from an HPLC to a UHPLC system when performing analysis in biopharmaceutical or clinical research. The effect of pressure on separations in reversed phase chromatography is well described, however such investigations on ion exchange columns were previously not conducted. In this study we describe the effect of pressure on retention properties of proteins, oligonucleotides and plasmid DNA in ion exchange chromatography. Different column inlet pressures were obtained by coupling restriction capillaries with column outlet and performing separations at a constant temperature and mobile phase flow rate. Macromolecules were separated in isocratic mode as well as with various linear gradients of salt concentration at a constant pH value. The measured retention time increase was up to 80% for isocratic and 20% for gradient separations for a 500 bar increase in pressure. The effect of pressure was validated on a separate instrument after few months from initial experiments. The influence of pressure on retention properties seems to be dependent on the size, shape and flexibility of the macromolecule and causes different retention shifts when separating a sample with diverse analytes. Such changes in retention time can sometimes exceed the criteria set by European Pharmacopoeia (Ph. Eur.) for the allowable method adjustment and are thus considered to be a result of a different separation method. Therefore, the pressure effect that follows method transfer from HPLC to UHPLC conditions should not be neglected even for gradient separations in ion exchange chromatography, as the resulting retention change may cause revalidation of the separation method.
Asunto(s)
Cromatografía por Intercambio Iónico , Sustancias Macromoleculares/aislamiento & purificación , Presión , Proteínas/aislamiento & purificación , Cromatografía Líquida de Alta Presión , Sustancias Macromoleculares/química , Oligonucleótidos/química , Oligonucleótidos/aislamiento & purificación , Proteínas/químicaRESUMEN
A new method for determination of underivatized biogenic amines in cheese based on ion exchange chromatography coupled with tandem mass spectrometric detection was proposed. The method was applied to the analysis of 10 biogenic amines (trimethylamine, putrescine, cadaverine, histamine, 2-phenylethylamine, spermine, spermidine, tryptamine, agmatine, and tyramine) in different types of cheese. The amines were extracted only with water without any additional derivatization step or sample cleanup. This is a great advantage in terms of simplicity of sample pretreatment procedure compared with other currently existing methods in the literature. Biogenic amines were separated using cation exchange column, under gradient elution conditions by mixing formic acid (1.00 M) and deionized water. Detection was achieved using tandem MS/MS, with the instrument set into multiple reaction monitoring mode to ensure high specificity. The detection and quantification limits were in the ranges of 12-46 µg/L and 40-153 µg/L, respectively. The exceptions were spermidine and spermine, with detection limits of 0.8 and 5.4 mg/L, respectively. The linearity for most of the biogenic amines was from 10 µg/L up to 10 mg/L. The best recoveries were observed for trimethylamine, tyramine, and cadaverine, and were 89, 94, and 102%, respectively. The results showed that this method can be used for routine determination of biogenic amines in different types of cheeses as well other food matrices. It must be stressed that the proposed method is capable of determining 10 biogenic amines, including tyramine, which is reported to cause food intoxication commonly associated with cheeses.
Asunto(s)
Aminas Biogénicas/análisis , Queso/análisis , Cromatografía por Intercambio Iónico/métodos , Análisis de los Alimentos/métodos , Espectrometría de Masas en Tándem/métodos , Cadaverina/análisis , Límite de Detección , Metilaminas/análisis , Espermidina/análisis , Espermina/análisis , Tiramina/análisisRESUMEN
Tetramantanes, and all diamondoid hydrocarbons, possess carbon frameworks that are superimposable upon the cubic diamond lattice. This characteristic is invaluable in assigning their (1)H and (13)C NMR spectra because it translates into repeating structural features, such as diamond-cage isobutyl moieties with distinctively complex methine to methylene signatures in COSY and HMBC data, connected to variable, but systematic linkages of methine and quaternary carbons. In all tetramantane C22H28 isomers, diamond-lattice structures result in long-range (4)JHH, W-coupling in COSY data, except where negated by symmetry; there are two highly symmetrical and one chiral tetramantane (showing seven (4)JHH). Isobutyl-cage methines of lower diamondoids and tetramantanes are the most shielded resonances in their (13)C spectra (<29.5 ppm). The isobutyl methylenes are bonded to additional methines and at least one quaternary carbon in the tetramantanes. W-couplings between these methines and methylenes clarify spin-network interconnections and detailed surface hydrogen stereochemistry. Vicinal couplings of the isobutyl methylenes reveal positions of the quaternary carbons: HMBC data then tie the more remote spin systems together. Diamondoid (13) C NMR chemical shifts are largely determined by α and ß effects, however γ-shielding effects are important in [123]tetramantane. (1)H NMR chemical shifts generally correlate with numbers of 1,3-diaxial H-H interactions. Tight van der Waals contacts within [123]tetramantane's molecular groove, however, form improper hydrogen bonds, deshielding hydrogen nuclei inside the groove, while shielding those outside, indicated by Δδ of 1.47 ppm for geminal hydrogens bonded to C-3,21. These findings should be valuable in future NMR studies of diamondoids/nanodiamonds of increasing size.
RESUMEN
A variant of purge/cryotrap/thaw/static headspace Solid Phase Microextraction (SPME) was developed as a means for preconcentrating Volatile Organic Compounds (VOC) in cheese. An originally designed cryotrap partially filled with glass beads was employed that facilitated efficient flow-through of purging gas and trapping of the volatiles. In stopped-flow mode, thawing was allowed, and the same vessel was used for the exposure of the appropriate SPME fiber, effectively achieving double preconcentration. Gas chromatography/mass spectrometry (GC/MS) was subsequently employed to identify components and assess their relative chromatographic peak areas. Monoterpenes were chosen as a model group of substances, and their relative concentration profiles were evaluated as potential markers for the respective geographic origin. The procedure was tested on samples of five traditional Slovenian cheeses featuring Protected Designation of Origin (PDO): Tolminc, Mohant, Nanoski cheese, together with Bovski cheese and Karst Ewe's cheese. The dataset of the peak areas of nine prominent monoterpenes (α-pinene, camphene, α-phellandrene, ß-pinene, 3-carene, 2-carene, limonene, tricyclene, and γ-terpinene) in cheese samples showed clustering that relates the cheeses to the area of production. According to the silhouette metrics, four clusters were identified by partitioning around medoids (PAM) method. The latter packed data for Tolminc and Bovski cheese into a single cluster, closely reflecting the vicinity of their geographic origin, but classified correctly the rest of the data into separate clusters for all other cheeses.
Asunto(s)
Queso/análisis , Cromatografía de Gases y Espectrometría de Masas/métodos , Monoterpenos/análisis , Microextracción en Fase Sólida/métodos , Animales , Bovinos , Análisis por Conglomerados , Geografía , Ovinos , EsloveniaRESUMEN
Volatile organic compounds (VOCs) play an important role in the chemistry of the atmosphere and in biogeochemistry. They contribute to the oxidative capacity of the atmosphere, particle and air pollutants, as well as to the production of greenhouse gases (for instance ozone). Among analytical techniques for their determination in the atmosphere gas chromatography coupled with mass spectrometry (GC-MS) offers several advantages. However, for an accurate quantification calibration with standard substances is necessary. A quantitative structure-property relationship (QSPR) model for the prediction of MS response factors was developed on basis of our experimental measurements for the quantification of ozone precursors present in the atmosphere. A linear correlation between chemical structures and response factors was established by using a 7-parameter MLR model. The average error in the prediction of response factors was calculated by cross-validation procedure and was below 20%, which is sufficient for the determination of VOCs in the air. The proposed procedure is time consuming so it is more suited for the quantification of tentatively identified organic compounds during the reprocessing of MS chromatograms in cases when the original sample is no longer available.
Asunto(s)
Aire/análisis , Cromatografía de Gases/métodos , Compuestos Orgánicos Volátiles/análisis , Cromatografía de Gases y Espectrometría de MasasRESUMEN
Experimental MS response factors were measured for 36 different saturated and unsaturated volatile organic compounds (VOC) containing carbon, hydrogen and halogen atoms. Chemical structure was encoded using various molecular descriptors. A quantitative structure-property relationship model was established using the multiple linear regression models. The cross-validation ability of the created model was estimated by leave-one-out cross-validation procedure. Error in the cross-validation of response factors was calculated by cross-validation procedure and was 15%, which is sufficient for the determination of VOCs in the air. The proposed procedure can be used for simultaneous qualitative and quantitative determination of volatile organic compounds in the atmosphere.
RESUMEN
The newly introduced signature of benzenoids (a sequence of six real numbers Si with i = 6-1) shows the composition of the pi-electron partition by indicating the number of times all rings of the benzenoid are assigned 6, 5, 4, 3, 2, or 1 pi-electrons. It allows the introduction of a new ordering criterion for such polycyclic aromatic hydrocarbons by summing some of the terms in the signature. There is an almost perfect linear correlation between sums S6 + S5 and S4 + S3 for isomeric cata- or peri-fused benzenoids, so that one can sort such isomers according to ascending s 6 + S5 or to descending S4 + S3 sums (the resulting ordering does not differ much and agrees with that based on increasing numbers of Clar sextets and of Kekule structures). Branched cata-condensed benzenoids have higher S6 + S5 sums than isomeric nonbranched systems. For nonisomeric peri-condensed benzenoids, both sums increase with increasing numbers of benzenoid rings and decrease with the number of internal carbon atoms. Other partial sums that have been explored are S6 + S5 + S3 And S6 + S2 + S1, and the last one appears to be more generally applicable as a parameter for the complexity of benzenoids and for ordering isomeric benzenoids.
RESUMEN
It is shown for a representative set of isomeric benzenoids that pi-electron partitions and signatures can serve for characterizing and ordering benzenoids. Benzenoid signatures (sequences s6 through s1 where the subscripts correspond to numbers of pi electrons in all rings) are obtained by examining the numbers of assigned pi electrons ranging from 6 to 1 for each ring in all resonance structures. The pi-electron partitions and signatures of all 33 non-isoarithmic peri-condensed benzenoid hydrocarbons with eight rings and four contiguous internal carbon atoms allow an ordering of these benzenoids that agrees fairly well with increasing numbers of Kekulé valence structures and Clar sextets. Interestingly, an excellent correlation (R2 > 0.99) is observed between s6 + s5 + s2 + s1 and s4 + s3, and an explanation for this observation is provided: the number P of pi electrons is divided unequally between two components: s34 = s4 + s3 and s1256 = s6 + s5 + s2 + s1 so that s1256 or the quotient s1256/s34 = Q can serve as a new metric for perfect matchings of polyhexes and a criterion for ordering and for evaluating the complexity of isomeric benzenoids quantitatively.
RESUMEN
Ion chromatography (IC) was used to establish isomer purity of the highly water-soluble sample of fullerenehexamalonic acid, Th-symmetric hexakis-adduct C66(COOH)12. Sharp and symmetric peaks were obtained by IC using 1.0 M potassium hydroxide as eluent and applying gradient elution program. The identity of the two largest peaks in the chromatogram was assigned to Th-C66(COOH)12 and C66H(COOH)11. The developed IC procedure can be used for the semi-quantitative determination of the extent of the partial decarboxylation of the sample. As an alternative analytical technique, a CE procedure was introduced and its performance against IC was compared for this particular case.
Asunto(s)
Cromatografía por Intercambio Iónico/instrumentación , Cromatografía por Intercambio Iónico/métodos , Fulerenos/química , Fulerenos/aislamiento & purificación , Química Física/instrumentación , Química Física/métodos , Electroforesis Capilar/métodos , Malonatos/química , Solubilidad , Torio/análisis , Torio/química , Agua/químicaRESUMEN
Dualists of benzenoids are a special type of graphs that have as vertices the centers of hexagons and as edges the pairs of condensed rings. Catafusenes (cata-condensed benzenoids) have acyclic dualists. Codes of catafusenes with h benzenoid rings start from one end of a dualist and consist of digits 0 (indicating linear annelation, angle of 180 degrees between two adjacent edges) and 1 or 2 for kinks (120 degrees or 240 degrees angles) with the convention of choosing the lowest number formed from these h-2 digits. A shape parameter (n) for the dualist consists of the number of adjacent zeros in the code plus 1. It is shown in the present communication that many molecular properties of catafusenes depend mainly on n, whereas most bulk properties depend mainly on h. Monoparametric or biparametric correlations in terms of the simple integer parameters n and/or h are presented for molecular properties (energy of the p-band in electronic absorption spectra, ionization potentials, electron affinities, hardness and softness) and bulk properties (normal boiling point, chromatographic retention index, the logarithm of the water solubility, and lipophilicity).
Asunto(s)
Benceno/química , Electrones , Calor , Interacciones Hidrofóbicas e Hidrofílicas , Iones/química , Estructura Molecular , Solubilidad , Análisis Espectral , Temperatura de Transición , Agua/químicaRESUMEN
Catabolism of a (14)C-labelled volatile monoterpene compound (geraniol) to (14)CO(2) was investigated in soils taken from the rhizosphere at distances up to 200 cm from the trunks of three small Populus tremula trees growing at different sites in Slovenia. Emissions of limonene of up to 18 microg m(-2) h(-1) were detected from the soil surface at each site. Evolution of (14)C-labelled CO(2) was measured as a product of catabolism of (14)C-labelled geraniol introduced into the soil samples. Indigenous soil microorganisms degraded the geraniol rapidly. There was a significant difference in relative lag times and rates of catabolism along the gradient from the tree trunks, with relatively longer lag times and lower rates occurring in soil samples from the farthest point from the tree.
Asunto(s)
Bacterias/metabolismo , Radioisótopos de Carbono/metabolismo , Raíces de Plantas/microbiología , Populus/microbiología , Microbiología del Suelo , Terpenos/metabolismo , Monoterpenos Acíclicos , Ecosistema , Eslovenia , Suelo/análisis , VolatilizaciónRESUMEN
The higher-order variable connectivity indices were introduced to account for the combination of positive and negative relative contributions of atoms and bonds in the construction of the quantitative structure-property relationships or quantitative structure-activity relationships models. The coding capabilities of modified descriptors were presented on the modeling of the atmospheric reaction rate constants of selected organic compounds with OH radicals. The optimization of diagonal weights of the augmented adjacency matrix pointed out the significant enhancing effect of oxygen and the suppressive effect of chlorine on the overall molecular atmospheric reactivity of organic compounds with OH radicals. The linear regression model, using a single structural descriptor, that is, a variable connectivity index of order one, produced a root-mean-square error of 0.343 log units. Although the obtained calculation error was higher than in previously reported multiple linear regression models, the new model offered important insight into the role of the individual structural components that are influencing the reactivity of organic compounds.
RESUMEN
Theoretical prediction of gas-chromatographic retention times could be used as an additional method for a more accurate identification of organic compounds during GC/MS analysis. Two separate quantitative structure-property relationship models were introduced for the calculation of thermodynamic values (DeltaH degrees, DeltaS degrees) for aliphatic and aromatic hydrocarbons. These values are required for the calculation of retention times in temperature programmed gas chromatography. Seven-descriptor and five-descriptor MLR models were selected for the calculation of DeltaH degrees and DeltaS degrees values, respectively, based on the best cross-validation abilities. The final prediction capabilities of the models were evaluated by a test set procedure. RMS errors calculated from the test set were 207 cal mol(-1) and 0.58 cal mol(-1) K(-1) for DeltaH degrees and DeltaS degrees prediction models, respectively. To evaluate the error of the models represented in the time scale, several chromatograms were simulated using experimental Pro ezGC and theoretically calculated thermodynamic data. Afterward a standard deviation of retention time residuals was calculated. It was found out that, although the standard deviation varies from one chromatographic condition to another, the ratio between the standard deviation and the maximum available separation space for the particular set of organic compounds remains constant and was around 5% of the maximum separation space available at selected chromatographic conditions. Our prediction model was able to accurately differentiate between the retention times of the consecutive compounds in the n-alkanes, 1-alkenes, and 2-alkenes homological series.
RESUMEN
Volatile organic compounds (VOCs) play an important role in different photochemical processes in the troposphere. In order to predict their impact on ozone formation processes a detailed knowledge about their abundance in the atmosphere as well as their reaction rate constants is required. The QSPR models were developed for the prediction of reaction rate constants of volatile unsaturated hydrocarbons. The chemical structure was encoded by constitutional and topological indices. Multiple linear regression models using CODESSA software was developed with the RMS(CV) error of 0.119 log units. The chemical structure was encoded by six topological indices. Additionally, a regression model using a variable connectivity index was developed. It provided worse cross-validation results with an RMS(CV) error of 0.16 log units, but enabled a structural interpretation of the obtained model. We differentiated between three classes of carbon atoms: sp2-hybridized, non-allylic sp3-hybridized and allylic sp3-hybridized. The structural interpretation of the developed model shows that most probably the most important mechanisms are the addition to multiple bonds and the hydrogen atom abstraction at allylic sites.
Asunto(s)
Radical Hidroxilo/química , Modelos Químicos , Hidrocarburos Policíclicos Aromáticos/química , Enlace de Hidrógeno , Modelos Lineales , Valor Predictivo de las Pruebas , Relación Estructura-Actividad Cuantitativa , Programas InformáticosRESUMEN
We report on the calculation of normal boiling points for a series of n = 58 aliphatic alcohols using the variable connectivity index in which variables x and y are used to modify the weights on carbon (x) and oxygen atoms (y) in molecular graphs, respectively. The optimal regressions are found for x = 0.80 and y = -0.90. Comparison is made with available regressions on the same data reported previously in the literature. A refinement of the model was considered by introducing different weights for primary, secondary, tertiary, and quaternary carbon atoms. The standard error in the case of the normal boiling points of alcohols was slightly reduced with optimal weights for different carbon atoms from s = 4.1 degrees C (when all carbon atoms were treated as alike) to s = 3.9 degrees C.