This manuscript deals with a mathematical analysis of the functions that should be used in the Clausius-Clapeyron thermodynamic modeling, which is usually modeled as a linear fit; this research emphasizes that the thermal models are nonlinear even taking into account the heat capacity functions as a constant. Specifically, the mathematical analysis of the thermal models proposes what equations should be used depending on the type of enthalpy function. Consequently, the enthalpy functions depend on the model of the heat capacity proposed by Albert Einstein. The magnitude of the errors that would be committed by using linear regressions was also estimated, as is the case for the vast majority of publications in this area. This study also shows how the models behave in a wide temperature range and how they are becoming apparently linear as the temperature range decreases.

Humic acids are produced by decomposition of organic soil material and from oxidation of mineral coals. In this study, the effect of oxidation and the yield of humic acids extracted from a sample of Colombian mineral coal were studied by response surface methodology (RSM). The variables used were: particle size (0.063, 0.106 and 0.150 mm), concentration of the oxidizing agent (KMnO 4 : 0.010, 0.020 and 0.050 M) and oxidation time (30, 60 and 90 minutes). The degree of oxidation was verified by infrared spectroscopy. Oxidation increased oxygen groups in the carbonaceous matrix, mainly due to oxidation of aliphatic components. Extraction yields above 24% were obtained with 0.063 mm particle size and 0.020 M KMnO 4 . © 2017. Acad. Colomb. Cienc. Ex. Fis. Nat.Key words: bituminous coal; humic acids; oxidation process; surface response; factorial design. Efecto del tamaño de partícula y la concentración del oxidante en el rendimiento de ácidos húmicos obtenidos de carbón mineral proveniente de Colombia usando la metodología de superficie de respuesta ResumenLos ácidos húmicos se producen por la descomposición de la materia orgánica de los suelos y por la oxidación de carbones minerales. En este estudio se analizó mediante superficies de respuesta el efecto de la oxidación en la extracción de ácidos húmicos de un carbón colombiano. Las variables de oxidación estudiadas fueron las siguientes: tamaño de partícula (0,063, 0,106 y 0,150 mm), concentración del agente oxidante (permanganato de potasio (KMnO 4 ): 0,010, 0,020 y 0,050 M) y tiempo de oxidación (30, 60 and 90 minutos). El grado de oxidación se verificó con espectroscopia infrarroja. La oxidación incrementó los grupos oxigenados en la matriz carbonácea debido, principalmente, a la oxidación de componentes alifáticos. Se obtuvieron porcentajes de extracción superiores a 24 % al usar partículas de 0,063 mm y KMnO 4 con 0,020 M.

Acetaminophen (AAP) is an active ingredient very used in many pharmaceutical preparations. AAP is a pain reliever and a fever reducer drug. Generally, it is used to treat many conditions such as headache, muscle aches, arthritis, backache, toothaches, colds, and fevers. Standard methods most used for AAP chemical detection are based on chromatography and spectrophotometry techniques, these methods generally imply a sample preparation step, while vibrational spectroscopy based methods do not. Hence, analytical methods based on vibrational spectroscopy are very important for the pharmaceutical industry and law enforcement agency, given that allow obtain a way easy and fast molecular information for its detection. An effort for attaining a reliable identification procedure for the qualitative determination of AAP in different pharmaceuticals product, an additional statistical treatment of ATR-FTIR data is proposed. The proposed method was tested on solid samples containing API. The statistical routine of Hit Quality Index (HQI) values yielded excellent results. The results show that ATR-FTIR, QCL and Raman spectra are useful for detection of AAP in the drugs tested. Using the proposed method allowed to know if the drug is present as a desired product or it is counterfeit drugs.