Whole Range Of Mole Fractions Research Articles

Volumetric, Acoustic, and Refractive Behavior of Acid Gas Absorbers: N-Vinyl-2-pyrrolidinone and Glycol Ethers (2-(2-Ethoxyethoxy)ethanol, 2-(2-Butoxyethoxy)ethanol, and 2-(2-(2-Methoxyethoxy)ethoxy)ethanol)

Thermophysical properties such as density (ρ), speed of sound (u), and refractive index (nD) for pure N-vinyl-2-pyrrolidinone (NVP) and binary mixtures of NVP with 2-(2-ethoxyethoxy)ethanol (DEGMEE), 2-(2-butoxyethoxy)ethanol (DEGMBE), and 2-(2-(2-ethoxyethoxy)ethoxy)ethanol (TEGMME) have been measured over the whole range of mole fraction from temperature T = (298.15 to 323.15) K and at 0.1 MPa pressure employing an Anton Paar vibrating U-tube density and sound velocity meter (DSA 5000 M) and an Abbemat refractometer, respectively. To quantify the nonideality in these systems, the experimental data has been used to evaluate various acoustical and thermodynamic parameters, such as excess molar volume (VmE), deviation in the speed of sound (Δu), isentropic compressibility (κs), excess isentropic compressibility (κsE), deviation in refractive index (ΔnD), molar refraction (Rm), and polarizability (α). Molecular interactions prevailing in these systems have been explained in terms of variation in the measured and calculated values of physicochemical parameters. The collected thermophysical data can be employed in the optimization and design of a desulfurization/CO2-capture process utilizing the studied solutions. Furthermore, this data can also be utilized for the theoretical model extension as well as in solving many difficult engineering problems such as fluid flow, heat and mass transfer, and energy transformations.

Densities, Viscosities, and Derived Properties for Binary Mixtures of Long-Chain Alcohols of 1-Hexanol + 1-Pentanol, + 2-Pentanol, + 2-Methyl-1-butanol, + 1-Heptanol, and + 1-Octanol from 288.15 to 338.15 K

Densities and viscosities for binary mixtures of long-chain alcohols are important to design transfer heat and mass equipment and to interpret the kind of interactions that occur in the studied blends. Current investigation indicated the measurements of densities and viscosities for liquid mixtures of 1-hexanol + 1-pentanol, + 2-pentanol, + 2-methyl-1-butanol, + 1-heptanol, and + 1-octanol from 288.15 to 338.15 K at atmospheric pressure and over the whole range of mole fractions. A vibrating tube densimeter and a glass capillary viscometer were used to measure the density and viscosity of the alcohol binary mixtures, respectively. Experimental measurements of the pure alcohols have been compared with the data reported in the literature using average absolute percentage deviation (AAPD) as a criterion. The obtained results demonstrated for density an AAPD of 0.023% and for viscosity an AAPD of 0.597%, which is a good agreement between the experimental findings and literature data. Excess molar volume and viscosity deviation present negative deviations for all the alcohol mixtures at the conditions considered in this research. These results indicate that the mixture suffers a volume contraction, which is caused by intermolecular forces of attraction between different alcohol molecules. The Redlich–Kister equation is used to fit the excess molar volume and viscosity deviation. Kinematic viscosities of the binary blends have been calculated through the Nava-Ríos et al. and McAllister equations.

Thermodynamic Properties of Binary Liquid Mixtures Containing Furfural with Chlorobenzene, Nitromethane, Diethylmalonate and 1-Butanol at 308.15K and 318.15K Supported by FTIR Spectral Studies

A study on thermodynamic properties of the liquid mixture is used in the industrial process, which often extends to solution chemistry. Density(ρ), Viscosity(η), and Ultrasonic velocity(U) were determined for binary liquid mixtures of furfural with chlorobenzene, nitromethane, diethyl malonate and 1- butanol at temperature of 308.15K and 318.15K at atmospheric pressure over the whole range of mole fractions. The calculated thermodynamic properties and some excess parameters such as Excess Volume(VE), Deviation in Isentropic Compressibility(∆KS), Deviation in Viscosity(∆η), Deviation in Intermolecular Free Length(∆LF), Deviation in Intermolecular Free Volume(∆VF), Deviation in Internal Pressure(∆π) and Deviation in Acoustic Impedance(∆Z) were calculated and applied to the Redlich-Kister type polynomial equation to determine the appropriate coefficients. The effects of composition and temperature on thermodynamic parameters have been studied in terms of molecule interaction in these liquid mixtures. Further, IR spectra of these liquid mixtures were recorded and the data were utilized to examine the mixing behavior of the components.

23Na‐NMR Data Based Donor Number and Their Correlation with Solvatochromic Parameters in Binary Solvent Mixtures

AbstractDonor numbers (DNs) of binary mixtures of acetonitrile with methanol, ethanol, ethylene glycol, 1‐butanol, and tert‐butanol were calculated in the whole range of mole fractions based on 23Na‐NMR chemical shift of sodium perchlorate dissolved in solvent. Data showed positive deviation from hypothetical linear ideal behavior. Solvatochromic parameters including empirical polarity, dipolar/polarizability, hydrogen bond donor, and hydrogen bond acceptor of the solvent mixtures were spectrophotometrically measured in order to investigate the correlations among parameters. The trend of data showed the preferential solvation along with synergistic behavior in some of mixtures. Applying preferential solvation model confirmed the solvent‐solvent interactions in the studied binary mixtures. Although no reasonable correlation was observed between DN with solvatochromic parameters, dual‐parameters regressions showed that some of solvatochromic parameters have linear relationships with DN. The presence of solvent‐solvent interactions in the media caused that the solvent mixtures didn't follow the known correlations as reported before.

Reaction kinetics investigation of Malononitrile with substituted benzaldehydes in aqueous solutions of ethaline as deep eutectic solvent

AbstractDue to increasing demands for ecofriendly processes within the framework of green chemistry, and having shown substantial properties, especially in terms of toxicity, biodegradability, cost, and ease of preparation under ambient conditions, deep eutectic solvents (DESs) have become a suitable candidate as green solvents for reaction media in the past decade. In this work, condensation reaction of some para‐ and meta‐substituted benzaldehydes and Malononitrile was kinetically investigated in ethylene glycol‐choline chloride (ethaline) as a DES mixed with water, in the whole range of mole fractions, at room temperature. The correlation of second‐order rate coefficients based on Hammett's substituent constants yield a linear straight line with positive slope in different mole fractions of ethaline–water mixtures. The measured second‐order rate coefficients of the reaction showed a dramatic variation in ethaline–water mixtures with the increasing mole fraction of water.

Effect of the Alkyl Chain on the Physical Properties of Imidazolium-Based Ionic Liquids with 1-Propanol, 1-Butanol, and 1-Pentanol Binary Mixtures

Viscosities and surface tensions were measured at temperatures of 298.15, 303.15, 308.15, and 313.15 K and a pressure of 101.3 kPa for 1,3-dimethyl and 1-ethyl-3-methyl imidazolium methylsulfates ([dmim][MeSO4] and [emim][MeSO4], respectively) with 1-alcohols (propanol, butanol, and pentanol) over the whole range of mole fractions. The corresponding deviation properties and excess Gibbs free energy were calculated using the experimental data. Furthermore, the Redlich–Kister polynomial was used to correlate excess and deviation properties. The measured viscosities of the binary systems under study were used to test the applicability of empirical models to binary systems involving ionic liquids. The effect of the alkyl chain of the two ionic liquids on the measured and calculated properties is discussed.

Association of 1-hexanol in mixtures with n-hexane: Dielectric, near-infrared and DFT studies

Association of 1-hexanol in n-hexane has been studied by measurements of nonlinear dielectric effect (NDE) and near-infrared (NIR) spectroscopy. Besides, the dipole moments of selected open and cyclic associates were determined by DFT (density functional theory) calculations. All measurements were performed in the whole range of mole fractions with a step of 0.1. From numerical fitting of the dielectric data we obtained populations of all species present in the mixture. Our results do not support common opinion about the exceptional role of cyclic tetramers. The most abundant cyclic species are trimers and population of the cyclic associates rapidly decreases with increasing size of associates. The variations in population of open associates are more complex and for mole fractions of 1-hexanol > 0.1 the relationships have a maximum, which shifts towards higher associates. In pure 1-hexanol this maximum is close to seven. From analysis of the dielectric data it results that at lower alcohol content dominate the cyclic species. When the concentration of 1-hexanol increases the equilibrium shifts towards formation of the linear associates.From NIR spectra we determined the overall population of the free OH in monomers and open associates. Next, these values were used for estimation of an average length of the open associates. It appears that an averaged size of the open associates determined from NIR spectra is higher than that from the dielectric data and these differences are more pronounced when the concentration of 1-hexanol increases. We discuss possible explanations of this observation. Assuming that the actual size of the open associates is between those obtained from both methods, one can estimate that the size of open associates is ranging from 3 to 15 in pure 1-hexanol. It seems that the higher associates are stabilized by interaction of the aliphatic chains.

Surface tension measurements of aqueous 1-alkyle-3-methylimidazolume tetrafluoroborate {[Cnmim][BF4] (n = 2, 4, 6)} solutions and modeling surface tension of ionic liquid binary mixtures using six various models

The surface tension of three ionic liquids: [C2mim][BF4] (1-ethyl-3-methylimidazolium tetrafluoroborate), [C4mim][BF4] (1-butyl-3-methylimidazolium tetrafluoroborate) and [C6mim][BF4] (1-hexyl-3-methylimidazolium tetrafluoroborate) blended with water were measured at temperatures from (298.15 K to 338.15) K and whole range of mole fraction. The measurements show that studied systems are highly nonideal and surface tension decrease as temperature rises in a linear order. In following, to describe the surface tension of the solutions as a function of temperature and concentration, simultaneously, a new model based on thermodynamics was developed using the nonelectrolyte NRTL nonrandom factor (N-NRTL-NRF) equation. Also, a comprehensive dataset consist of 19 binary ionic liquid solutions with 989 data points at various conditions was collected. The new model, as well as five other models, were applied to the dataset and the performance of the six models was compared to experiments and to each other. The new model shows a deviation with the experiment as RMSD = 0.4559%.

Tracking small heterogeneity in binary mixtures of aliphatic and aromatic hydrocarbons: NIR spectroscopic, 2DCOS and MCR-ALS studies

To our best knowledge, this is the first spectroscopic study of small heterogeneity at a molecular level in binary mixtures of aliphatic and aromatic hydrocarbons. The composition-dependent spectra of benzene/toluene, benzene/n‑hexane, benzene/cyclohexane, n‑hexane/n‑heptane and n‑hexane/cyclohexane mixtures were recorded by NIR transmission technique in the whole range of mole fractions. A comprehensive exploration of the experimental data was performed by two-dimensional correlation analysis (2DCOS) and chemometric methods. In addition, we calculated excess NIR molar absorption spectra and parameter of ER, which allows for comparison of the degree of deviation from ideality for various mixtures. Our results reveal that all studied mixtures deviate from the ideal mixture. The extent of these deviations is small for the mixtures were both components are aromatic or aliphatic and increases for aromatic/aliphatic mixtures. In addition, molecular shapes have an important effect on the degree of deviation from the ideal mixture. As expected, benzene/n‑hexane is the most non-ideal mixture, while behavior of n‑hexane/n‑heptane and benzene/toluene mixtures is close to the ideal one. Our results suggest that in the mixtures with the largest deviations from ideality are present homoclusters of both components and heteroclusters. The heteroclusters exist in the whole range of compositions, while the homoclusters appears above a certain concentration limit. If both components of the mixture are similar, the molecules with equal probability form the homo- and heteroclusters. In the case of unlike components, the molecules prefer to form the homoclusters. The homoclusters of both components in the mixture are similar as those observed in bulk constituents. This means that deviation from the ideal mixture results from presence of the heteroclusters.

Preferential Solvation and Solvatochromic Parameters in Mixtures of Poly(ethylene glycol)-400 with Some Molecular Organic Solvents

Polyethylene glycols have become more popular alternate reaction media due to interesting properties like non-toxicity, bio-degradability, and full miscibility with water and organic solvents. Binary mixtures of polyethylene glycols with common solvents can be useful to tune their physical and chemical properties and to facilitate chemical and physical processes. In this study, solvatochromic parameters were spectrophotometrically determined for binary solvent mixtures of poly(ethylene glycol)-400 (PEG-400) with methanol, 2-propanol, 1-butanol, dimethyl sulfoxide, N,N-Dimethylformamide, and dichloromethane under ambient conditions, over the whole range of mole fractions. The solvatochromic parameters showed different trends in protic and aprotic solvents mixed with PEG-400. Methanol/PEG-400 mixtures showed special properties in polarity and polarizability so that the mixtures are more dipolar/polarizable than their pure components. Positive or negative deviations from ideal behavior confirmed that the indicators were involved in a preferential solvation process in the solvent mixtures. These deviations from ideality can be attributed to strong solvent–solvent interactions in the binary mixtures.

Microheterogeneity in binary mixtures of water with CH3OH and CD3OH: ATR-IR spectroscopic, chemometric and DFT studies

Here we report ATR-IR spectroscopic study on the separation at a molecular level (microheterogeneity) and the degree of deviation of H2O/CH3OH and H2O/CD3OH mixtures from the ideal mixture. Of particular interest is the effect of isotopic substitution in methyl group on molecular structure and interactions in both mixtures. To obtain comprehensive information from the multivariate data we applied the excess molar absorptivity spectra together with two-dimensional correlation analysis (2DCOS) and chemometric methods. In addition, the experimental results were compared and discussed with the structures of various model clusters obtained from theoretical (DFT) calculations.Our results evidence the presence of separation at a molecular level and deviation from the ideal mixture for both mixtures. The experimental and theoretical results show that the maximum of these deviations appears at equimolar mixture. Both mixtures consist of three kinds of species: homoclusters of water and methanol and mixed clusters (heteroclusters). The heteroclusters exist in the whole range of mole fractions with the maximum close to the equimolar mixture. At this mixture composition near 55–60% of molecules are involved in heteroclusters. In contrast, the homoclusters of water occur in a limited range of mole fractions (XME < 0.85–0.9). Upon mixing the molecules of methanol form weaker hydrogen bonding as compared with the pure alcohol. In contrast, the molecules of water in the mixture are involved in stronger hydrogen bonding than those in bulk water. All these results indicate that both mixtures have similar degree of deviation from the ideal mixture.

Excess molar volumes and excess isentropic compressibilities of liquid mixtures formed by tetrahydropyran, piperidine and cyclic ketones at temperature from 293.15 to 308.15 K.

The densities, ρ, ρ123 and speeds of sound, u, u123 of binary Tetrahydropyran (1)+Piperidine (2) and ternary Tetrahydropyran (1)+Piperidine (2)+Cyclohexanone or Cycloheptanone (3) mixtures have been measured over the whole range of mole fraction at 293.15, 298.15, 303.15, 308.15K and atmospheric pressure. The observed data have been utilized to determine excess molar volumes, (VE)12, V123E and excess isentropic compressibilities, (κSE)12, (κSE)123 for the binary and ternary liquid mixtures respectively. The (VE)12, V123E and (κSE)12, (κSE)123 data have been fitted to Redlich-Kister equation to determine binary as well as ternary adjustable parameters along with standard deviations. The Moelywn-Huggins concept of interaction between the surfaces of the binary mixture constituents has been extended (Graph theory) to evaluate excess molar volumes and excess isentropic compressibilities of ternary mixtures using the concept of connectivity parameter of third degree of molecules, 3ξ (which deals with the topology of the constituents in pure and mixed state) to obtain an expression that describe well the measured data.

Effect of the Amphotericin B and Its Copper Complex on a Model of the Outer Leaflet of Human Erythrocyte Membrane.

A comparative study on the effect of an antibiotic amphotericin B (AmB) and its copper complex on the multicomponent monolayers imitating the outer leaflet of human erythrocyte membrane has been performed by means of the Langmuir monolayer technique. The properties of mixed films were analyzed by thermodynamic description of the interactions between the molecules complemented with the morphology of monolayers established by Brewster angle microscopy (BAM). The results revealed differences in the molecular organization of the two antibiotic forms at the air/water interface, which were explained by the different spatial structure of the complex. The lipophilicity of the complex contributed to considerably more effective interactions with the components of the model membrane, compared to pure antibiotic, expressed by negative values of the excess of free energy of mixing ΔGexc in the whole range of mole fractions. The mixed films with AmB were more stable as the proportion of lipids in the mixture increased. BAM images demonstrated that the addition of antibiotic at high content into the lipid mixture led to the formation of crystallite structures within the film, probably caused by the expelling of AmB molecules from mixed monolayers. These findings could help to explain the mechanism of the hemolytic activity of polyene antibiotics.

Solvation analysis of some Solvatochromic probes in binary mixtures of reline, ethaline, and glyceline with DMSO

Binary mixtures of solvents are widely used in chemical processes in order to tune the polarity properties of the media and to facilitate chemical and physical processes. In this study, deep eutectic solvents (DESs) were considered as new green media for chemical processes. Solvatochromic behavior was investigated at 25°C over the whole range of mole fractions of binary mixtures of dimethyl sulfoxide with urea-choline chloride (reline), ethylene glycol-choline chloride (ethaline), and glycerol-choline chloride (glyceline) with as common DESs. In these DESs the molar ratio of choline chloride to urea, ethylene glycol and glycerol is 1:2. Results showed that the polarity and hydrogen bond donor ability of the DESs decreases with increasing mole fraction of dimethyl sulfoxide as a molecular solvent, while hydrogen bond acceptor ability of the media increases with mole fraction of DMSO. Deviation from ideal behavior, observed for solvatochromic parameters, confirmed preferential solvation of the solutes in these media. On the other hand, molecular dynamic simulations and quantum mechanics calculations concluded interaction energies between DES components and showed clearly different compositions in the solvation shells of the solutes in the solvent mixtures.

Excess enthalpies and excess volumes of binary mixtures containing a linear carboxylic acid + di-iso-propyl ether at 298.15 K and 0.1 MPa

Molar heat of mixing and volume change of mixing, coinciding with molar excess enthalpies, H E, and molar excess volumes, V E, respectively, of binary mixtures composed by a linear saturated aliphatic acid of general formula: CH3(CH2)u-2–CO2H [u = 2, 3, 4, 5, 6, 7, 8] + di-iso-propyl ether, [(CH3)2CH−]2O, have been measured in the whole range of mole fraction at 298.15 K and 0.10 MPa. The H E experimental determinations have been realized by means of a mixing flow calorimetric apparatus, and V E have been calculated from density data acquired by using a vibrating tube densitometer. Mixing is exothermic for all investigated systems. The values at equimolar composition, H x=0.5 E , are in the range: (−385 ± 1 to −140 ± 4) J mol−1. The more negative value is attributable to butanoic acid-containing mixture; then, H E decrease in absolute value as the alkyl chain of the acid increases. For the same systems, the V E trends are different: the value at equimolar composition, V x=0.5 E , always negative, increase regularly in absolute value as the alkyl chain length of the acid increases from –1.12 × 10−6 m3 mol−1 for mixtures containing ethanoic acid to −1.75 × 10−6 m3 mol−1 for octanoic acid-containing mixtures.

Miscibility of dl-α-tocopherol β-glucoside in DPPC monolayer at air/water and air/solid interfaces

The role of newly synthesized tocopherol glycosidic derivative in modifying molecular organization and phase transitions of phospholipid monolayer at the air/water interface has been investigated. Two-component Langmuir films of dl-α-tocopheryl β-D-glucopyranoside (BG) mixed with dipalmitoyl phosphatidylcholine (DPPC) in the whole range of mole fractions were formed at the water surface. An analysis of surface pressure versus mean molecular area (π-A) isotherms and Brewster angle microscope images showed that the presence of BG molecules changes the structure and packing of the DPPC monolayer in a BG concentration dependent manner. BG molecules incorporated into DPPC monolayer inhibit its liquid expanded to liquid condensed phase transition proportionally to the BG concentration. The monolayers were also transferred onto solid substrates and visualized using an atomic force microscope. The results obtained indicate almost complete miscibility of BG and DPPC in the monolayers at surface pressures present in the biological cell membrane (30-35·10-3 N·m-1) for a BG mole fraction as high as 0.3. This makes the monolayer less packed and more disordered, leading to an increased permeability. The results support our previous molecular dynamics simulation data.

Vapor–Liquid Equilibria, Excess Enthalpy, and Density of Aqueous γ-Valerolactone Solutions.

Thermodynamic measurements were made for the binary mixture of water + γ-valerolactone (GVL) and for pure GVL to facilitate the development of the technology of lignin removal from lignocellulosic biomass (Fang, W.; Sixta, H. Advanced Biorefinery based on the Fractionation of Biomass in γ - Valerolactone and Water. ChemSusChem 2015, 8, 73−76). The density and vapor pressure of pure GVL as a function of temperature were measured and correlated for a wide range of the temperatures and pressures. Isothermal vapor–liquid equilibrium (VLE) data of the binary mixture of water + GVL were measured at 350.2 K with a static total pressure apparatus. Absence of an azeotrope was confirmed by circulation still measurements with diluted GVL solutions. Excess molar enthalpy (hE) of the mixture for the whole range of mole fractions including infinite dilution was measured using a SETARAM C80 calorimeter equipped with a flow mixing cell at 322.6 and 303.2 K. The VLE and hE data were used for the optimization of UNIQUAC an...

Miscibility of Perylene Derivatives with Fatty Acid in Two-Dimensional Binary Mixture

Two component mixtures of a uorescent perylene dye (derivative of 3,4,9,10-perylenetetracarboxylic acid) with arachidic acid in the whole range of mole fraction have been investigated in form of molecular monolayers at the air water interface at di erent pH of the water subphase. Miscibility of the components in the Langmuir monolayers have been examined for pH 3 and pH 13 of the subphase. Using the Langmuir Blodgett technique the monolayers were transferred onto freshly cleaved mica sheets and morphology of the lms was analyzed using atomic force microscopy working in tapping mode. Investigation of the components miscibility in monolayers, determined by mean molecular area and surface pressure analysis reveals di erent behavior of the mixtures depending on pH of the subphase. Atomic force microscopy morphology images of the Langmuir Blodgett lms strongly support conclusion about the components mixing and coverage of the mica surface. It has been found that onto acidic subphases components are only miscible in vestigial form, whereas on alkaline the miscibility is strongly a ected by the dye concentration.

Volumetric and viscometric behaviour of the binary systems of N-methyldiethanolamine and diethanolamine with 1-butyl-3-methylimidazolium acetate at various temperatures

In the present work, density and viscosity of two binary mixtures of N-methyldiethanolamine (MDEA) and diethanolamine (DEA) with 1-butyl-3-methylimidazolium acetate ([bmim][acetate]) are measured. The experiments were carried out at atmospheric pressure and at T=(293.15 to 343.15)K for density and from 293.15K to 353.15K for viscosity over the whole range of mole fraction. Using the density and viscosity results, several physical and thermodynamic properties such as excess molar volumes (VE), coefficients of thermal expansions (α), viscosity deviation (Δη),molar activation entropy (ΔS), molar activation enthalpy (ΔH) and molar activation Gibbs free energy (ΔG) for these binary mixtures are calculated.The experimental results of the density and viscosity for the pure systems as well as the binary systems show a decrease with increasing temperature as expected. The results of density measurements show that over all ranges of temperatures investigated the density of the pure components show the following trend: DEA>[bmim][acetate]>MDEA. Therefore, in the binary mixtures of the (MDEA+[bmim][acetate]), the density of the mixture reduces with decreasing concentration of the ionic liquid and for the (DEA+[bmim][acetate]) mixture the density of the blend enhances to reduce the concentration of the ionic liquid. Moreover, the calculated excess molar volumes show a positive deviation from ideality for the two binary mixtures. The behaviour of change of viscosity against concentration for the (MDEA+[bmim][acetate]) system is different from the (DEA+[bmim][acetate]) mixture so that for the first system the value of the viscosity rises with increasing [bmim][acetate] mole fraction, but in the second system there is a minimum viscosity point in the DEA-rich region.

Thermodynamic properties of dimethyl phthalate + vinyl acetate, diethyl phthalate + vinyl acetate or bromocyclohexane, and dibutyl phthalate + vinyl acetate or 1,2-dichlorobenzene at T = 298.15–308.15 K

AbstractThermodynamic properties (densities and viscosities) of binary mixtures of diethyl phthalate (DEP) + bromocyclohexane, dibutyl phthalate (DBP) + 1,2-dichlorobenzene, and vinyl acetate (1) + dimethyl phthalate (DMP) (2), + diethyl phthalate (2), or + dibutyl phthalate (2) were measured over the whole range of mole fractions at atmospheric pressure and different temperatures (T = 298.15 K to 308.15 K). For these mixtures, their excess molar volumes (V E) and viscosity deviations (Δη) were calculated from the experimental data. These results were correlated with the Redlich-Kister polynomial equation to derive the coefficients and standard errors.