Buffers for the Physiological pH Range: Thermodynamics of the Second Dissociation of N-(2-Hydroxyethyl)piperazine-N′-2-hydroxypropanesulfonic Acid From 5 to 55°C

The second acidic dissociation constants pK ₂ of the ampholyte N-(2-hydroxyethyl) piperazine-N-2-hydroxypropanesulfonic acid (HEPPSO) have been determined at seven temperatures from 5 to 55°C from emf measurements utilizing hydrogen and silver–silver chloride cells without liquid junction. The thermodynamic quantities, G°, H°,S°, and C _p ^o have been calculated from the temperature coefficient of pK ₂. At 25°C, the pK ₂ = 8.042 and at 37°C, pK ₂ = 7.876; hence, buffer solutions of HEPPSO and NaHEPPSOate are important for pH control in the region close to that of clinical fluids (blood serum). Conventional pH values from 5 to 55°C as well as those obtained from liquid junction correction at 25 and 37°C have been reported for three buffer solutions with the compositions (molality scale): (1) equimolal mixture of HEPPSO (0.04 m) + NaHEPPSOate (0.04 m) + NaCl (0.12 m); (2) HEPPSO (0.08 m) + NaHEPPSOate (0.08 m); and (3) HEPPSO (0.08 m) + NaHEPPSOate (0.08 m) + NaCl (0.08 m).     

果糖-水混合溶液中多组分电解质热力学

恒定混合溶液总离子强度I=1.0000 mol•kg－1,改变果糖-水混合溶液中果糖的质量分数w=2.5％、5.0％和7.5％的条件下,应用电动势方法测定下列无液体接界电池(A)和(B)在278.15、283.15、288.15、293.15、298.15、303.15、308.15、313.15、318.15 K等9个温度下的电动势: Pt, H2 (105 Pa)│HCl(m), C6H12O6(w), H2O(1－w)│AgCl-Ag (A) Pt, H2 (105 Pa)│HCl(mA), NaCl(mB), C6H12O6(w), H2O(1－w)│AgCl-Ag (B) 根据测得电池的电动势,计算出混合溶剂中AgCl-Ag电极的标准电极电势和HCl的标准迁移吉布斯自由能、迁移熵和迁移焓; 求出四元混合溶液中HCl的活度系数γA.结果表明在溶液中总离子强度I保持恒定,HCl的活度系数服从Harned规则,进一步讨论了混合物中HCl的介质效应.     

Computation of Rotation Matrices Making Lined‐Up to the Local Cartesian Coordinates

Rotation matrices were expressed in terms of Gaunt coefficients and complex spherical harmonics. The rotation matrices were calculated using two different ways. In the first, Gaunt coefficients and normalized complex spherical harmonics were directly calculated using binomial coefficients; in the second, Gaunt coefficients and complex spherical harmonics were recursively calculated. The methods were compared with respect to accuracy and computation time (CPU) for low and very high quantum numbers.     

Kováts' coefficients for predicting polarities in silicone stationary phases and their mixtures

Summary A correlation between the retention polarity and the Kováts' coefficient has been found for a number of commercial stationary phases used in gas chromatography. The correlation has been used to predict the polarity of a few mixed stationary phase columns prepared as binary mixtures of OV-101 with OV-25, DC-550 or Carbowax 20M, and also mixtures of OV-225 with SP-2340. A linear relationship was found between polarity and mixture composition. The temperature dependence of the Kováts' coefficient was investigated and found to increase linearly with temperature, the rate of increase depending on the polarity of the stationary phase, with greater increases for more polar stationary phases.     

Solubility of 1-Butene in Water and in a Medium for Cultivation of a Bacterial Strain

Solubility measurements of 1-butene in water, from 20 to 50°C and at atmospheric pressure, were carried out using a Ben-Naim/Baer-type apparatus. The experimental results have a precision of about ±0.3%. Using accurate thermodynamic relations, the Ostwald coefficients at the experimental conditions and at infinite dilution, the mole fractions of the dissolved gas at the gas partial pressure of 101.325 kPa and the Henry coefficients at the water vapor pressure were calculated. The mole fraction of dissolved gas were fitted to the Clarke, Glew, and Weiss equation and thermodynamic quantities, standard molar Gibbs energy, entropy, and enthalpy changes, for the process of transferring the 1-butene molecules from the gaseous to the water phase, were computed. Moreover, solubility measurements of 1-butene in an aqueous medium for the cultivation of Xanthobacter Py2 in the same temperature range were also performed at atmospheric pressure. These solubility data are approximately 2.6% lower than those observed in pure water.     

Inequalities for linear combinations of monomials in p-Newton sequences

The partial order on monomials that corresponds to domination when evaluated at positive Newton sequences is fully understood. Here we take up the corresponding partial order on linear combinations of monomials. In part using analysis based upon the cone structure of the exponents in p-Newton sequences, an array of conditions is given for this new partial order. It appears that a characterization in general will be difficult. Within the case in which all coefficients are 1, the situation in which, for general sequence length, there are two monomials, each of length two and nonnegative integer exponents, the partial order is fully characterized. The characterization is combinatorial, in terms of indices in the monomials, and, already here there is much more than term-wise domination.     

The equation of state of the hard-disc fluid revisited

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.     

Evaluation of mean and variance integrals without integration

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential calculus. The general nature of the technique has potential for wider applications.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.