关于球形小液滴热力学公式及其气液平衡条件的讨论

依据热力学第一和第二定律,从不同角度导出了球形小液滴的热力学基本公式。明确指出公式中的压力为液体相的压力,不是气相压力。分别用熵判据和Gibbs自由能判据证明了小液滴的气液相平衡条件为物质在两体相的化学势相等。强调指出:相平衡条件具有普适性,与是否为孤立体系或封闭体系及其类型无关,不仅适于球形液滴,对其他形状的液体也适用。对文献中存在的相关问题进行了较详细的讨论,澄清了一些容易模糊的认识。     

物理化学课程中相平衡理论的教学策略

针对物理化学相平衡章节体系多变、知识点繁多、相图抽象等问题提出了一套系统的教学策略。首先对相平衡中的基本概念和定律进行论述,并强调重、难点;随后对章节知识点进行总结归纳,通过表格系统罗列相图的体系、相律、应用和术语;最后提出相图解读通行方法,并结合具体例子讲解这些方法、相律以及杠杆规则如何使用。     

关于弯曲界面气液两相相平衡化学势相等热力学判据的讨论

Thermodynamic criterion of equal chemical potential for phase equilibrium between gas and liquid in curved interface has been introduced in many textbooks and papers. In this paper, the process of the derivation of the criterion is proved to be wrong with analysis. In order to solve the problem, a proof procedure for the thermodynamic criterion of equal chemical potential is provided based on the definition of chemical potential. At the same time, a new thermodynamic criterion of two-phase equilibrium in curved interface is established using Gibbs interface thermodynamics and a new method for derivation of Kelvin equation is put forward based on the thermodynamic criterion of two-phase equilibrium. The new criterion which is derived directly from the second law of thermodynamics has a specific thermodynamic significance and clear physical model.     

多组分体系相图中的杠杆原理形式

讨论了两相和三相多组分体系中杠杆原理的两种形式。对两组分体系,利用三相线上的杠杆原理关系式和凝固点降低公式,解释了熔化物体系冷却过程中的步冷曲线。另外,还讨论了三组分体系相图中,同一直线段上三个物系点之间的类杠杆原理关系式。该关系式可以用于不同浓度溶液的配制和三相体系相图的绘制。     

两相平衡范特霍夫方程的应用

应用相平衡常数讨论了范特霍夫方程在简化一些两相平衡热力学公式推导时的应用。     

Thermodynamic modeling for clathrate hydrates of ozone

We report a theoretical study to predict the phase-equilibrium properties of ozone-containing clathrate hydrates based on the statistical thermodynamics model developed by van der Waals and Platteeuw. The Patel–Teja–Valderrama equation of state is employed for an accurate estimation of the properties of gas phase ozone. We determined the three parameters of the Kihara intermolecular potential for ozone as a = 6.815 · 10⁻² nm, σ = 2.9909 · 10⁻¹ nm, and ε · k_B⁻¹ = 184.00 K. An infinite set of ε–σ parameters for ozone were determined, reproducing the experimental phase equilibrium pressure–temperature data of the (O₃ + O₂ + CO₂) clathrate hydrate. A unique parameter pair was chosen based on the experimental ozone storage capacity data for the (O₃ + O₂ + CCl₄) hydrate that we reported previously. The prediction with the developed model showed good agreement with the experimental phase equilibrium data within ±2% of the average deviation of the pressure. The Kihara parameters of ozone showed slightly better suitability for the structure-I hydrate than CO₂, which was used as a help guest. Our model suggests the possibility of increasing the ozone storage capacity of clathrate hydrates (∼7% on a mass basis) from the previously reported experimental capacity (∼1%).     

表面活性剂溶液油水界面相平衡研究

以Butler方程为基础,导出了1组通用的界面相平衡计算方程。利用此方程计算了多个实际体系,结果令人满意。根据实验现象及计算结果,提出了一种多组分界面相物理模型并探讨了表面活性物质在油水界面上的相互作用规律,为乳状液、微乳状液等研究提供了有益的信息。     

合成氨反应动力学平衡常数与热力学平衡常数的关系

根据当前普遍被接受的氨合成和氨分解机理,明确了氨合成及分解反应的速度控制步骤,确定了氨合成和氨分解反应的动力学方程,进而导出合成氨反应的动力学平衡常数表达式,与热力学平衡常数进行了比较,明确了2者之间的关系。有助于理解合成氨热力学平衡常数与反应速率的关系。     

The La2S3-LaS2 system: Thermodynamic and kinetic study

A detailed thermodynamic study of the LaS₂-La₂S₃ system in the temperature range 350-1000 °C was performed, starting from high quality crystals LaS₂ as the highest polysulfide in the system, and using a sensitive static tensimetric method with a quartz Bourdon gauge and a membrane as a null-point instrument. The p_S-T-x diagram obtained has shown that the phase region covering the composition between LaS₂ and La₂S₃, which was previously described as a single grossly nonstoichiometric phase, consists of three discrete stoichiometric phases, LaS_2.00, LaS_1.91, and LaS_1.76, where compositions could be determined with an accuracy of ±0.01 f.u. The thermodynamic characteristics of evaporation of the polysulfides as well as standard heat of LaS₂ formation were calculated. The role of kinetics in the formation of ordered superstructures of sulfur-poorer polysulfides with different formal concentration of vacancies is considered.     

A Combined Kinetic and Thermodynamic Approach for the Interpretation of Continuous‐Flow Heterogeneous Catalytic Processes

The heterogeneous proline‐catalyzed aldol reaction was investigated under continuous‐flow conditions by means of a packed‐bed microreactor. Reaction‐progress kinetic analysis (RPKA) was used in combination with nonlinear chromatography for the interpretation, under synthetically relevant conditions, of important mechanistic aspects of the heterogeneous catalytic process at a molecular level. The information gathered by RPKA and nonlinear chromatography proved to be highly complementary and allowed for the assessment of optimal operating variables. In particular, the determination of the rate‐determining step was pivotal for optimizing the feed composition. On the other hand, the competitive product inhibition was responsible for the unexpected decrease in the reaction yield following an apparently obvious variation in the feed composition. The study was facilitated by a suitable 2D instrumental arrangement for simultaneous flow reaction and online flow‐injection analysis.     

一个考虑沉积物孔径分布特征的水合物相平衡模型

天然气水合物的相平衡条件一直是水合物相关研究的重点和难点. 本文探讨了沉积物孔隙大小及其分布特征对水合物相平衡条件的影响机理, 提出了有效孔隙半径的概念, 并利用沉积物孔隙大小分布特征, 假设孔径分布呈正态分布, 建立了水合物饱和度和有效孔隙半径之间的定量关系; 与传统的van der Waals-Platteeuw相平衡模型相结合, 提出了一个考虑沉积物孔隙大小及其分布特征的相平衡模型. 相对于传统模型, 本模型所表达的相平衡条件不再是二维平面的p-T曲线, 而是温度、压力以及水合物饱和度之间的三维定量关系. 这一特征使得所建模型既能较为真实地反映水合物形成与分解机理, 又能有效地考虑孔隙大小分布对水合物相平衡条件的影响. 通过与实验数据对比, 证明了所建模型的预测结果优于其他模型. 本模型在温度和压力条件确定的情况下还可以预测沉积物中水合物的饱和度, 因此, 可用于地层中水合物储量计算.     

固定相优化液相色谱法对候选新药雷公藤衍生物进行有关物质检查

采用固定相优化液相色谱法(POPLC)建立了候选新药雷公藤衍生物(T8)中有关物质的检查方法.分别采用5种不同类型的固定相色谱短柱对含有T8和有关物质的混合溶液进行实验,流动相为乙腈-水(35:65,V/V),流速为0.5 mL/min,柱温为30 ℃,检测波长为219 nm,获得相应各柱死时间、各组分保留时间和理论板...     

硫酸铯/乙醇双水相体系的相平衡

采用自制的相平衡研究装置，测定了硫酸铯/乙醇双水相体系在0、10、20和40 ℃四个温度下的等温平衡溶解度，并且获得了醇相溶液和水相溶液的折光率数据，发现温度对该体系的液-液和固-液相平衡均没有显著影响.利用“湿渣结线法”确定出四个温度下平衡固相均为无水盐，同时给出了该体系的完整相图，在相图中观察到五个相区，为该体系的进一步应用研究提供了参考数据.     

CuSO4-氨化P507-n-C6H14体系平衡常数的计算

用热力学方法研究了酸性磷萃取剂与金属体系间的平衡计算模型,萃取体系的水相采用Pitzer半经验公式求算γCu²⁺,有机相用热力学关系求出了水、正已烷和萃取剂的活度系数.实验结果用Scatchard-Hildebrand模型关联,并经回归处理,得到了萃取反应热力学平衡常数(K=1.26×10^-7～5.26×10^-7)及萃合物的活度系数.     

关于稳定单变度曲线自动判别的一种简便的普适性方法

无变度点周围各单变度曲线稳定性的自动判别，是多体系稳定平衡相图计算机成图理论中十分关键而棘手的问题。它既令化学家感兴趣，更为地质地球化学家、冶金学家、材料学家所关注。在这方面，已有不少学者做过探讨，其基本依据是“等温等压下达到平衡时体系的Ｇｉｂｂｓ自...     

The Area method for pure fluids and an analysis of the two-phase region

The Area method, developed recently for solving multicomponent phase equilibrium problems, has been extended to pure fluids. The method is based on maximizing a single objective function in the Helmholtz-volume surface along any given isotherm, which reduces the number of independent variables to only two: the saturated liquid and vapour volumes. Two techniques are employed to find the maximum of the objective function, the integral and iterative. The integral always finds the thermodynamically stable solution without any prior assumptions about the values of the molar volumes. This factor distinguishes the integral from the iterative technique and also from methods based on the Maxwell equal-area principle. The method has been applied to a group of high accuracy non-cubic equations of state and some of the thermodynamic inconsistencies which occur inside the two-phase region are explored. A new inequality constraint which eliminates these inconsistencies during the development of new equations of state is proposed, and initial results with fitting a preliminary Helmholtz equation of state for benzene are encouraging.     

Mass Variables and Chemical Potentials in the Gibbs and De Donder Formulations of Chemical Equilibrium

The classical thermodynamic treatment of chemical equilibria in closed systems is founded on theoretical formulations by J.W. Gibbs and Th. De Donder. These two theories represent mathematically equivalent energy variation problems, related to each other through a mass variable transformation analogous to coordinate transformations in mechanics. Associated with the change in mass variables, chemical potentials of reactive substances are defined differently in the two theories, and are subject to different sets of constraints. Traditionally, the two sets of constraints have been merged into one, by assuming that the chemical potential represents the same variable in both theories, an assumption that is formally inconsistent with the difference in chemical potential definitions. Merging of constraints is still possible if chemical potentials remain invariant in value as a manifestation of symmetry under a Gibbs – De Donder mass transformation, but such symmetry has not been investigated. Here we demonstrate chemical potential invariance by reformulating De Donder’s theory using Lagrange multipliers, and combining the resulting constraints on chemical potentials with the classical Gibbs constraints, in a phase equilibration thought experiment. A new form of the Gibbs–Duhem (GD) relation is derived in the De Donder mass system. Comparing this relation to the classical GD equation in Gibbs’ component framework, subject to chemical potential invariance, directly yields the linear operator mapping the De Donder mass variables onto the set of Gibbs component masses. Results are illustrated for a simple ion exchange reaction, in the process solving the longstanding problem of determining solid exchanger activities in ion exchanging mixtures. It is pointed out that, even though the Gibbs and De Donder formulations are mathematically equivalent, the formal structure of De Donder’s theory allows a more explicit and systematic treatment of constraints, and also defines chemical masses in a form more naturally adapted to typical experimental measurements.     

298.16 K时Na+, Mg2+//Cl-, SO42-, NO3-, H2O体系中NaCl饱和区域相平衡

采用等温溶解平衡法研究了五元体系Na+, Mg2+//Cl-, SO42-, NO3-, H2O在298.16 K下氯化钠饱和平衡体系的溶解度, 获得了相应的投影干盐图、氯图和水图. 研究结果表明, 在298.16 K下氯化钠饱和时, 该五元体系投影干盐图由8个二盐共饱和的双变面、13条三盐共饱的单变线和6个四盐共饱的零变点构成, 存在两种复盐, 8个二盐共饱双变面分别对应于NaCl+NaNO3, NaCl+Na2SO4, NaCl+MgCl2·6H2O, NaCl+MgSO4·Na2SO4·4H2O, NaCl+Mg(NO3)2·6H2O, NaCl+NaNO3·Na2SO4·2H2O, NaCl+MgSO4·7H2O 和NaCl+MgSO4·(1—6)H2O. 讨论了该相图在新疆硝酸盐矿开发利用过程中的应用.     

五元交互体系Li+,Na+,K+//CO32-,Cl--H2O在298.15K的相平衡研究

针对西藏扎布耶盐湖卤水组成,采用等温溶解平衡法研究了五元交互体系Li+,Na+,K+//CO32-,Cl--H2O于298.15K时的相平衡,并绘制了相图(空间立体图和Li2CO3饱和的投影图).结果表明,该五元体系相图含有7个结晶区、13条单变量线和4个无变量点.7个结晶区由6个单盐结晶区和1个复盐结晶区组成,分别为LiCl·H2O,NaCl,KCl,Li2CO3,K2CO3·3/2H2O,Na2CO3·10H2O和NaKCO3·6H2O,没有形成固溶体和天然碱(Na2CO3·NaHCO3·2H2O).4个无变量点标记成K1,K2,K3和K4,所对应的平衡固相盐分别是:Li2CO3+NaKCO3·6H2O+Na2CO3·10H2O+KCl,Li2CO3+NaKCO3·6H2O+K2CO3·3/2H2O+KCl,Li2CO3+NaCl+KCl+LiCl·H2O和Li2CO3+NaCl+Na2CO3·10H2O+KCl.     

高二学生掌握化学平衡命题的潜在类别分析和Apriori算法研究*

高中生对化学平衡的理解是重要且仍待深入探索的研究问题。潜在变量模型和数据挖掘有助于研究者从新角度了解学生的化学平衡概念学习情况。本研究使用自编的化学平衡命题测验,应用潜在类别分析和Apriori算法呈现722名高二年级学生对化学平衡命题的掌握情况。研究发现:(1)学生适合被分为3个组别,分别为高掌握水平组、中掌握水平组和低掌握水平组;(2)根据本研究设定的参数条件,未在高掌握水平组学生的作答中获得关联规则,在中掌握水平组和低掌握水平组学生的作答中获得了一些关联规则。潜在类别分析和Apriori算法可被用于化学概念学习和其他主题的研究。