关于吉布斯-杜亥姆方程的推导

吉布斯 杜亥姆方程是物理化学及化学热力学中的主要方程 ,在处理溶液问题时有广泛的应用 ,由其出发还可导出马居耳 杜亥姆 (Margules Duhem)等主要公式。该方程的推导方法虽然简单 ,但是在国内外流行的 2 0余部物理化学及相关教材中 ,推导方法都有问题。笔者对此进行了探讨 ,指出了错误的原因 ,并提出了正确的处理方法。     

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.     

关于一种开尔文方程推导方法的讨论

不同版次物理化学教材对开尔文方程推导的方法不同。本文通过对吉布斯界面热力学基本方程中球状液滴压强的分析,并依据对于弯曲液滴,附加压力本质上就是由弯曲液面表面张力引起的,得出某物理化学教材中,对小液滴的气液两相平衡过程,其吉布斯自由能的变化为零。对于恒温下,把处于外压为p0的平面液滴分割为处于外压为p_r的小液滴的过程,其吉布斯自由能的变化为2σM/ρr。     

关于等温循环方法推导开尔文公式的讨论

等温循环方法是物理化学教材中推导开尔文公式的一个经典方法。本文从热力学基本原理出发,明确指出其中小液滴可逆相变为气体的吉布斯自由能变化值应由吉布斯自由能判据求解,并对温度恒定、两相压强分别恒定时的判据进行了重新推导。同时,本文还提出了一种对推导开尔文公式的等温循环法的新理解方式,该方式在建立的"箱管模型"辅助下,意义明确,便于理解,更适宜教学使用。     

开尔文公式的推导方法新思路

应用解决热力学问题的重要方法--状态函数法,依据宏观实际过程设计途径,从相平衡条件及热力学基本关系式入手,推导出开尔文公式。有助于通过感性认识更好地理解开尔文公式及亚稳状态的本质。     

关于开尔文公式推导的讨论

应用弯曲界面存在的气液平衡条件和界面热力学方法,分析讨论了物理化学教材中开尔文公式的推导方法和过程,指出了存在的一些容易产生误解的问题。明确指出:等温下小液滴饱和蒸气压相对于平面液体饱和蒸气压的增大是由弯曲液面下液体的附加压力引起的,而不是界面自由能变化所致。并提出了一些教学建议。     

活用dF=δW'推导热力学公式

应用dF=δW'推导了拉普拉斯方程、开尔文方程、毛细管液柱高度计算公式、杨方程、贝林方程和大气分布定律等热力学公式,给出了这类推导的一般思路。     

外压法推导开尔文公式的探究

液体的饱和蒸气压受外压的影响,根据外压对液体饱和蒸气压的影响公式可以推导出液滴、弯曲液面的开尔文公式。     

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。     

关于熵判据、亥姆霍兹函数判据和吉布斯函数判据的讨论

通过理论推导和举出反例的方法,指出了熵增原理的应用限制。对亥姆霍兹函数判据和吉布斯函数判据也提出了应延伸其外延的教学建议。     

Kelvin方程的一种理论推导

从液滴平衡条件推导出严格意义的Kelvin方程, 验证了其在宏观尺度可以转化为经典形式. 利用Tolman方程, 在考虑表面张力与曲率半径关系的条件下, 给出在液体压缩性可忽略时, 饱和蒸气压、蒸气密度、蒸气摩尔体积和曲率半径等关系; 液体压缩性不可忽略时, 得出以等温压缩系数和Tolman长度表示的饱和蒸气压与液滴半径的关系.     

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。     

Extending the Gibbs tangent plane semicontinuous mixtures

The computation of phase equilibrium for semicontinuous mixtures results in a set of algebraic-functional equations which are commonly solved using the pseudocomponent approach or reducing the order of the functional equations to a set of algebraic equations by means of a Petrov–Galerkin approach. Both approaches can be taken as particular cases of the method of weighed residuals. In order to perform stability analysis of phase equilibrium, the classical tangent plane criterion algorithms can be used as the first approach. There is a lack of functional formulation for the stability criterion in the literature. In some special cases, such as mixtures containing continuous families of heavy-components, a new formulation of the tangent plane criterion is required. In the present work, functional extensions of the Gibbs tangent plane criterion are described. The use of the proposed criteria was exemplified by calculating solid–liquid phase equilibrium of a crude oil containing asphaltenes on titration with a precipitating agent, n-pentane.     

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

Determining the Gibbs energy of ion transfer across water-organic liquid interfaces with three-phase electrodes.

Ions can be transferred between immiscible liquid phases across a common interface, with the help of a three-electrode potentiostat, when one phase is an organic droplet attached to a solid electrode and containing a redox probe. This novel approach has been used in studies to determine the Gibbs energy of anion and cation transfer, ranging from simple inorganic and organic ions to the ionic forms of drugs and small peptides. This method of studying ion transfer has the following advantages: (1) no base electrolytes are necessary in the organic phase; (2) the aqueous phase contains only the salt to be studied; (3) a three-electrode potentiostat is used; (4) organic solvents such as n-octanol and chiral liquids such as D- and L-2-octanol can be used; (5) the range of accessible Gibbs energies of transfer is wider than in the classic 4-electrode experiments; (6) the volume of the organic phase can be very small, for example, 1 microL or less; (7) the experiments can be performed routinely and fast. Herein, the basic 5 principle is outlined, as well as a summary of the results obtained to date, and a discussion on the theoretical treatments concerning the kinetic regime of the three-phase electrodes with immobilized droplets.     

Meaning and Measurability of Single‐Ion Activities,the Thermodynamic Foundations of pH,and the Gibbs Free Energy for the Transfer of Ions between Dissimilar Materials

Considering the relationship between concentration and vapor pressure (or the relationship between concentration and fugacity) single‐ion activity coefficients are definable in purely thermodynamic terms. The measurement process involves measuring a contact potential between a solution and an external electrode. Contact potentials are measurable by using thermodynamically reversible processes. Extrapolation of an equation to zero concentration and ionic strength enables determination of single‐ion activity coefficients. Single‐ion activities can be defined and measured without using any extra‐thermodynamic assumptions, concepts, or measurements. This method could serve as a gold standard for the validation of extra‐thermodynamic methods for determining single‐ion activities. Furthermore, it places the concept of pH on a thermodynamically solid foundation. Contact potential measurements can also be used to determine the Gibbs free energy for the transfer of ions between dissimilar materials.