一元弱酸溶液中氢离子浓度计算公式的使用条件

利用质子条件式（PBE）推导了一元弱酸溶液中氢离子浓度的各类计算公式，对它们的使用条件进行了解释。     

酸碱混合溶液酸度的统一计算方法

本文应用质子条件得到酸碱混合溶液氢离子浓度的表示式为: [H~+]-[OH]+b-a+(?)c_(?)Q_i-(?)c_iQ_j=0根据此式设计了计算程序。并算得一系列不同酸碱混合溶液的pH值,与文献值对照相符。     

数学方法推导一元弱酸溶液氢离子浓度的近似公式及适用条件

近似计算一元弱酸HA溶液的氢离子浓度[H+]（相对误差在±5%以内）是分析化学工作者需要掌握的方法。利用严谨的数学方法,获得了各类近似公式的使用条件和浓度适用范围。例如,从近似式[H+]AV1=1/2（-Ka+√Ka2+4cKa+4c）出发,推导出了计算氢离子浓度的其他2个近似公式：（1）c越小,[H+]AV1越趋向c。计算表明,当满足c≤1/19Ka和c≥5.0×10-7 mol/L时,弱酸HA就可作强酸处理,此时得到近似式[H+]AV4=c,这极大简化了弱酸溶液氢离子浓度的计算。（2）c越大,[H+]AV1越接近√cKa。当满足c≥105Ka和cKa≥10Kw时,弱酸溶液氢离子浓度可按最简式[H+]AV2=√cKa计算。还解释了c≥105Ka和c≤1/19Ka时所包含的物理意义。需要强调的是,本文首次给出了各近似式的浓度适用范围,比如忽略水的解离时,除了满足cKa≥10Kw,还必须要求c≥6.0×10-6 mol/L。     

多元弱酸氢离子浓度计算条件的比较

在大学化学教学中,多元弱酸溶液氢离子浓度计算条件在不同的教材中有不同的版本,这给教师和学生的教与学都带来了困惑。由氢离子浓度计算的最简式所要求的相对误差确定了多元弱酸氢离子浓度计算允许的相对误差,通过讨论可忽略二级酸解离产生的氢离子浓度所需的一级和二级酸常数的比值条件,选出了具有相对通用性的计算条件和一种更具普遍适用性的计算策略。     

一元弱酸弱碱盐溶液中氢离子浓度的计算问题

无机化学中，关于弱酸弱碱盐溶液中氢离子浓度的计算公式，是以NH4Ac为例推导的，其公式为[1]:推导此公式的前提条件是Ka=kb，所以计算Ka与Kb相差不大的弱酸弱碱盐溶液中氢离子的浓度，无疑是可以的。如NH4AC：Kb=1.76×10（－5）；Kb=1．774×10（－5）。那么，对于Ka与Kb相差较大的弱酸弱碱盐，如NH4CN：Ka=4.93×10（－10）；Kb=1．774×10（－5），能否用此公式计算氢离子浓度呢？本文就此问题作如下讨论。一、计算一元弱酸弱碱盐溶液中氢离子浓度的精确公式以一元弱酸铵盐为例进行推导。设分子式为NH4A，在溶液中同时有NH4＋…     

状态法直接书写质子守恒式

质子守恒式(proton balance equation,缩写PBE)亦称质子条件,是用酸碱质子理论处理酸碱平衡问题的重要环节。固然它可以根据溶液体系的电荷平衡及物料平衡关系式导出,但更为简单的一种方法是根据溶液中质子接受体和给予体间得失质子总数的关系直接写出。因此,国内外的书刊多采用所谓“零水准法”直接书写质子守恒式,即首先选择溶液中大量存在     

磷酸和氢氧化钠混合后溶液的主要组成及pH计算*

磷酸和氢氧化钠混合后溶液的组成较为复杂,氢离子浓度的计算较为繁琐。但在pH的近似计算中,通常只需考虑2者混合后溶液的主要组成,根据主要组成再选择相应的公式计算即可,因此分析混合后溶液的主要组成成为此类溶液氢离子浓度计算的关键。首先分析了磷酸和氢氧化钠以不同的物质的量之比混合后溶液的主要组成,重点讨论和导出了2者混成不同缓冲溶液的有关计算公式,公式规律性强,简单实用,易于掌握和应用。     

基于质子条件式的终点误差精确式

容量分析中,滴定终点的误差决定了该分析方法的可靠性。根据质子条件式,可推导出终点误差的精确式。该表达式用滴定开始前而不是终点时物质的浓度进行计算;用滴定终点时的p H进行计算,不需要计算化学计量点时的p H;所得出的精确式具有通用性,能有效降低学习与记忆的难度,提高计算结果的准确度。     

一元弱酸溶液氢离子浓度近似计算的课程新设计

通常情况下,一元弱酸HA溶液氢离子浓度可按近似式■估算。不同于现有教科书,本文以新的方式导出上述公式,并用数学方法推导出了[H~+]_(AV1)和[H~+]_(AV2)近似式的使用条件。(1)溶液中[H~+][OH-]时,可忽略水的离解,此时可用[H~+]_(AV1)估算溶液pH。[H~+]_(AV1)与氢离子准确浓度[H~+]T相对误差不大于±5%时,需要满足两条件c6.0×10~(-6)mol·L~(-1)和c K_a≥10K_w;(2)用[H~+]_(AV2)估算溶液pH的条件为[H~+]■[OH-]和[HA]≈c,即同时忽略水的离解和忽略HA的离解。[H~+]_(AV2)与[H~+]T相对误差不大于±5%时,要求满足c K_a≥10K_w和c≥105K_a。本文首次用数学方法推导出c K_a≥10K_w或c≥105K_a等条件,与现教科书有关内容比较,具有判据严谨、边界条件清晰、学生容易理解等优点,对提高教学效果具有积极意义。     

水化介孔氧化硅表面酸碱平衡常数的测定

采用自动电位酸碱滴定技术研究了水化介孔氧化硅的表面脱质子反应.基于悬浮液的酸碱滴定数据,用Gran图法计算得到了介孔氧化硅表面氢离子键位点浓度.利用FITEQL4.0软件,采用双电层恒电容模型计算得到了相应的表面酸碱平衡常数.结果表明,与无定形氧化硅不同,介孔氧化硅表面存在对应于双齿表面硅羟基≡Si2OH和单齿表面硅羟基≡SiOH的两个脱质子常数,分别为pKa1=6.78±0.15,pKa2=10.25±0.22.根据测定得出的介孔氧化硅表面脱质子常数,构建了不同pH条件下,介孔氧化硅表面优势组分分布图,并讨论了表面电容预赋值对氧化硅表面组分分布的影响.     

一元强碱滴定一元弱酸溶液的林邦滴定曲线方程及其应用

以林邦副反应思想为基础,用质子条件式PBE、物料平衡式MBE、滴定分数和条件稳定常数等知识推导出一元强碱滴定一元弱酸溶液的林邦滴定曲线方程,并用滴定曲线方程讨论了滴定开始至化学计量点时任意一点p H的计算。     

一元强碱滴定二元弱酸的林邦滴定曲线方程及pH_(sp)计算

用质子条件式PBE、物料平衡式MBE、副反应系数和条件稳定常数等知识,推导出一元强碱滴定二元弱酸溶液的林邦滴定曲线方程,并用其推导出第一、第二化学计量点pH_(sp1)和pH_(sp2)的计算公式。     

Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water–proton bath for protein simulations at constant pH is presented. The implicit water–proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water–proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom–atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water–proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH‐dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water–proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH‐dependent ionization‐conformation coupling, and proton transfer events. © 2012 Wiley Periodicals, Inc.     

Hydrogen-bond configuration in hydrogen-bond solutions. 1. Alcohol/alcohol solutions

A theory based on the hydrogen-bond configuration is proposed and applied to alcohol/alcohol binary solutions. The theory leads explicit expressions for the mixing Gibbs energy and reproduces the experiments on the crystal–liquid phase-diagrams of pure crystals and co-crystals and mixing heats with the parameters common to these experiments. The mixing entropy arises from the increase in the hydrogen-bonding availability of proton donors to approach hydrogen-bond-free proton acceptors. The mixing heat arises from a balance between the contribution from maintaining the original associations in pure liquids and the contribution from a construction of hydrogen bonds freely to hydrogen-bond-free acceptors. When hydrogen-bond associations between component-1 and component-2 are distinguished statistically from associations in each pure component, we call the solution as a cooperative solution that has at least one stoichiometric cooperative concentration point. Some shorter alcohol/alcohol solutions and some aromatic alcohol/aromatic alcohol solutions, however, have no cooperative point and we call those solutions as the ideal hydrogen-bond solutions of which properties are mainly governed by the ideal-gas-like mixing hydrogen-bond entropy. The hydrogen-bond energies of various combinations of the proton acceptor and the proton donor have been estimated consistently from the fittings of the theory, the shifts by hydrogen bonding of the OH stretching in the Raman or IR spectroscopy, and the sublimation energy of crystals. The present theory reveals the characteristics of hydrogen-bond solutions and gives some predictions.     

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.     

论化学平衡中的独立等量关系

物料平衡等式(MBE)、电荷平衡等式(CBE)和质子平衡等式(PBE)是化学平衡定量解析中的常用等量关系。本文从理论上证明了CBE可以由MBE导出,因此在计算中不是一个必不可少的独立条件。由于H~+来源的多样性,在涉及酸碱的化学平衡中,CBE比MBE的计算效率更高。这些结论与计算实践相一致,即在配位平衡、氧化还原平衡和沉淀平衡的计算中,MBE为主,CBE起辅助作用;在酸碱平衡计算中,CBE为主,MBE为辅。PBE也不是一个独立等量关系,而且仅适用于酸碱平衡,可以完全被效率更高的CBE代替。本研究明确了化学平衡中的独立等量关系,不仅有助于提高化学平衡定量解析的效率,而且使其理论结构更加简洁明晰。     

A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

Proton diffusion determination and dual structure model for nickel hydroxide based on potential step measurements on single spherical beads

Potential step measurement is carried out on single beads of spherical nickel hydroxide to determine the proton diffusion coefficient (D) and concentration of the effective proton vacancies (C). The semi-infinite diffusion equation for the initial stage and the finite diffusion equation for the long-term of the current response to potential step are used for deducing the D and C values. The diffusion coefficients deduced from short and long-term current responses are in the order of magnitude 10(-7) and 10(-10) cm2 s(-1), respectively. The sum of the effective proton vacancy concentrations associated with the two D values comes out to be equal within experimental error to the effective proton vacancy concentration converted from the released electricity during discharge. A dual structure model is proposed to interpret the above-mentioned findings, featuring densely packed grains within which proton diffusion is slow and an inter-grain matrix where proton diffusion is fast. With this model the huge difference (about 6 orders of magnitude) in D values reported in the literature as well as the controversy of the dependence of diffusion coefficient on the state of charge can be largely rationalized. This dual structure model is supported by SEM and AFM observations.     

面向过程的分析化学酸碱平衡体系定量解析策略

在微机高度普及和数值计算软件迅速发展的背景下,本文提出了面向过程的解析策略,用于酸碱平衡体系的定量计算。证明了酸碱平衡体系中"质子条件"不独立于"物料平衡"和"电荷平衡",而且不如后二者直观、容错性高。因此,面向过程的解析策略基于"物料平衡"和"电荷平衡"两种基本定量关系式。相对于传统的公式计算,面向过程的解析策略的重点是对平衡体系的分析以及定量关系式的建立,数值计算则由软件完成。结果表明,面向过程的解析策略方便直观、容易实施,不需要任何近似条件,不需要记忆公式,原则上能解决所有酸碱平衡体系的计算问题。在教学中应用这种策略,不仅能够显著减轻学生的记忆负担,提升学习兴趣,教师也会有更多的课时用于复杂酸碱平衡体系的深入讲解。本研究作为当前形势下分析化学教学改革的一个尝试,对传统课程内容进行优化重组,去冗存精,使其简明凝练,重点突出,定量分析的主旨更加明晰。