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For many years, we have devoted our research to the study of the thermodynamic properties of hydrophobic hydration processes in water, and we have proposed the Ergodic Algorithmic Model (EAM) for maintaining the thermodynamic properties of any hydrophobic hydration reaction at a constant pressure from the experimental determination of an equilibrium constant (or other potential functions) as a function of temperature. The model has been successfully validated by the statistical analysis of the information elements provided by the EAM model for about fifty compounds. The binding functions are convoluted functions, RlnKeq = {f(1/T)* g(T)} and RTlnKeq = {f(T)* g(lnT)}, where the primary linear functions f(1/T) and f(T) are modified and transformed into parabolic curves by the secondary functions g(T) and g(lnT), respectively. Convoluted functions are consistent with biphasic dual-structure partition function, {DS-PF} = {M-PF} ∙ {T-PF} ∙ {ζw}, composed by ({M-PF} (Density Entropy), {T-PF}) (Intensity Entropy), and {ζw} (implicit solvent). In the present paper, after recalling the essential aspects of the model, we outline the importance of considering the solvent as “implicit” in chemical and biochemical reactions. Moreover, we compare the information obtained by computer simulations using the models till now proposed with “explicit” solvent, showing the mess of information lost without considering the experimental approach of the EAM model.

The processes at the molecule level, which are the source of the ergodic properties of thermodynamic systems, are analyzed with special reference to entropy. The entropy change produced by increasing the temperature T depends on the increase of velocity of the particles with a decrease of the squared mean sojourn time (τm2) and gradual loss of instant energy intensity. The diminution, which is due to dilution, of the number of terms in the summation of cumulative sojourn time (τi2)Σ produces loss of energy density, thus generating a gradual increase of density entropy, dSDens. The ergodic property of thermodynamic systems consists of the equivalence of density entropy (dependent on dilution) with intensity entropy (dependent on temperature). This equivalence has been experimentally verified in every hydrophobic hydration process as thermal equivalent dilution. An ergodic dual-structure partition function {DS-PF} represents the state probability of every hydrophobic hydration process, corresponding to the biphasic composition of these systems. The dual-structure partition function {DS-PF} (Kmot·ζth) is the product of a motive partition function {M-PF} (Kmot) multiplied by a thermal partition function {T-PF} (ζth = 1). {M-PF} gives rise to changes of density entropy, whereas {T-PF} gives rise to changes of intensity entropy. {M-PF} is referred to a reacting mole ensemble (reacting solute) composed of few elements (moles), ruled by binomial distribution, whereas {T-PF} is referred to a nonreacting molecule ensemble (NoremE) (nonreacting solvent), which is composed of a very large population of elements (molecules), ruled by Boltzmann statistics. Statistical thermodynamic methods cannot be applied to {M-PF} that can be calculated by numerical methods from the experimental titration data. By development of the dual-structure partition function {DS-PF}, parabolic convoluted binding functions are obtained. The tangents to the binding functions represent the dual enthalpy, −ΔHdual = (−ΔHmot – ΔHth), and the dual entropy, ΔSdual = (ΔSmot + ΔSth). The connections between canonical and grand-canonical partition functions of statistical thermodynamics with thermal and motive partition functions of chemical thermodynamics, respectively, are discussed. Special attention has been devoted to the equality ΔHth/T + ΔSth = 0, typical of NoremEs, as an entropy–enthalpy compensation with ΔGth/T = 0. The thermodynamic potential change Δμ, as proposed by potential distribution theorem (PDT) for iceberg formation from {T-PF} of the solvent, is nonexistent because the excess solvent is at a constant potential (Δμsolv = 0). The information level offered by the ergodic algorithmic model (EAM) is more complete and correct than that offered by the potential distribution theorem (PDT): the stoichiometry of the water reaction in hydrophobic hydration processes is determined by the EAM as the function of the number ±ξw. Quasi-chemical approximation, renamed the chemical molecule/mole scaling function (Che. m/M. sF), is a fundamental breakthrough in the application of statistical thermodynamics to chemical reactions. Boltzmann statistical molecule distribution of the thermal partition function {T-PF} is scaled with binomial mole distribution of the motive partition function {M-PF}. For computer-assisted drug design, the alternative calculation procedure of Talhout, based on the previous experimental determination of binding functions, is recommended. The ergodic algorithmic model (EAM), applied to the experimental convoluted binding functions, can recover the distinct terms of intensity entropy (ΔHmot/T) and density entropy (ΔSmot), together with other essential information elements, lost by computer simulations.

The thermodynamic properties of hydrophobic hydration processes have been analyzed and assessed. The thermodynamic binding functions result to be related to each other by the mathematical relationships of an ergodic algorithmic model (EAM). The active dilution dA of species A in solution is expressed as dA = 1/(Φ·xA) with thermal factor Φ = T–(Cp,A/R) and (1/xA) = did(A), where did(A) = ideal dilution. Entropy function is set as S = f(did(A),T). Thermal change of entropy (i.e., entropy intensity change) is represented by the equation (dS)d = Cp dln T. Configuration change of entropy (i.e., entropy density change) is represented by the equation (dS)T = (−R dln xA)T = (R dln did(A))T. Because every logarithmic function in thermodynamic space corresponds to an exponential function in probability space, the sum functions ΔHdual = (ΔHmot + ΔHth) and ΔSdual = (ΔSmot + ΔSth) of the thermodynamic space give birth, in exponential probability space, to a dual-structure partition function {DS-PF}: exp(−ΔGdual/RT) = Kdual = (Kmot·ζth) = {(exp(−ΔHmot/RT))(exp(ΔSmot/R))}·{exp(−ΔHth/RT) exp(ΔSth/R)}. Every hydrophobic hydration process can be represented by {DS-PF} = {M-PF}·{T-PF}, indicating biphasic systems. {M-PF} = f(T,did(A)), concerning the solute, is monocentric and produces changes of entropy density, contributing to free energy −ΔGmot, whereas {T-PF} = g(T), concerning the solvent, produces changes of entropy intensity, not contributing to free energy. Entropy density and entropy intensity are equivalent and summed with each other (i.e., they are ergodic). From the dual-structure partition function {DS-PF}, the ergodic algorithmic model (EAM) can be developed. The model EAM consists of a set of mathematical relationships, generating parabolic convoluted binding functions R ln Kdual = −ΔGdual/T = {f(1/T)*g(T)} and RT ln Kdual = −ΔGdual = {f(T)*g(ln T)}. The first function in each convoluted couple f(1/T) or f(T) is generated by {M-PF}, whereas the second function, g(T) or g(ln T), respectively, is generated by {T-PF}. The mathematical properties of the thermodynamic functions of hydrophobic hydration processes, experimentally determined, correspond to the geometrical properties of parabolas, with constant curvature amplitude Campl = 0.7071/ΔCp,hydr. The dual structure of the partition function conforms to the biphasic composition of every hydrophobic hydration solution, consisting of a diluted solution, with solvent in excess at constant potential.

The hydrophobic hydration processes have been analysed under the light of a mixture model of water that is assumed to be composed by clusters (W 5 ) I , clusters (W 4 ) II and free water molecules W III . The hydrophobic hydration processes can be subdivided into two Classes A and B. In the processes of Class A, the transformation A (− ξ w W I → ξ w W II + ξ w W III + cavity) takes place, with expulsion from the bulk of ξ w water molecules W III , whereas in the processes of Class B the opposite transformation B (− ξ w W III − ξ w W II → ξ w W I − cavity) takes place, with condensation into the bulk of ξ w water molecules W III . The thermal equivalent dilution ( TED ) principle is exploited to determine the number ξ w . The denaturation (unfolding) process belongs to Class A whereas folding (or renaturation) belongs to Class B. The enthalpy Δ H den and entropy Δ S den functions can be disaggregated in thermal and motive components, Δ H den = Δ H therm + Δ H mot , and Δ S den = Δ S therm + Δ S mot , respectively. The terms Δ H therm and Δ S therm are related to phase change of water molecules W III , and give no contribution to free energy (Δ G therm = 0). The motive functions refer to the process of cavity formation (Class A) or cavity reduction (Class B), respectively and are the only contributors to free energy Δ G mot . The folded native protein is thermodynamically favoured (Δ G fold ≡ Δ G mot S red ≫ 0. The native protein can be brought to a stable denatured state (Δ G den ≡ Δ G mot III , with creation of cavity and negative entropy production, Δ S for ≪ 0. The negative entropy change reduces and at last neutralises the positive entropy of folding. In molecular terms, this means the gradual disruption by cavity formation of the entropy-driven hydrophobic bonds that had been keeping the chains folded in the native protein. The action of the chemical denaturants is similar to that of heat, by modulating the equilibrium between W I , W II , and W III toward cavity formation and negative entropy production. The salting-in effect produced by denaturants has been recognised as a hydrophobic hydration process belonging to Class A with cavity formation, whereas the salting-out effect produced by stabilisers belongs to Class B with cavity reduction. Some algorithms of denaturation thermodynamics are presented in the Appendices.

Piscimetrics deals with software implementation of experimental design, second-generation artificial intelligence tools, viz. Neural Nets (NNs), genetic algorithms, Fuzzy Logic, Expert Systems, Wavelets and Image analysis in the field of fisheries. A brief sketch of NNs is followed by a review of their applications in forecasting, classification, distribution and fisheries management since 1978. Forecasting in fisheries covers distribution of eggs, recruitment, fish growth/age, biomass and fish catch. Other major areas are identification, abundance and food products, environmental factors and collapse of fishery industry. The data structures are given in tensorial notation. The need for the paradigm shift from classical to multi-level hybrid NNs is emphasized.

The entropy changes, ΔS app, (i) for dissolution in water of non-polar substances and (ii) for protein-ligand complexation show linear dependences on the logarithm of the absolute temperature. For every compound, the slope m (S)=ΔC p for the line ΔS app=f(ln T) depends on the size of the molecule and is exactly equal to the slope m (H)=ΔC p found in the diagram ΔH app=f(T). This means that the slopes are rigorously proportional (with a ratio m (S)/n w=C p,w) where n w is the number of involved water molecules as determined from the enthalpy change ΔH app=f(T). It is also worth noting that the value of n w is positive (as well as m (S) and m (H)) in the dissolution of non-polar substances, whereas it is negative (as well as m (S) and m (H)) in bio-complex formation and in micelle formation. The number n w (n w>0) involved in the dissolution of non-polar substances depends on the size of the cavity (excluded volume) formed in the structure of water. These water molecules that have been excluded from the structure of the solvent absorb thermal energy that compensates for the negative enthalpy change, whereas the formation of the cavity implies there should be a large negative entropy contribution. The low solubility of non-polar substances in water depends on the highly negative entropy effect due both to cavity formation and to loss of configurational entropy by the gas trapped in a cage of water molecules. In processes involving association, as in micelle formation and in protein complexation, the cavities surrounding the separate units coalesce and the resultant cavity is smaller than the sum of the previous ones. The n w water molecules (n w

The equilibria between base A and proton H can be calculated in the probability space by means of partition functions Z A and Z H , mathematically represented by binding polynomials. The partition functions are expressed as functions of affinity constants, k j and cooperativity coefficients, b j , specific for each class j of sites. We have undertaken a series of potentiometric measurements of equilibria of polyamines with protons at 25 °C, I =0.1 KCl, in order to calculate these parameters from the experimental data by application of a special computer program. The transformation from the probability space ( Z H (or Z A ), k j and exp( b j )), to the free energy space (−Δ G = RT ln Z H (or Z A )) made possible the evaluation of the cooperativity potential Δ μ γ =− RTb i . The cooperativity potential between two amine groups separated by aliphatic chain (CH 2 ) n  depends on the length of the chain i.e. it decreases exponentially with the increase of the number of methylene groups. On the other hand, the cooperativity coefficient can be brought to the scale of the constants of Hammett equation by dividing b i by 2.303. It is then possible to calculate Taft constants σ * for substituents in primary, secondary and tertiary amines.

The relationships between statistical thermodynamics and equilibrium constants, either cumulative, stepwise or specific site constants are investigated. In order to show the link between equilibrium constants and statistical thermodynamic microscopic properties, a distinction has been introduced between non-reacting and reacting systems. The non-reacting systems are those for which continuous statistical distributions of enthalpies can be assumed. The distribution function can be obtained as an integral of the interparticle potential extended to the whole ensemble. Molecular partition functions ζA, are used to describe the properties of the ensembles. The reacting ensemble is represented by distinct distributions of enthalpies, each distribution being grouped around a mean value. Each level is representative of one species. Around each mean level the distribution is continuous as in non-reacting ensembles. The reacting ensemble of particles is described by a grand canonical molar partition function ZM=(1+kγ(i)[A])t where k is the specific site constant, γ(i) is the cooperativity function, [A] is the concentration of free ligand, and the power t indicates the maximum number of i sites in one class. The specific site constant k is proportional to the affinity of binding and is related to the depth of the minimum of the potential function. The factor γi is the cooperativity factor given by the value of the cooperativity function γ(i) at the ith level and indicates how the depth of the potential function is affected by previous binding of a ligand. The values of the stability constant and cooperativity factor can be optimized by a computer program. The derivatives of the partition function ZM with respect to ln[A] correspond to the formation function 〈n〉 (first derivative) and to the buffer capacity BC (second derivative). The derivatives of the partition function ZM with respect to temperature are reaction enthalpy ΔH (first derivative with −(1/T)) and apparent heat capacity ΔCp,app (second derivative with ln T). The denaturation heat obtained by integration of ΔCp,app dT for many proteins explains why the denaturation enthalpy depends linearly upon T.

The solubility of oxygen in water at different temperatures has been analysed in the light of a statistical thermodynamic model. According to the model, the oxygen‐water system is considered as a convoluted ensemble consisting of a reacting system, formed by oxygen molecules and structured solvent with enthalpy difference DH f between discrete enthalpy levels, and of a non-reacting system with continuous distribution of enthalpy levels. The enthalpy change of the reaction between oxygen and water, as determined either by measuring the solubility of substances in water at different temperatures either by measuring heat calorimetrically, is partially absorbed by some nw water molecules. The relaxed water molecules occupy part of the cavity formed around solute. The part of heat absorbed, DHw depends linearly upon the temperature and causes the observed changes with temperature of apparent enthalpy DHapp for the dissolution of oxygen and many other inert substances in water. The number nw is proportional to the size of solute as shown by comparison with noble gases and other inert substances slightly soluble in water. The solubilization process of all these substances is clearly analogous. © 2000 Elsevier Science B.V. All rights reserved.

The isobaric heat capacity in non-reacting and in reacting systems has been analysed. The isobaric heat capacity Cp in non-reacting systems depends on continuous distribution of enthalpy levels, according to the statistical thermodynamic model. The heat capacity in non-reacting systems is measured by supplying heat to the system and is related to the distribution of molecules either among enthalpy levels or among entropy configurations without any possibility of distinction. The isobaric heat capacity ΔCp,app in reacting systems is related to changes in distribution of molecules among enthalpy levels separated by well defined large differences ΔH as assigned by the model. Therefore, the isobaric heat capacity is apparent because it depends also on the heat intrinsically produced by the reaction inside the system. The heat capacity ΔCp,app produced by changes of temperature in differential scanning calorimetry experiments is bound to changes of association fraction α(T) inside the system. It is shown how the denaturation heat determined by integration of the experimental curve can be reproduced by integration of the function of the association fractions in a two-state denaturation process. The treatment has been extended to macromolecules constituted by different domains giving origin to more complex profiles at the denaturation.

The 'hydrophobic effect' of the dissolution process of non-polar substances in water has been analysed under the light of a statistical thermodynamic molecular model. The model, based on the distinction between non-reacting and reacting systems explains the changes of the thermodynamic functions with temperature in aqueous systems. In the dissolution of non-polar substances in water, it follows from the model that the enthalpy change can be expressed as a linear function of the temperature (ΔH app =ΔH o +n w C p,w T ). Experimental solubility and calorimetric data of a large number of non-polar substances nicely agree with the expected function. The specific contribution of n w solvent molecules depends on the size of solute and is related to destructuring (n w >0) of water molecules around the solute. Then the study of 'hydrophobic effect' has been extended to the protein denaturation and micelle formation. Denaturation enthalpy either obtained by van't Hoff equation or by calorimetric determinations again depends linearly upon denaturation temperature, with denaturation enthalpy, ΔH den , increasing with T . A portion of reaction enthalpy is absorbed by a number n w of water molecules (n w >0) relaxed in space around the denatured moieties. In micellization, an opposite process takes place with negative number of restructured water molecules (n w

The partition functions of solution thermodynamics at the macroscopic level of description correspond to typical distributions of particles at the microscopic molecular level. The partition functions can be represented in probability space which is the domain of formation constants, dilution, concentrations, probability correlation function, free-energy probability, enthalpy probability, and entropy probability. Types of ensembles, either reacting or non-reacting, yield characteristic probability diagrams. The first moment of the probability distribution belongs to thermodynamic space which is the domain of the extensive thermodynamic variables. The ratios of heat, free energy, enthalpy, entropy to thermal energy RT, as well as logarithm of activity coefficient, logarithm of probability correlation function, and logarithm of equilibrium constant can be measured in affinity thermodynamic space. The properties of the ensembles can be also represented in kinetic energy probability space which corresponds to the experimental domain of thermal dilutions, with variable {(1/[A])T} and in kinetic energy thermodynamic space which is the domain of absolute free energy, enthalpy and entropy, of −RT ln[A], and of heat and work.

BAQOR is a computer readable database for equilibrium constants in presence of different percentages of water miscible cosolvents. The present version with user friendly software in dBase III+ contains 740 records and runs on any IBM compatible PC. The physico-chemical properties of binary and ternary water-cosolvent mixtures, the equilibrium constants of proton- and metal-ligand complexes are retrievable through pop-up menus. Specific searches by metal-, ligand-, solvent-, and stoichiometry-wise and their combinations is possible. Several display modes-monitor, file and hard copy-are available for the numerical fields as well as for literature citation.

In order to obtain experimental evidence for the complexation between β-cyclodextrin and piroxicam (4-hydroxy-2-methyl-N-2-pyridyl-2H-1,2-benzothiazine-3-carboxamide-1,1-dioxide) and to investigate the thermodynamics of this interaction, a flow microcalorimetric study of this system has been undertaken. In fact, the mixing of ,β-cyclodextrin and piroxicam in ratio 1:1 in given experimental conditions gives rise to a system showing better pharmacological properties than piroxicam alone. The results confirm the formation of a complex between β-cyclodextrin and piroxicam and allow the evaluation of the equilibrium constant for the process, assuming the formation of a 1: 1 complex. It results in log K ′ = 3.54, where K ′ is the apparent formation constant at pH 9.00, in good agreement with literature data for similar compounds. The values of ΔH and ΔS are also reported.

The statistical probability of state of a solution containing a reacting receptor M, a ligand A (and eventually proton H) is described by a molar partition function Z M = exp(- ΔG / RT ) referred to M, or Z A or Z H , respectively. The partition function for one class of sites can be expressed as the function of site constants k j and cooperativity functions γ j , i = exp{ b j ( i − 1)}. Binding in a single class can be represented by a vector J p(t) whose elements correspond to single species. For more classes of sites, the joined probability is obtained as tensor product of single class vectors giving rise to complexation matrices M pqr . There is one partition function for each component of the system. If the complexes are of type H P M Q A R there are three partition functions Z H , rmZ M and Z A . The relationships between partition functions and total analytical amounts T H , T M , T A , respectively are given. The experimental data obtained in a potentiometric titration with electrode reversible to [H] or other free component can be reproduced as the function of site constants k j and cooperativity functions exp{ b j (i -1)} for each class j . The best values of k j and b j , can be calculated following a nonlinear least squares procedure by means of a computer program that is here presented.

The protonation constants log k aPP of a series of disubstituted benzoic acids in aqueous solution at different temperatures between 5° and 55°C have been determined potentiometrically. The data of log k aPP have been analyzed under the light of a statistical thermodynamic model. The curvature of the function log k app = f (1/ T ) is related to the number n w of water molecules involved in the protonation and hydration reaction. The upward concavity of the curves of dinitro compounds are steeper that those for monosubstituted acids and imply higher number of water molecules. The curves of polyalkyl-substituted benzoic acids as determined by other authors show opposite (downward concavity) curvatures corresponding to negative numbers n w of water molecules. The values of log k aPP at 25°C of disubstituted and polyalkyl-substituted benzoic acids plotted against the Hammett substituent constants δ Ham deviate significantly from the line of the Hammett model.

The isobaric heat capacity of liquid H2O, Cp, as a function of temperature, decreases between 0° and about 35°C and then increases up to 100°C. Analogous behaviour is shown by liquid D2O. A statistical thermodynamic model has been applied to the experimental heat capacity data. The behaviour is explained by assuming that an equilibrium A + B = AB is established between clusters A and AB of water of different composition. The total heat capacity is considered as the sum of three terms Cp = (1 − α)Cp,0,AB + αCp,0,A + ΔCp,app. The term ΔCp,app depends explicitly on the reaction enthalpy. In H2O, the enthalpy ΔH = − 18.4 kJ mol−1 for the dissociation reaction and the heat capacity Cp,B = 47.8 J K−1 mol−1 for free water molecules are calculated. Analogous calculations performed for D2O yield the enthalpy, ΔH = − 1.64 kJ mol−1 and the heat capacity, Cp,B = 49.18 J K−1 mol−1.

The thermodynamic statistical model based on the distribution of molecular populations among energy levels has been employed for the analysis of the solubility of hydrocarbons and other inert gases or liquids in water at different temperatures. The statistical distribution is described by a convoluted partition function ZG·ζs. The product of a grand canonical partition function ZG represents the distribution of the species in the reaction while the canonical partition function ZG represents the properties of the solvent. The first derivative of the logarithm of the partition function with respect to 1/T is the apparent enthalpy which is the result of the contributions of the separate partition functions, {ΔHaap}T=ΔHo+nwCp,wT, where {ΔHapp}T refers to ZG, nwCp,wT=−ΔHw to ζs, and ΔHo is the change in enthalpy of hydrocarbon-water reaction. The plot {ΔHapp}T vs/ T results in a straight line with slope nw at constant Cp,w. The apparent enthalpy is obtained from the coefficients of the polynomial fitting of the solubility data, as a function of 1/T. Alternatively, the apparent enthalpy can be determined calorimetrically. The enthalpy thus obtained is a linear function of the Kelvin temperature. The values of nw range from 1.6, 1.9, 5.6 to 5.8 for helium, hydorgen, butane and hexane, respectively. For fluorocompounds the range of nw is 10.1 to 11.1 indicating that nw is a function of the number of water molecules expelled from the cage of solvent to form a cavity to host the solute molecule. The analysis of several sets of calorimetric or solubility data with the present molecular thermodynamic model yields values of ΔHo and nw consistent with the size of the dissolved molecules.

The macromolecular system where denaturation takes place, is considered from a molecular thermodynamic point of view as a convolution of a grand canonical ensemble, gce and a canonical ensemble ce. The former corresponds to the solute, the latter to the solvent. The properties of this system can be represented by a convoluted partition function obtained by the product of a grand canonical partition function ZN, and a canonical partition function, ξW. If the experimental equilibrium constant, Kden = [Dhyd]/[N] is substituted for ZN and [W]nW for ξW, the convoluted partition function is K0 = Kden [W]nW, where [W] is the concentration of the solvent in the bulk and nW is the number of water molecules involved in the reaction. According to this model, by calculating the derivative ∂ ln Kden/ ∂(1/T), values of the denaturation enthalpy ΔHden should be obtained which are a linear function of the absolute temperature. The slope of the straight line ΔHden = ƒ(T) is dependent upon nW. The experimental equilibrium constant conforms to the model. The apparent isobaric heat capacity, Cp,app of the solute is calculated by double mixed derivation of ln ZN with respect to ln[W]−nW and ln T. By integration between two temperatures, as in DSC experiments, the apparent isobaric heat capacity yields the apparent enthalpy ΔHden of the denaturation process. The enthalpy thus calculated ΔHden should be a linear function of the denaturation temperature Tm in agreement with the denaturation enthalpy obtained by deriving the logarithm of the denaturation equilibrium constant. In fact, the heat supplied is comprehensive of the enthalpy due to the change of the conformation of the protein from native to denatured ΔHconf, of the hydration enthalpy, ΔHhyd, and of a term, nWCp,WTm, due to the heat absorbed by nW water molecules involved in the reaction ΔHden = ΔHconf + ΔHhyd + nWCp,WTm The hen egg white lysozyme (mol. wt. 14 100 Da) changes the denaturation enthalpy, and correspondingly the denaturation temperature Tm by changing the pH or the concentration of denaturant. The influence of pH is related to changes in the structure of the solvent rather than to an actual reaction process. In accordance with this hypothesis, the dependence of the denaturation enthalpy either from ln T or from pH or from denaturant concentration follows the same law. Values of ΔHden for hen egg white lysozyme plotted as the function of temperature give a unique straight line with slope corresponding to nW = 88.9 water molecules. The same treatment has been applied to the denaturation enthalpy for wild lysozyme of the bacteriophage T4 (mol. wt. 18 700 Da), as determined in DSC experiments. The slope of the line yields nW = 122.0 water molecules. The difference in the number of water molecules is related to the different size of the macromolecules and probably to the proportional number of hydrophobic residues. The number of water molecules changes with different substituents. Mutants of wild lysozyme appear to involve nW = 131.4 and 139.8 for T157A and R96H, respectively. These numbers are in agreement with the increased hydrophobic character of the entering groups. The process seems to be related to the formation of a cage of water molecules around the denatured protein.

The analysis of equilibria in solution by the partition function method has shown how the total chemical amounts [T[M], [TA], and [TH] of the components M, A, and H respectively can be expressed and determined as functions of different powers of site affinity constants kj and cooperativity functions γ(ij,bj), whereas the cumulative formation constants βPQR cannot be used as statistically independent parameters to be refined in least-squares processes. The same drawback holds for molar enthalpies, ΔHPQR. A special algorithm has been developed by which the heat evolved can be expressed as a function of specific site enthalpies Δj and specific cooperativity enthalpies Δhγj for each class j of sites. The algorithm represents the mathematical analog of the interconnections between components in the types of complex macrospecies MPAQHR, MPAQ, AQHR, MPHR, MP(AQHR), etc., of the chemical model assumed and their deconvolution into microspecies MPAQHR. Each class j of sites with site constant kj and cooperativity coefficient bj is described by a polynomial where Yj is any ligand M, A, or H and it is the number of sites in the class j. The concentrations of the microspecies are calculated as single terms of the polynomials Jj or by products of more terms, each of which belongs to a different Jj. Each term of the polynomial is labeled by its own index (pj, or qj, or rj, or in general ij), which is the exponent of the term and contains the statistical factor mij. calculated as the coefficient of the term of the polynomial. The product of more terms is labeled by the indices of the component terms. The relations are therefore represented by combinations of indices . In order to perform the calculation of concentrations of the microspecies and macrospecies by a procedure suitable for computer programming, each polynomial Jj is associated with a vector Jj whose elements [ij] are the terms of Jj. The cooperativity factors are set in a diagonal matrix Γj, whose elements are and then introduced into the non-cooperative polynomials Jj by vector products . The product of terms giving for each microspecies the contribution to the total concentrations [TM], [TA], and [tH] is calculated as the element of a matrix obtained as tensor product: (1,2= j1J2 or etc. Depending on the chemical model, there are additional different matrices Ll. The combination of indices of each element of Ll is . The indices are said to define an index space {i.s.}, parallel to the affinity cooperativity space. The elements of the matrices Ll are also used to set a matrix ΔC, whose elements Δcpqr are the changes of concentration of the microspecies during the thermochemical reaction. The i.s. is parallel to the concentration space also. The enthalpy change at the nth experimental point for each microspecies Mp,AqHr is calculated from the quantities which are then summed for all the indices p,q,r. This relation can also be put in a matrix form: . All these matrices define spaces which are parallel to {i.s.}. The observed heat at the nth experimental point is the scalar product where the elements of the vector Xj, with 1 ⩽ j' ⩽2jmax are the whole set of j couples of variables Δhj, Δhyj, and the elements of the vector aj' are weighted experimental thermochemical values. By repeating the calculations and summing successively the values for all the n experimental points, the system of normal equations Axj' = ΔQ is set up, where the elements of ΔQ are sums of n weighted experimental heats. By solution of the system, the values of Δhj and Δhyj for all the j classes are obtained.

The thermodynamics of binding of a ligand A and/or proton H to a macromolecule M is treated by the partition function method. In complex systems, the representation of the equilibria by means of cumulative constants βPQR used as coefficients in partition functions ZM, ZA, and ZH is ill-suited to least-squares refinement procedures because the cumulative constants are interrelated by common cooperativity functions Γj(i) and common site affinity constants kj. There is therefore the need to express ZM, ZA, ZH as functions of site constants kj, and cooperativity coefficients bj. This is done by developing an algebra of partition functions based on the following concepts: (i) factorability of partition functions; (ii) binary generating function Jj = (1 + kj[Y])it, for each class j of sites, represented by column {Jj} and row [Jj] vectors; (iii) cooperativity between sites of one class described by functions Γj,(i), represented by diagonal matrices Γj; (iv) probability of finding microspecies represented by elements of tensor product matrix Ll = {J1}[J2]; (v) statistical factors mij obtained from Newton polynomials, Jj; (vi) power operators Oi′, O(i−1)′, and O(it−1)′, transforming vectors Jj; and (vii) operators Oi or O(i−1) indicating tensor products of i or (i − 1) vectors Jj. Vectors Jj combined in tensors Ll, give rise to both an affinity / cooperativity space and a parallel index space. The partition functions ZM, ZA, and ZH and the total amounts TM, TA, and TH can be obtained as an appropriate sum of elements of matrices Ll, each of which is represented in an index space by a combination p1, P2,⋯q1, q2⋯r1, r2,⋯ of indices ij. From these indices the contribution of that element to partition function ZM, ZA, or ZH and to total amount TM, TA, or TH is calculated in the affinity / cooperativity space as product of factors: [it!/i!(it - i)!]kji(exp[bj(i - 1)i])[X]i, i being any index p, q, r and X an component M, A, or H. Future applications of this algorithm to practical problems of macromolecule-ligand-proton equilibria are outlined.

By developing a statistical thermodynamic model for the equilibria in solution, in nonreacting systems, the correspondence between heat capacity and dilution entropy change produces thermal equivalent dilution, TED. The principle of thermal equivalent dilution is validated by statistical thermodynamic relationships. Examples are given of the interpretation of experimental data by means of TED.

Computer readable databases have become an integral part of chemical research right from planning data acquisition to interpretation of the information generated. The databases available today are numerical, spectral and bibliographic. Data representation by different schemes--relational, hierarchical and objects--is demonstrated. Quality index (QI) throws light on the quality of data. The objective, prospects and impact of database activity on expert systems are discussed. The number and size of corporate databases available on international networks crossed manageable number leading to databases about their contents. Subsets of corporate or small databases have been developed by groups of chemists. The features and role of knowledge-based or intelligent databases are described.

An algorithm is proposed for the estimation of binding parameters for the interaction of biologically important macromolecules with smaller ones from electrometric titration data. The mathematical model is based on the representation of equilibria in terms of probability concepts of statistical molecular thermodynamics. The refinement of equilibrium concentrations of the components and estimation of binding parameters (log site constant and cooperativity factor) is performed using singular value decomposition, a chemometric technique which overcomes the general obstacles due to near singularity. The present software is validated with a number of biochemical systems of varying number of sites and cooperativity factors. The effect of random errors of realistic magnitude in experimental data is studied using the simulated primary data for some typical systems. The safe area within which approximate binding parameters ensure convergence has been reported for the non-self starting optimization algorithms.

The critical micelle concentration (c.m.c.) for four cationic surfactants, alkyl-trimethyl-ammonium bromides, was determined as a function of temperature by conductivity measurements. The values of the standard free energy of micellisation DeltaG degrees(mic) at different temperatures were calculated by using a pseudo-phase transition model. Then, from the diagram (-DeltaG degrees(mic)/T)=f(1/T), the thermodynamic functions DeltaH(app) and DeltaS(app) were calculated. From the plots DeltaH(app)=f(T) and DeltaS(app) = f(ln T) the slopes DeltaC(p) = n(w(H))C(p,w) and DeltaC(p)=n(w(S))C(p,w) were calculated, with the numbers n(w(H)) and n(w(S)) negative and equal and therefore defined simply as n(w). The number n(w)0, indicating condensed water molecules, depends on the reduction of cavity that takes place as a consequence of the coalescence of the cavities previously surrounding the separate aliphatic or aromatic moieties. The analysis, based on a molecular model consisting of three forms of water, namely W(I), W(II), and W(III), respectively, was extended to several other types of surfactants for which c.m.c. data had been published by other authors. The results of this analysis form a coherent scheme consistent with the proposed molecular model. The enthalpy for all the types of surfactant is described by DeltaH(app)= -3.6 + 23.1xi(w)-xi(w)C(p,w)T and the entropy by DeltaS(app)= +10.2+428xi(w)-xi(w)C(p,w) ln T where xi(w)= |n(w)| represents the number of molecules W(III) involved in the reaction. The term Deltah(w)= +23.1 kJ mol(-1) xi(w)(-1) indicates an unfavourable endothermic contribution to enthalpy for reduction of the cavity whereas the term Deltas(w)= +428 J K(-1) mol(-1) xi(w)(-1) represents a positive entropy contribution for reduction of the cavity, what is the driving force of hydrophobic association. The processes of non polar gas dissolution in water and of micelle formation were found to be strictly related: they are, however, exactly the opposite of one another. In micelle formation no intermolecular electronic short bond is formed. We propose, therefore, to substitute the term "hydrophobic bond" with that of "hydrophobic association".

Molecular interpretations are here presented of the hydrophobic effect, which is the cause of the low solubility of apolar substances in water. The solubilization process of substances such as the noble gases consists in the formation of a cavity in the solvent with expulsion of nw water molecules. The process is associated to an entropy/enthalpy (S/H) compensation linearly dependent upon the temperature. The observed enthalpy ΔHapp, either determined calorimetrically or by van’t Hoff equation, shows ΔCp,app ≠ 0 and positive. We set ΔCp,app = nwCp,w where Cp,w is the isobaric heat capacity of water. The number nw (nw > 0) of relaxed water molecules is proportional to the size of the solute molecule and hence of the cavity. The term nwCp,wT is actually an entropy term, which compensates for part of the reaction enthalpy (ΔH0 0) of water molecules. The presence of polar groups and/or charges in the solute molecule, on the other hand, exerts on the water molecules the same action as that produced by micellisation (nw

The statistical analysis of variance has been applied to the values of the equilibrium constants of the glycinate-proton and glycinate-nickel systems, determined in different laboratories by pH-titration in aqueous solution. The analysis shows how the main part of the error derives from the variability from one titration to another even in the same laboratory. Therefore the data for a single titration (k) must be processed separately, thus yielding a mean value for the equilibrium constant logbeta (pqr)(k) of the species M(p)H(q)L(r); from these mean values for different titrations in each laboratory l, a within-laboratory grand average, logbeta (pqr)(l), can be calculated; the variance of this grand average measures the experimental error. A further analysis of the data from the different participating laboratories shows that there were no significant differences between laboratories for the constants reported. From these results it can be inferred that all the values of the mean constants logbeta (pqr)(k) for one species, as determined separately for each titration in four laboratories, belong to the same population. A chi(2) analysis of these populations demonstrates that the stability constants of the species HL, H(2)L(+), NiL(+), NiL(2) (with L(-) = glycinate) are normally distributed, but not that for NiL(-)(3). Therefore, general mean values of the first four constants can be calculated and proposed as reliable standard values at 25 degrees and I = 1.0M Na(Cl): protonation of glycinate, log beta(011) = 9.651(12), log beta(021) = 12.071(26); nickel-glycinate complexes, log beta(101) = 5.615(35), log beta(102) = 10.363(62). These values indicate that the standard deviations are rather higher than those often reported in the literature.

Homogeneous sets of data from strong acid-strong base potentiometric titrations in aqueous solution at various constant ionic strengths have been analysed by statistical criteria. The aim is to see whether the error distribution matches that for the equilibrium constants determined by competitive potentiometric methods using the glass electrode. The titration curve can be defined when the estimated equivalence volume VEM, with standard deviation (s.d.) sigma (VEM), the standard potential E(0), with s.d. sigma(E(0)), and the operational ionic product of water K(*)(w) (or E(*)(w) in mV), with s.d. sigma(K(*)(w)) [or sigma(E(*)(w))] are known. A special computer program, BEATRIX, has been written which optimizes the values of VEM, E(0) and K(*)(w) by linearization of the titration curve as a Gran plot. Analysis of variance applied to a set of 11 titrations in 1.0M sodium chloride medium at 298 K has demonstrated that the values of VEM belong to a normal population of points corresponding to individual potential/volume data-pairs (E(i); v(i)) of any titration, whereas the values of pK(*)(w) (or of E(*)(w)) belong to a normal population with members corresponding to individual titrations, which is also the case for the equilibrium constants. The intertitration variation is attributable to the electrochemical component of the system and appears as signal noise distributed over the titrations. The correction for junction-potentials, introduced in a further stage of the program by optimization in a Nernst equation, increases the noise, i.e., sigma(pK(*)(w)). This correction should therefore be avoided whenever it causes an increase of sigma(pK(*)(w)). The influence of the ionic medium has been examined by processing data from acid-base titrations in 0.1M potassium chloride and 0.5M potassium nitrate media. The titrations in potassium chloride medium showed the same behaviour as those in sodium chloride medium, but with an s.d. for pK(*)(w) that was smaller and close to the expected instrumental noise, whereas the titrations in nitrate medium had a high noise level and even the determination of VEM was less certain. Procedures are also proposed for obtaining reference sets of data and checking the conformity of the solutions and apparatus to the chosen reference.

An evaluation of the cooperativity effect in metal-ligand and protein-ligand complexes can be made by means of dimensionless parameters Kγ (homotropic), and Kγ′ (heterotropic). Starting from the relation n = ∂ ln ϵM/∂ ln [A] between formation function n and partition function ϵM = 1 + β1[A] + β2 [A]2 + …βi[A]i… + βt [A]t it is shown that on the Bjerrum plane n = f(ln [A]), the standard free-energy ▵G° and therefore the standard chemical potentials ▵μ°γ = RT ln Kγ and ▵μ°γ′= RT ln Kγ′ can be obtained exactly from a convoluted or saturation function FcM, which has the property of being 1 when ▵μ° = O, as do the equilibrium constants. The standard convoluted function FcM° for multi- step equilibria coincides with the maximum term, /gBt, of ϵM and can be calculated on the Bjerrum plane as balance between two integrals, one integral giving the contribution to free-energy of the ‘association’ partition function, ϵM, the other giving the contribution to free-energy of the ‘dissociation’ partition function, ϵDM. FcM can be calculated as the product of stepwise equilibrium constants K1,K2,…,Kt. Differences between areas on the Bjerrum plane measure ▵μ°γ/RT and ▵μ°γ′/RT. The statistical factors for homotropic and heterotropic complexes are equal. The chemical potential changes due to the cooperativity effect can be better evaluated from Kγ = βi1/i/(K1kst(γ)) (average cooperativity effect) rather than by Kγ = (βi/βi -2)1/2/(kst(γ)βi-1/βi-2) (stepwise cooperativity effect). The former is well correlated with the successive additions of ligands. The cooperativity effect is strongly influenced by changes in ionic strength, thus confirming the interpretation of the phenomenon as due to ligand-ligand external interactions. The cooperativity effect, although small (0 < ▵μ°γ▵ < 6 kJ/mol), is significantly greater than the experimental error. The cooperativity effect in homotropic and heterotropic metal complexes is of the same order of magnitude as the cooperativity effect in macromolecule-ligand equilibria.

Homogeneous sets of data from strong acid-strong base potentiometric titrations in a mixed solvent medium (9:1 v/v methanol/water), performed by means of the glass electrode, at various constant ionic strengths and with different reference electrodes, have been analysed by statistical criteria. A standardized procedure has been established to obtain reliable potentiometric data in mixed solvents. It has been demonstrated how, with the aid of a proper linearized model, analysis of variance (ANOVA) applied to the standardization titrations can be used to test the reliability of a potentiometric chain in a medium other than pure water. The error expected in the stability constants thus evaluated is related to the intertitration error of the operational pK*(')(w), for the same medium and the same chain. The results obtained by applying ANOVA to the mixed solvent data substantially confirm the trend found for aqueous media, the intertitration error being larger than the intratitration error for all the parameters investigated (E(')(0), pK*(')(w), mean equivalence volume). The stochastic error thus obtained depends on the ionic medium used and on the kind of reference electrode employed in the electrochemical chain.

The partition function ∑A = 1 + β1[H] + β2[H]2 + ... + βi[H]i + ... + βt[H]t is used to interpret the variation in the stepwise formation constants for the equilibria between base A and proton H. The cumulative protonation constant of the saturated complex HtA, βt = [HtA]/([H]t[A]), is equal to the ratio between the formation partition function ΣA and the dissociation partition function ΣDA, the former giving the probability of finding compounds HiA of the ligand H binding to A and the latter giving the probability of finding species HiA by dissociation of protons from HtA. The saturation function βt = ∑A/∑AD can be factorized as a product of stepwise constants βt = K1.K2 ... Ki ... Kt. Comparisons between K1 and the geometric means βi 1 i enable a calculation to be made of the average cooperativity constants Kγ(i) which are explicit functions of i. The cooperativity functions γ(i) require that the equilibria are described by means of model partition functions depending on the site affinity constant k and the coefficients of the cooperativity function γ(i) = exp{2.302[a + b(i-1)]}. By analysing the cumulative protonation constants of polysite receptors it is possible to determine if there actually are separate classes of sites each with site constant kj and class cooperativity function γ(ij). The analysis of the equilibrium constants of some polyprotic acids shows how both the site affinity constants k and the slope b of log γ(i) depend on the charge density of the base. The paramount importance of the electrostatic effect in the binding of the proton to the base is clearly apparent. The analysis of the contribution of enthalpy to the cooperativity effect for the same compounds shows varying behaviour. This needs to be investigated further.

Stability constants for equilibria between copper(II) and chelating ligands are analyzed for comparison with equilibria involving “energy-rich” bonds in biochemical reactions. Equilibria between copper(II) and α-aminoacids and between copper(II) and aminoethanols give a consistent explanation of the experimental behavior only if both processes of deprotonation and complexation are considered at the same time. At pH = 7 the free-energy changes are close to the free energy for hydrolysis of ATP to ADP. The same holds for free-energy changes for equilibria between copper(II), proton, and oligopeptides. It is also shown that the free-energy changes for equilibria between nickel(II), proton, and oligopeptides are near the value of the free energy of hydrolysis of glycerol-3-phosphate.

The equilibria between metals or receptors and ligands are described by the formation function n = ligand bound/total receptor From the experimental formation function, the binding polynomial Σ M = 1 + β 1 [A] + … + β i [A] i + … + β t [A] t or formation (gran canonical) partition function is obtained as function of the cumulative constants β i . Σ M can be related to the stepwise equilibrium constants by introducing a dissociation partition function and a saturation function F c M = Σ M /Σ D . The standard value, F e⊝ M coincides with β t = K t = K 2 … K i … K t of the completely saturated receptor or metal. By calculating K γ =(β i 1/i / K 1 )(1/ k st( γ ) ) one obtains an average cooperativity effect between binding molecules. In nickel-ammonia system at 30 °C the cooperativity effect comes out to be Δμ° γ (i) = −0.752 + 0.621( i − 1) kJ/mol and in the system of bovine serum albumin (BSA) with copper(II) at 25 °C is Δμ° γ (i) = 0.034 + 0.123( i − 1) kJ/mol. By comparing the experimental binding polynomial with a model partition function for cooperative equal binding, Σ M.CE , e.g. for three site receptors or metals Σ M.CE = 1 + 3 k [A] + 3 γ 2 k 2 [A] 2 + γ 3 k 3 [A] 3 with k = equal intrinsic site constant, one obtains γ 2 = K γ 2 and γ 3 = K γ 3 . The values of γ 2 , γ 3 thus obtained are then introduced in a corrected formation function n corr which gives very good linear correlations on the Scatchard plot. From these plots the values of the intrinsic binding constant k are obtained which are k = 92.4 for nickel-ammonia at 30 °C and k = 1.3 × 10 3 for copper-BSA at 25 °C. These values correspond to values Δμ° k = − RT In k of −11.41 kJ/ mol and −17.8 kJ/mol, respectively. Also the equilibrium constants of the nickel-ammonia system at other temperatures and ionic strengths as well those of the cobalt(II)-ammonia system, have been analysed following the same procedure. In the nickel-hydrazine system the cooperativity is almost null and in the cadmium-ammonia system two different sets of sites are put in evidence. The strict parallelism and possible coupling of chemical and biochemical systems are discussed.

A flow microcalorimeter operating in mixing mode generates a type of “continuous titration” when one of the feeding pumps is connected to a continuous gradient generating device. The proper correction of the instrumental signal for the thermal lag of the calorimeter can be performed by chemical calibration, through an evaluation of the parameters of Tian's equation, modified for the microcalorimeter. This equation relates the instrumental signal to the actual power developed by the reaction. This paper shows how a continuous exponential gradient method can be applied to the determination of the enthalpy changes of metal-ligand-proton equilibrium reaction in solution. The enthalpies obtained for the protonation of D-cycloserine and for the formation of CuL and CuL2 complexes in the Cu(II)-Glycine system are in substantial agreement with published values. The computer programs, in BASIC language on an IBM-XT PC, used to process gradient data, are presented.

Chelate and cooperativity effects both in the field of complexes formed in solution by metal ion with ligands and in the field of binding between protein and ligands were examined on the basis of thermodynamic arguments. The analysis was carried out by means of the formation function n = ∂ ln ΣM/∂ ln[A] where ΣM is a partition function having free metal or macro-molecule as basis reference level and A is a ligand. The chemical potential changes due to cooperativity and chelation are calculated from differences between areas of the diagram n = f(ln[A]). The chemical potentials are: Δμ°γ = -RT ln Kγ (homotropic co-operativity), Δμ°γ′ = -RT ln Kγ′ (heterotropic co-operativity), Δμ°ϵ = -RT ln Kϵ (homotropic chelation), Δμ°ϵ′ = -RT ln Kϵ′ (heterotropic chelation). The cooperativity and chelation parameters Kγ, Kγ′, Kϵ, Kϵ′ are related to each other by other parameters Kη = Kϵ·Kγ and Kη′= Kϵ′·Kγ′. All these dimensionless parameters are derived as ratios of experimental equilibrium constants. Therefore a corresponding consistent chemical potential scale can be obtained from experimental data for all these effects, leading to quantitative comparisons between cooperative and chelate effects, either homotropic or heterotropic. Thermodynamic function changes in metal-ligand complexes can also be compared on this same scale with the energetic changes in protein-ligand complexes.

The crystals of calcium diiodate(V) hexahydrate, Ca(IO3)2. 6H2O are orthorhombic, space group Fdd2 with 8 molecules in the unit cell. The structure consists of pyramidal anions joined to one another in chains by intermolecular I ... O interactions. The chains are held together by calcium ions and by hydrogen bonds between water molecules and anions. The coordination polyhedron around calcium can be described as a square antiprism, with distances Ca- O=2.43-2.57 A. In the pyramidal anion the distances between oxygen and iodine atoms are I-O=1.78, 1.90, 1.85 A. The environment of the iodine atom is approximately octahedral: the coordination is completed by two water molecules and by one oxygen atom of another anion.

The crystals of thiocarbohydrazide dihydrochloride dihydrate, SC(NH-NH3)2Cl2. 2H2O are monoclinic, space group C2/c. The structure has been determined from three-dimensional data measured by automatic diffractometer. The final agreement factor was R = 3.8% with hydrogen atoms contribution. In the crystal structure, the cation possess a binary symmetry axis. Its trans, trans, conformation is different from the cis, trans conformation of the neutral molecules. Other relevant differences between diprotonated and neutral form concern the displacement of the terminal groups - N + H3 with respect to the plane of the thioureide group, NCSN, and the distribution of the single-double bond character between the bonds CN and SC. In the cation, in fact, the double bond character of S-C=1.645(3) A is more, and that of CN(1)=1.363(5) A less pronounced than in the neutral molecule. These results agree with the behaviour of thiocarbohydrazide in acidic or in alkaline solutions. The anion-cation, water-anion and water-cations interactions correspond to hydrogen bonds.

The crystals of bis(thiocarbohydrazideN,S)cadmium dichloride, Cd(SC(NHNH 2 ) 2 ) 2 Cl 2 , belong to monoclinic space group P2 1 /c. The structure of the compound, determined from three-dimensional data, consists of trans -octahedral complexes where the ligand molecule forms pentatomic chelate rings with N,S as donor atoms. The chlorine atoms lie along the normal to the plane containing metal and organic molecules. The distances CdN=2.34(3) and CdS=2.59(1) A are slightly shorter than those found in non-chelate cadmium complexes; CdCl=2.73(1) A is very close to the sum of ionic radii. The configuration of the ligand, with on -NH 2 group turned towards SC, repeats that of crystallized thiocarbohydrazide. Some differences, however, in distances, planarity, and angles between complexed or free ligand can be detected. The complexes are held together in layers parallel to (102) by weak hydrogen bonds NH⋯Cl.

The proton ionisation constants of DL-4,4′-dithiobis-(2-aminobutyric acid), (abbrev. DIENK) and of S,S′-methylene-di-L-cisteine,(abbrev. HOMC) have been determined potentiometrically at different temperatures and ionic strengths, μ. The constants at 25.0°C and μ = 0.1 M KCl are for DIENK: −log K1=8.954(8), −log K12 = 8.158(11), −log K13 = 2.200(13), −log K14∼1.50; and for HOMC: −log K1 = 9.413(10), −log K12 = 8.676(13), −log K13 = 2.523(14), −log K14 ∼ 1.60. All the ionisation constants are larger than the corresponding ones of α-aminoacids without sulphur atoms in the chain. The capacity to increase the acidic character or to lower the basic character of any group seems to be a general property of sulphur atoms. The thermodynamic functions ΔH and ΔS have been calculated from data of ionisation constants at temperatures between 5° and 30δC. The ionisation constants at different ionic strengths up to 2 M (KCl) have been determined.

The protonation constant of oxamic acid, H2NCOCOOH, was determined potentiometrically and resulted to be log K1 = 1.836 in 0.1 M KCl at 25.0 °C. No protonation or deprotonation is detectable in alkaline media. The calculation of the protonation constant has been carried out by a computer program based on the Sillen method. The estimated standard deviation of log K1 has been determined from the statistical analysis of the distribution diagram of Δp[H] = p[Ho] -p[Hc] against p[Ho]. This method can detect systematic errors affecting the data. Effects of (i) ionic strength (up to 2 M, (ii) temperature (in the range 5 ÷ 30 °C, (iii) solvent (in the mixture H2O (40%)-tetrahydrofuran(THF) (60%)) on the equilibrium have been investigated. The effects of ionic strength and temperature are those typical for monocarboxylic acids. The protonation constant increases up to log K1 = 2.897 in the mixture H2OTHF. This variation is compared with the variations of log K1 for other acids in water and in the same mixture; the possible influence of the dielectric constant of the solvent is considered. The coordinating power of oxamic acid toward divalent ions is very low and it is not enhanced by the changing of solvent.