Rates of Dissociative Ionic Reactions in Aqueous Mixtures Correlated with Opposing Gibbs Energies of Transfer of Single Ions: Solvolysis of Chloropentacyanocobaltate(III) Anions in Water + Ethanol and Water + Urea

The kinetics of the solvolysis of Co(CN)₅Cl^3– have been investigated in water with an added structure former, ethanol, and with added urea, which has only a weak effect on the solvent structure. As this solvolysis involves a rate-determining dissociative step corresponding closely to a 100%; separation, Co³⁺ Cl^-, in the transition state, a Gibbs energy cycle relating Gibbs energies of activation in water and in the mixtures to Gibbs energies of transfer of individual ionic species between water and the mixtures, G _t ^o (i), can be applied. The acceleration of the reaction found with both these cosolvents results from the compensation of the retarding positive G _t ^o (Cl^- by the negative term [G _t ^o [Co(CN) ₅ ^2- ]-G _t ^o [Co(CN)₅Cl^3- arising from G _t ^o [Co(CN)₅Cl^3-]> G _t ^o [Co(CN) ₅ ^2- ]. Moreover, only a small tendency to extrema in the enthalpies and entropies of activation is found with both these cosolvents, as was also found with added methanol or ethane-1,2-diol, but unlike the extrema found when hydrophobic alcohols are added to water. With the latter, much greater negative values for G _t ^o [Co(CN) ₅ ^2- ]- _t ^o [Co(CN)₅Cl^3-] are found. When G G _t ^o [Co(CN) ₅ ^2- ]-G G _t ^o [CO(CN)₅Cl^3-] becomes low enough not to compensate for the positive G _t ^o (Cl^-), as with added hydrophilic glucose, the reaction is retarded. Compensating contributions of the various G _t ^o (i) involved in the Gibbs energy cycle with added methanol or ethane-1, 2-diol allow log (rate constant) to vary linearly with the reciprocal of the relative permittivity of the medium.     

Transfer free energies of some ions from water to dimethylsulfoxide-water and urea-water mixtures

The standard free energies of transfer (G _t ^o ) of some electrolytes from water to aqueous mixtures of dimethylsulfoxide (DMSO) and of urea have been split into the contribution from individual ions by use of the reference electrolyte Ph ₄ AsBPh ₄ (RE), where Ph=phenyl. For each of the solvents, G _t ^o (Ph ₄ AsBPh ₄ ) was determined from the solubility products of the salts KBPh ₄ , Ph ₄ AsPi, and KPi, where Pi=picrate ion. The observed G _t ^o (i) values for the individual ions are strikingly different from the corresponding values obtained by the simultaneous extrapolation (SE) procedure reported earlier.     

Heats of solution of 1:1 electrolytes in 1,2- and 1,1-dichloroethane and derived enthalpies and entropies of transfer of electrolytes from water to these solvents

Heats of solution of nine electrolytes in 1,2-dichloroethane and of three electrolytes in 1,1-dichloroethane have been determined calorimetrically at various electrolyte concentrations and extrapolated to zero concentration to yield H _s ^o values for these electrolytes. It is shown that values of H _t ^o for transfer from water to the dichloroethanes of 11 electrolytes are often negative, so that these electrolytes can be more stable enthalpically in the less polar solvents. Combinations of the H _t ^o values with previously determined G _t ^o values yield values of S _t ^o for transfer of 11 electrolytes from water to the dichloroethanes. These S _t ^o values are mostly very negative; they can be correlated very well by the method of Abraham, and in this way S _t ^o values for transfer of numerous other anions and cations have been predicted. The Ph₄As⁺/Ph₄B^– convention yields single-ion entropies of transfer from water to the dichloroethanes in reasonable agreement with values calculated by the correspondence-plot method.     

Model calculations of changes of thermodynamic variables for the transfer of nonpolar solutes from water to water-d2

A recently introduced modified hydration shell hydrogen bond model for rationalizing the thermodynamic consequences of hydrophobic hydration is adapted for use with heavy water. The required adjustment of parameters employs the assumption that breaking hydrogen bonds in water-d₂ involves a greater enthalpy change and a larger entropy increase than bond breaking in ordinary water. It also makes some use of information derived from studies of gas solubilities in the two solvents, although a review of the data leads to serious questions about the reliability of results obtained in this way. The model permits calculations of hydrogen bonding contributions to the changes, G _t ^o , H _t ^o , S _t ^o , and C _p,t ^o , for transfer of nonpolar solutes from water to water-d₂ and implies that such data should show regular trends. Although some of the numerical results depend strongly on the values chosen for the parameters, the pattern defined by these trends is nearly independent of parameters. Predicted values of C _p,t ^o are large and positive for all nonpolar solutes, while S _t ^o is expected to be negative near 0°C, becoming progressively less negative on warming and eventually positive. Both of these quantities should be proportional to the molecular surface area of the solute. Analogous predictions regarding G _t ^o and H _t ^o can also be made, but only if it is permissible to neglect possible contributions to these quantities from van der Waals interactions.     

Kinetics of the solvolysis oftrans-dichlorotetra-(4-t-butylpyridine)-cobalt(III) ions in water +t-butyl alcohol mixtures

Rates of solvolysis of the complex cation [Co(4tBupy)₄Cl₂]⁺ have been determined in mixtures of water with the hydrophobic solvent, t-butyl alcohol. The solvent composition at which the extremum is found in the variation of the enthalpy H^* and the entropy S^* of activation correlates well with the extremum in the variation of the relative partial molar volume of t-butyl alcohol in the mixture and the straight line found for the variation of H^* with S^* is coincident with the same plot for water + 2-propanol mixtures. A free energy cycle is applied to the process initial state (C ⁿ⁺) going to the transition state [M⁽ⁿ⁺¹⁾⁺...Cl^–] in water and in the mixture using free energies of transfer of the individual ionic species, G _t ^o (i), from water into the mixture. Values for G _t ^o (i) are derived from the solvent sorting method and from the TATB/TPTB method: using data from either method, changes in solvent structure on going from water into the mixture are found to stabilize the cation in the transition state, M⁽ⁿ⁺¹⁾⁺, more than in the initial state, C ⁿ⁺. This is compared with the application of the free energy cycle to the solvolysis of complexes [Co(Rpy)₄Cl₂]⁺ and [Coen₂LCl]⁺ in mixtures of water with methanol, 2-propanol or t-butyl alcohol: the above conclusion regarding the relative stabilization of the cations holds for all these complexes in their solvolyses in water+alcohol mixtures using values of G _t ^o (Cl^–) from either source.     

Ionic enthalpies of transfer from water to water-sulfolane mixtures

NaCl, NaBr, NaI, NaClO₄, KCl, KClO₄, NaBPh₄, and Ph₄PBr solution enthalpies were measured in water-sulfolane mixtures at 30°C. Ionic enthalpies of transfer from water to mixed solvents were calculated on the basis of the assumption H _s ^o (BPh ₄ ^– )=H _s ^o (Ph₄P⁺). The variation of the ionic enthalpies of transfer with solvent composition is discussed in terms of ion-solvent interactions and of the effects caused by sulfolane on the structure of water.     

Complex formation constants and thermodynamic parameters for La(III) and Y(III)L-serine complexes

Summary The stoichiometric stability constants for La(III) and Y(III)L-serine complexes were determined by potentiometric methods at different ionic strengths adjusted with NaClO₄ and at different temperatures. The overall changes in free energy (G ^o), enthalpy (H ^o), and entropy (S ^o) during the protonation ofL-serine and that accompanying the complex formation with the metal ions have been evaluated.

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Komplexbildungskonstanten und thermodynamische Parameter für La(III)- und Y(III)-L-Serin-Komplexe

Zusammenfassung Die stöchiometrischen Komplexbildungskonstanten für La(III)- und Y(III)-L-Serin-Komplexe wurden mittels potentiometrischer Methoden bei verschiedenen Ionenstärken (mit NaClO₄ adjustiert) und bei verschiedenen Temperaturen bestimmt. Die Änderungen in der freien Energie (G ^o), Enthalpie (H ^o) und Entropie (S ^o) während der Protonierung und der Komplexbildung mit den Metallionen wurden ermittelt.

     

Free energy of transfer of cobalt(III) complexes from water into water—t-butyl alcohol mixtures

The solubility of trans-(Coen₂Cl₂)₂ReCl₆ has been determined in water and in water +t-butyl alcohol mixtures. By comparzng these values with the solubility of Cs₂ReCl₆ in similar mixtures, values for the difference in free energy of transfer, G _t ^o (i) between water and water + t-butyl alcohol can be calculated for i =[Coen₂Cl₂]⁺ and Cs⁺. The introduction of G _t ^o (Cs⁺) then produces values for G _t ^o (Coen₂Cl₂ ⁺). The difference in G _t ^o (i) for i=[Coon₂Cl]²⁺ in the transition state and i=[Coen₂Cl₂]⁺ in the initiad' tate for the solvolysis of the trans-[Coen₂Cl₂]⁺ ion in water + t-butyl alcohol can be derived from the application of a free energy cycle: using G _t ^o (Coen₂Cl₂ ⁺) determined from the solubility measurements allows the calculation of values for G _t ^o (Coen₂Cl²⁺). G _t ^o (i) in water + t-butyl alcohol for bis (1,2-diamino) cobalt (III) ions are compared with G _t ^o (i) for tetrapyridinecobalt (III) ions.     

Effect of intramolecular rotational reorganization of reagents on the ratio between free energies of activation and reaction

Conclusions The relationship between the free energies of activation G and reaction G_o for proton transfer processes have been analyzed, taking into account the effect of hindered rotation of the reagents. We have shown that the considered effect can considerably affect the shape of the G=f(G_o) curve.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 77–81, January 1989.     

The kinetics of the solvolysis of chloropentacyanocobaltate(III) ions in water containing 2-methoxyethanol or diethylene glycol: A contrast with the effect of more hydrophobic cosolvents

The kinetics of the solvolysis of [Co(CN)₅Cl]^3– have been investigated in water +2-methoxyethanol and water + diethylene glycol mixtures. Although the addition of these linear hydrophilic cosolvent molecules to water produces curvature in the variation of log(rate constant) with the reciprocal of the dielectric constant, their effect on the enthalpy and entropy of activation is minimal, unlike the effect of hydrophobic cosolvents. The application of a Gibbs energy cycle to the solvolysis in water and in the mixtures using either solvent-sorting or TATB values for the Gibbs energy of transfer of the chloride ion between water and the mixture shows that the relative stability of the emergent solvated Co(III) ion in the transition state compared to that of Co(CN)₅Cl^3– in the initial state increases with increasing content of cosolvent in the mixture. By comparing the effects of other cosolvents on the solvolysis, this differential increase in the relative stabilities of the two species increases with the degree of hydrophobicity of the cosolvent.List of Symbols v₂ partial molar volume of the cosolvent in water + cosolvent mixtures - V ₂ ^o molar volume of the pure cosolvent - H _mix ^E excess enthalpy of mixing water and cosolvent - S _mix ^E excess entropy of mixing water and cosolvent - G _t ^o (i)_n the Gibbs energy of transfer of speciesi from water into the water + cosolvent mixture excluding electrostatic contributions - k _s first order rate constant for the solvolysis in water + cosolvent mixtures - D _s dielectric constant of the water + cosolvent mixture - H ^* the enthalpy of activation for the solvolysis - S ^* the entropy of activation for the solvolysis - G ^* the Gibbs energy of activation for the solvolysis - V ^* the volume of activation for the solvolysis - i ^* speciesi in the transition state for the solvolysis - H _o Hammett Acidity Function - TATB method for estimating the Gibbs energy of transfer for single ions assuming those for Ph₄As⁺ and BPh ₄ ^– are equal     

Enthalpies of solution of thymine and uracil in water and dimethylsulfoxide

Enthalpies of solution of thymine and uracil in water and in dimethylsulfoxide (DMSO) were measured calorimetrically in the temperature range 25–40°C. H _s ^o at 25°C for thymine and uracil in water were found to be 23.1±0.5 and 29.5±0.3 kJ-mol^–1, respectively. In DMSO, H _s ^o were 7.9±0.1 and 10.2±0.1 kJ-mol^–1, respectively. In aqueous solution C _p ^o for the two nucleic acid bases were relatively large and positive with C _p ^o of thymine being larger. Both transfer quantities H _t ^o and C _p,t ^o for the proceses H₂ODMSO for the two nucleic acid bases were negative. It is proposed that, the differences in the values obtained for the two bases is due principally to increased order in the water adjacent to the methyl group in thymine.     

Apparent molar heat capacities and volumes of electrolytes and ions in acetonitrile-water mixtures

Apparent molar volumes V and heat capacities C_p, of NaCl, KCl, KNO₃, AgNO₃, KI, NaBPh₄ and Ph₄PCl have been measured in acetonitrile (AN)-water mixtures up to x_AN=0.25 by flow densitometry and flow microcalorimetry. Limited data have also been obtained for NaF, LiCl and KBr up to x _AN =0.15. Single ion volumes and heat capacities of transfer were obtained using the assumption _tX(PH₄P⁺) = _tX(BPh₄-) where X=V or C _p and _tX is the change in X for a species on transfer from H₂O to AN-H₂O mixtures. Volumes and heat capacities for simple salts show relatively little dependence on solvent composition. However, _tX for simple ions show more pronounced variations, exhibiting at least one extremum. These extrema are similar to but much less pronounced than those derived previously for ions in t-butanol-water mixtures. Surprisingly little correlation is found between the present data and other thermodynamic transfer functions. This is attributed to the predominance of ion-solvent over solvent-solvent interactions in AN-H₂O solutions. _tV and _tC_p, for the silver ion differ markedly from those of the alkali metal ions as a result of the well-known specific interaction between Ag⁺ and AN.     

Influence of o-benzoquinone nature on initiation of radical polymerization by the o-benzoquinone—tert-amine system

o-Benzoquinones initiate radical polymerization of methacrylates under visible light irradiation in the presence of tertiary amines. Spectral sensitivity of the initiating system coincides with absorption bands of o-benzoquinone attributed to the S(*) (_max 400 nm) and S(n*) (_max 600 nm) transitions. The amine radicals (Am^·) initiating polymerization are generated by the photoreduction of Q in the presence of AmH from the triplet radical pair ³(QH^·, Am^·). The yield of Am^· depends on the difference between the volumes of substituents in the 3 and 6 positions of the quinoid ring and is maximal for symmetrically substituted o-benzoquinones. For a series of derivatives of symmetrical 3,6-di-tert-butyl-o-benzoquinone, the rate of photopolymerization of ,-bis(methacryloyloxyethyleneoxycarbonyloxy)ethyleneoxyethylene (OCM-2) in the presence of N,N-dimethylaniline is determined by the free energy (G _e) of electron transfer from the amine to photoexcited o-benzoquinone. The G _e value includes the energies of oxidation of the amines and reduction of the o-quinones and the energy of the 00 transition of the triplet excited state of o-benzoquinones, which are equal to their redox potentials. The photopolymerization rate is maximal for G _e 0.     

Solubility of inert gases and liquid hydrocarbons in water

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 Z_G·_s. The product of a grand canonical partition function Z_G represents the distribution of the species in the reaction while the canonical partition function Z_G 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, {H_aap}_T=H^o+n_wC_p,wT, where {H_app}_T refers to Z_G, n_wC_p,wT=–H_w to _s, and H^o is the change in enthalpy of hydrocarbon-water reaction. The plot {H_app}_T vs/ T results in a straight line with slope n_w at constant C_p,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 n_w range from 1.6, 1.9, 5.6 to 5.8 for helium, hydorgen, butane and hexane, respectively. For fluorocompounds the range of n_w is 10.1 to 11.1 indicating that n_w 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 H^o and n_w consistent with the size of the dissolved molecules.List of Symbols p pressure - H _ij average enthalpy - H _i level enthalpy (=H) - H _i enthalpy difference - H _ij intersublevel energy difference - i index of level - j index of sublevel - Z_G grand canonical partition function - _S canonical partition function - Z_G- convoluted partition function - –G ^o/RT standard Gibbs energy normalized toRT - –H ^o/RT standard enthalpy normalized toRT - S ^o/R standard entropy normalized toR - C _p molar heat capacity - T absolute temperature - H _G- enthalpy of the convoluted ensemble - H _G enthalpy of the solute - H enthalpy of the solvent - H _app apparent enthalpy - H _w enthalpy of water - C_yH_z hydrocarbon - W water - K _s solubility equilibrium constant - x ₂ molar fraction of solute - C_yH_zW_(x-nw) hydrocarbon molecule trapped in a cavity - K _H Henry constant - P _s solubility product - [W] concentration of water - reference temperature - a, b, c, d coefficients of the fitting polynomial - {H _app}_T apparent enthalpy at temperatureT - {H }_T standard enthalpy at temperatureT - {H _w}_T water contribution to enthalpy at temperatureT - C _p,w isobaric molar heat capacity of water - L Ostwald coefficient - C _p isobaric heat capacity difference - Bunsen coefficient - C _p,app apparent isobaric heat capacity difference - n _C number of carbon atoms in the chain - h _w interaction enthalpy of one water molecule - H ₀ intercept for the extrapolated enthalpy     

Gibbs Energy and Entropy of Mixing in the NaNO2-KNO3 System

The activity and activity coefficients of the components of the NaNO₂-KNO₃ system, determined from the experimental data on the saturated vapor pressure at 798, 823, and 848 K, are used to calculate the relative and excess partial molar Gibbs energies (G _i and G _i ^{e x c}), entropies (S _i and S _i ^{e x c}), and integral relative and excess thermodynamic functions (G, G ^{e x c}, S, and S ^{e x c}) of the system.     

Heats of solution of 1∶1 electrolytes in 1-propanol,and derived enthalpies of transfer from water

Heats of solution of 13 11 electrolytes in 1-propanol have been determined calorimetrically at various electrolyte concentrations, and extrapolated to zero concentration to give H _s ^o values for these electrolytes. Together with literature data on three additional 11 electrolytes, these measurements yield a self-consistent set of single-ion enthalpies of transfer from water to 1-propanol. Values are tabulated for 10 univalent cations and five univalent anions. It is shown that the H _t ^o (Ph ₄ As⁺)=H _t ^o (Ph ₄ B^–) assumption yields chemically reasonable single-ion values. Using this assumption, it may be deduced that all the univalent ions studied have about the same enthalpy in 1-propanol as in methanol.     

Numerische Auswertung von Enzymanalysen

Zusammenfassung Für eine numerische Auswertung von Enzymanalysen erscheint es zunächst naheliegend, in die Meßpunkte eine Ausgleichsgerade einzupassen und deren Steigung als Schätzwert für die gesuchte Anfangsgeschwindigkeit E/t ₀ zu nehmen. Die Steigung der Ausgleichsgeraden liefert aber die mittlere Reaktionsgeschwindigkeit über die gesamte Meßzeit und unterschätzt E/t ₀ immer dann, wenn die Reaktion gegen Ende der Meßzeit etwas langsamer läuft. Bei automatischen Geräten muß das Auswerteverfahren auch in solchen Fällen E/t ₀ richtig schätzen. In der vorliegenden Arbeit wird eine einfache Möglichkeit, die zu diesem Ziel führt, diskutiert, nämlich die Schätzung von E/t ₀ mit einer Ausgleichsparabel, die dem Reaktionsverlauf folgen kann.

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Numerical evaluation of enzyme analyses

To calculate enzyme concentrations numerically, it seems obvious to fit a straight line into the data points and take the slope as an estimate for the starting velocity E/t ₀. This slope, however, is proportional to the average reaction rate over the total measurement interval and always underestimates E/t ₀ when the reaction is slowing down towards the end. Automatic analyzers must correctly estimate E/t ₀ even in such cases. As discussed in this article, this can be achieved by fitting a second order parabola, that can follow the reaction, into the data points.

     

Thermodynamic quantities for the protonation of amino acid amino groups from 323.15 to 398.15 K

Flow claorimetry has been used to study the interaction of protons with glycine, DL--alanine, -alanine, DL-2-aminobutyric acid, 4-aminobutyric acid, and 6-aminocaproic acid in aqueous solutions at temperatures from 323.15 to 398.15 K. By combining the measured heats for amino acid solutions titrated with NaOH solutions with the heat of ionization for water, the log K, H^o, S^o, and C_p ^o values for the protonation of the amino groups of these amino acids have been obtained at each temperature studied. Equations are given expressing these values as functions of temperature. The H^o and S^o values increase while log K values decrease as temperacture increases. The trends for log K, H^o, S^o, and C_p ^o are discussed in terms of changes in long-range and short-range solvent effects. The trend in H^o, S^o, and C_p ^o values with temperature and with charge separation in the zwitterions is interpreted in terms of solvent-solute interactions and the electrostatic interaction between the two oppositely charged groups within the molecule.     

Thermochemistry of aqueous solutions of alkylated nucleic acid bases V. Enthalpies of hydration of N-methylated adenines

Enthalpies of solution in water, H _sol ^o , and of sublimation, H _subl ^o , were determined experimentally for a number of crystalline N-methyl adenines: m⁶Ade, m ₂ ^6,6 Ade, m⁹Ade, m ₂ ^6,9 Ade, and m ₃ ^6,6,9 Ade. Derived standard enthalpies of hydration H _hydr ^o , were corrected for the calculated cavity terms H _cav ^o to yield enthalpies of interaction H _int ^o of the solutes with their hydration shells. The increments of H _int ^o per unit area of the water-accessible molecular surface S _B , H _int ^o (CH₃)/S _B (CH₃), for the particular methyl groups: is considered to be the net effect of the gain in the energy resulting from van der Waals' interactions and of the loss in the energy due to polar interactions upon methyl substitution. It proved to vary somewhat numerically in agreement with the theoretically predicted hydration schemes of adenine. Comparison of H _int ^o /S _B value for adenine with those previously determined for uracil and thymine indicates that the aminopurine moiety is less hydrated than the diketopyrimidine ring.     

Formation Enthalpy and Entropy of Exciplexes with Variable Extent of Charge Transfer in Solvents of Different Polarity

Temperature dependence was studied for relative quantum yields of emission from some exciplexes of pyrene, 1,12-benzoperylene, and 9-cyanoanthracene with methoxybenzenes or methylnaphthalenes in solvents of different polarity (ranging from toluene to acetonitrile). The enthalpy H _Ex ^*, the entropy S _Ex ^*, and the Gibbs free energy G _Ex ^*of formation of the exciplexes were determined. Depending of the Gibbs free energy of excited-state electron transfer (G _et ^*) and solvent polarity, the values of H _Ex ^*, S _Ex ^*, and G _Ex ^*vary over the ranges from –5 to –40 kJ mol^–1, from +3 to –90 J mol^–1K^–1, and from +3 to –21 kJ mol^–1, respectively. The possibility is discussed that the effect of solvent polarity G _et ^*on the exciplex formation enthalpies can be rationalized in terms of the model of correlated polarization of an exciplex and the medium.