Equilibrium Constant K1 Research Articles

Dynamic mechanism of the self-assembly process of tobacco mosaic virus protein studied by rapid temperature-jump small-angle X-ray scattering using synchrotron radiation

The self-assembly process of tobacco mosaic virus protein (TMVP) was observed by rapid temperature-jump time-resolved solution X-ray small-angle scattering using synchrotron radiation. The temperature-jump device used for the X-ray measurements is rapid enough to cope with even the fastest-assembling process of TMVP, and accumulates data of reasonable signal-to-noise ratios with a minimum total counting time of 7.5 seconds. The measurements suggested that the 20 S disk of TMVP polymerized to stacked disks (short rods). The time to complete stacking varied from approximately 25 seconds to approximately 1200 seconds, depending on the solution condition and magnitude of the temperature gap. Higher protein concentration, ionic strength and temperature favoured faster association. The results were analysed in terms of a set of kinetic equations that describe the two-stage aggregation of TMVP with an equilibrium constant K1, and two rate constants k+2 and k-2 for association and dissociation of disks, respectively. The consistency of the analysis suggests that the TMVP assembly proceeds in two steps of: (1) the aggregation of A-proteins into double-layered disks; and (2) the stacking of double-layered disks. The kinetic analysis indicated that the stacking belongs to the lowest range of protein-protein interaction system.

A quantitative approach to the inorganic carbon system in aqueous media used in biological research: dilute solutions isolated from the atmosphere

Abstract. The changes in the distribution of dissolved inorganic carbon systems resulting from biological activity are described using the dissociation equations and considering eight variables: the concentrations or activities of H+, OH−, CO2, H2CO3, HCO3−, CO32−, total carbon ∑CO2, carbonate alkalinity A− and base excess B+. Equations for the equilibrium constants K1, K2 and K3, giving their dependence on temperature, are provided. These thermodynamic constants are defined on the infinite dilution scale and their dependence on the pH‐convention adopted is stressed. From the dissociation equations and the eleclroneutrality condition a set of 15 equations were deduced, each representing the relationship between the H+‐activity and one pair of the other variables. The knowledge of two variables will, therefore, enable the calculation of all the other variables, furnishing a complete description of the C‐system. Such a description is needed to permit the calculation of the ionic strength (I) of a solution. Knowing I makes it possible to calculate the activity‐coefficients for bicarbonate and carbonate ions (Debye‐Hueckel equations), which are needed to calculate the working constants K1 and K2 from the thermodynamic ones. Hints for computer programs, some of them including iterative subroutines, are given. Suggestions are made for the experimental determination of K1 and K2. The discussions arc restricted to dilute solutions isolated from a gaseous phase, at 1 atm, external pressure and having an ionic strength of not more than 70 mol m−3. The difficulty of providing causal explanations in studies involving the C‐system is briefly discussed.

The kinetics and thermodynamics of the reaction H+NH3⇄NH2+H2 by the flash photolysis–shock tube technique: Determination of the equilibrium constant, the rate constant for the back reaction, and the enthalpy of formation of the amidogen radical

Equilibrium constants K1 for the reaction H+NH3⇄NH2+H2 were measured over the temperature range 900 to 1600 K using a flash photolysis–shock tube apparatus. The experimental values of K1 ranged from 1.0 at 900 K to 2.2 at 1620 K with an estimated experimental error of about ±10%. The value obtained from the third law analysis for the enthalpy of formation of the amidogen radical, ΔH0f298 (NH2), is 45.3 kcal/mol (ΔH0f0 =46.0). The corresponding value for the bond dissociation energy, D0(NH2–H), is 107 kcal/mol. These values are in good agreement with the data tabulated in the revised JANAF tables (1982), with those derived from new measurements of the photoionization threshold for the amidogen radical, and with those from independent measurements of the rate constants of the forward and back reactions. The Arrhenius rate expression derived for reaction (−1), NH2+H2→NH3+H, is k−1(T)=5.38×10−11 exp(−6492/T) cm3 molecule−1 s−1 for the temperature range 900–1620 K. The estimated error in k−1(T) is about ±25%.

ChemInform Abstract: Cooperativity Effect in Metal‐Ligand and Macromolecule‐Ligand Equilibria

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.

Synergic extraction of nickel/II/ by 2-thenoyltrifluoroacetone and tribenzylamine in chloroform from perchlorate media

Synergic extraction of Ni/II/ at pH 1 to 10 was studied using a mixture of 2-thenoyltrifluoroacetone /HTTA/ and tribenzylamine /TBA/ in chloroform. The synergist TBA enhances the extraction of Ni/II/ by an order of 5 from pH 3 to 5 having ionic strength 0.1M /H+, ClO4−/. The synergic adduct was found to be Ni/TTA/2.2TBA. The equilibrium constants K2,0 and K2,2 and stability constant β2,2 have been ascertained radiometrically. The influence of various cations and anions on the extraction of Ni/II/ has been examined under optimal conditions. Back extraction of the adduct species in different acids of varying concentrations has been studied.

Cooperativity effect in metal-ligand and macromolecule-ligand equilibria

An evaluation of the cooperativity effect in metal-ligand and protein-ligand complexes can be made by means of dimensionless parameters K γ (homotropic), and K γ′ (heterotropic). Starting from the relation n = ∂ ln ϵ M/∂ ln [A] between formation function n and partition function ϵ M = 1 + β 1[A] + β 2 [A] 2 + …β i [A] i… + β t [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 K γ and ▵μ° γ′=  RT ln K γ′ can be obtained exactly from a convoluted or saturation function F c M, which has the property of being 1 when ▵μ° = O, as do the equilibrium constants. The standard convoluted function F c M° for multi- step equilibria coincides with the maximum term, /gB t , of ϵ M 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, ϵ M, the other giving the contribution to free-energy of the ‘dissociation’ partition function, ϵ D M. F c M can be calculated as the product of stepwise equilibrium constants K1 , K 2,…, K t . 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 K γ = β i 1/ i /( K 1 k st( γ ) ) (average cooperativity effect) rather than by Kγ = (β i /β i -2 ) 1/2/( k st(γ)β i-1 /β i-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.

Single and double bridged viologenes and intramolecular pimerization of their cation radicals

As an extension of our studies dealing with reversible redox systems, six tetraquaternary salts have been synthesized. These compounds contain two 4,4'-bipyridinium units which are connected by either one or two rigid bridges. The single bridged systems (o-, m-3, p-3) contain one o-, m- or p-xylylene bridge. The double bridged systems (o,o-4, o,m-4 and m,m-4) contain two xylylene bridges and represent a new class of cyclophanes. A new and very simple high dilution technique is described for the synthesis of these compounds. Depending upon ring size, some of the systems show different internal mobility with regard to flipping of the bridges and rotation of the pyridinium rings. By voltammetry of compounds 3 and 4, only two or three of the expected four potentials are observed. This is probably due to the highly stabilized diradical dications 3SEM/SEM and 4SEM/SEM. From a study of the concentration and temperature dependent UV/VIS spectra of the cation radicals, the equilibrium constants K1 and K2 for intra- and intermolecular pimerization (CT complexation) together with their thermodynamic data are evaluated. The strongest intramolecular pimerization is observed with o-3SEM/SEM and o,o-4SEM/SEM, which exist exclusively as pimers.

The ATPase mechanism of skeletal and smooth muscle acto-subfragment 1.

The transient and steady-state kinetic parameters for the ATPase cycle of the complex of skeletal muscle actin with smooth or skeletal muscle subfragment 1 (S-1) were determined over a wide range of actin concentrations from measurements of protein tryptophan fluorescence, the transient hydrolysis step, and the steady-state rate. The properties of the completely associated system were determined by using S-1 covalently cross-linking to actin. A four-state model was found to provide a good approximation to the kinetic and steady-state behavior: (sequence; see text) where T, D, and Pi refer to ATP, ADP, and inorganic phosphate, respectively. The formation of AM1T and M1T occurs by a rapid equilibrium binding of T followed by a very fast step. Actin is in rapid equilibrium with M1T and M2.DPi, with association constants K2 and K4. The three rate constants k1, k-1, and k5 were obtained by fitting observed rate constants from transient state measurements and VM to the model using values of k3 and k-3 determined for S-1 alone. To fit the data for skeletal or smooth muscle acto-S-1, the calculated rate constant of the hydrolysis step k1 and the equilibrium constant K1 had to be 2-3 times smaller than the corresponding parameters (k3, K3) for S-1. The calculated effective rate constant for product release must be large for striated muscle (85 s-1 at 20 degrees C, low ionic strength) and relatively small for smooth muscle (3 s-1). The difference in the actin-concentration dependence of association and of steady-state ATPase activity was predicted correctly from the rate constants fitted to the transient evidence. While the proposed mechanism does not exclude the possibility of additional ATP or product intermediate states, the properties of such states cannot be deduced from the kinetic evidence.

Electron affinities from electron transfer equilibria in the gas phase and the electron affinity of SO2

Measurements of gas phase electron transfer equilibria [Eq. (1)] A−+B=A+B− were performed with a pulsed electron beam high ion source pressure mass spectrometer. The equilibrium constants K1 were used to evaluate ΔG01=−RT ln K1. The ΔG01 were found to change little with temperature such that ΔG01≊ΔH01. Good agreement was observed between the present results and earlier measurements by Fukuda and McIver, which used ion cyclotron resonance and worked at much lower pressures. Absolute electron affinities were obtained by anchoring the relative electron affinities (ΔH1 values) to known absolute E.A.’s from the literature. The relative results agree well with differences predicted by absolute measurements. The resulting E.A. are in eV: CH3NO2, 0.49; CS2, 0.54; (C6H5)CO, 0.64; 2, 4, 6-trimethyl nitrobenzene 0.68; 2, 3-butanedione 0.71; 2, 3-dimethyl nitrobenzene, 0.83; 2-methyl nitrobenzene, 0.88; 3-methyl nitrobenzene, 0.94; nitrobenzene, 0.97; 1-fluoro-4-nitrobenzene, 1.06; SO2 1.11; 1-chloro-3-nitrobenzene, 1.23; maleic anhydride, 1.42; 1,3-dinitrobenzene, 1.6; 2, 5-dimethyl-p-benzoquinone, 1.72; methyl-p-benzoquinone, 1.78; p-benzoquinone, 1.86. The assignment of the present absolute values disagrees with that by Fukuda and McIver based on ICR bracketing experiments. It is suggested that the bracketing experiments were misleading due to presence of excitation in the ionic reactants used.

Telechelics, 7. Polytetrahydrofuran with acetate end groups

AbstractTetrahydrofuran (THF) was polymerized by protic and non‐protic cationic initiators in presence of acetic anhydride (Ac2O) in methylene dichloride. Due to a low transfer coefficient (CAc2o = 0,058) the molecular weight increases during the early part of the reaction. The consumption of Ac2O continues even when the THF concentration approaches zero, which results in a lowering of the number‐average degree of polymerization Pn. Degradation of poly(THF) continues until the Ac2O is exhausted. The equilibrium concentration of THF can reach almost zero at small Pn. The equilibrium constants K2, K3, K4, etc., up to K23 for the successive monomer additions are obtained from gel permeation chromatography. With the exception of K2 the equilibrium constants Kn are independent of n.

ChemInform Abstract: THERMOCHEMISTRY AND KINETICS OF THE REACTION OF METHYL MERCAPTAN WITH IODINE

The gas-phase reaction CH3SH + I2 has been studied spectrophotometrically over the temperature range of 476–604 K. It was found that the reaction undergoes H abstraction by I at ≤575 K, leading to the formation of MeSI and followed by a secondary reaction which leads to the formation of MeSSMe: Taking into consideration the effect of reaction (2), the equilibrium constant K1 (554 K) has been evaluated to be 0.025 ± 0.004. This value was combined with the estimated values S (CH3SI, g) = 73.7 ± 1.0 eu and 〈ΔC〉 = 0.87 ± 0.3 eu to obtain ΔH = 4.03 ± 0.73 kcal/mol. This yields ΔH (CH3SI, g) = 7.16 ± 0.73 kcal/mol when combined with known thermochemical values for CH3SH, HI, and I2. A kinetic study was vitiated by the concurrent heterogeneous reaction of MeSH and I2 at lower temperatures and the rather complicated chemistry occurring at elevated temperatures. However, attempts at measuring rate constants at 554 K lead to a lower limit of ΔH (CH3S·, g) ≥ 29.5 ± 2 kcal/mol when an estimated value of A = 1010.8 ± 0.2 L/mol·s for the reactionc is used. DH (CH3S–I) is estimated to be 49.3 ± 1.7 kcal/mol. The bond strengths of some divalent sulfurs and the reaction mechanisms are discussed. A crude estimate of DH0(H–CH2SH) = 96 ± 1 kcal has been obtained from the kinetic data.

Thermochemistry and kinetics of the reaction of methyl mercaptan with iodine

AbstractThe gas‐phase reaction CH3SH + I2 has been studied spectrophotometrically over the temperature range of 476–604 K. It was found that the reaction undergoes H abstraction by I at ≤575 K, leading to the formation of MeSI and followed by a secondary reaction which leads to the formation of MeSSMe: equation image Taking into consideration the effect of reaction (2), the equilibrium constant K1 (554 K) has been evaluated to be 0.025 ± 0.004. This value was combined with the estimated values S (CH3SI, g) = 73.7 ± 1.0 eu and 〈ΔC〉 = 0.87 ± 0.3 eu to obtain ΔH = 4.03 ± 0.73 kcal/mol. This yields ΔH (CH3SI, g) = 7.16 ± 0.73 kcal/mol when combined with known thermochemical values for CH3SH, HI, and I2. A kinetic study was vitiated by the concurrent heterogeneous reaction of MeSH and I2 at lower temperatures and the rather complicated chemistry occurring at elevated temperatures. However, attempts at measuring rate constants at 554 K lead to a lower limit of ΔH (CH3S·, g) ≥ 29.5 ± 2 kcal/mol when an estimated value of A = 1010.8 ± 0.2 L/mol·s for the reactionc equation image is used. DH (CH3S–I) is estimated to be 49.3 ± 1.7 kcal/mol. The bond strengths of some divalent sulfurs and the reaction mechanisms are discussed. A crude estimate of DH0(H–CH2SH) = 96 ± 1 kcal has been obtained from the kinetic data.

Stabelity of mixed ligand complexes of copper(II): ESR studies

Three new mixed ligand complexes of Cu(II) obtained by combining any two of the three ligands, diethyldithiocarbamate, N-benzoyl-N′-diethylthiocarbamide and acetylacetonate have been identified in reaction mixtures using electron spin resonance (esr), by estimating the equilibrium constantK associated with the ligand exchange reaction. TheK values were also determined for fifteen other mixed ligand complexes of Cu(II) reported earlier. The stability of these mixed ligand complexes was correlated with the difference in the strengths of covalent bonding between the metal ion and the two ligands. The bondings involving both the $$d_{x^2 } - _{y^2 } $$ andd xy orbitals on the metal were necessary. In addition, the extent of metal 4s-orbital mixed in the unpaired electron orbital contributed to the magnitude ofK. The diagrams similar to the ones used in our correlation could be useful in predicting the probable yield of mixed ligand complexes in reaction mixtures.

A kinetic and mechanistic study of the reaction between bis-p-ethoxyphenyl ditelluride and molecular iodine in solution

The title reaction in toluene has been examined spectrophotometrically. The data are consistent with equations (1)–(3)(R =p-EtOC6H4). The rate constants k1 and k3 are 56 ± 2 dm3 mol–1 s–1 at R2Te2+ [graphic omitted] 2RTel (1) RTel + I2 [graphic omitted] RTe(I3)(2) RTe(I3) [graphic omitted] RTel(I)3(3) 7 °C and 6.2 × 10–4 s–1 at 25 °C, respectively. The equilibrium constant K2 is 1 570 dm3 mol–1 at 25 °C, and ΔH2=–22 ± 4 kJ mol–1. The activation parameters for the final step are ΔH‡= 44 ± 5 kJ mol–1 and ΔS‡=–160 ± 15 J K–1 mol–1.

Hydrogen bonding of O—H and C—H hydrogen donors to Cl−. Results from mass spectrometric measurements of the ion–molecule equilibria RH + Cl− = RHCl−

Equilibrium constants K1 for reaction [1] RH + Cl− = RHCl− in the gas phase were measured with a high pressure mass spectrometer under chemical ionization conditions. Data for some 40 compounds RH are presented. It is found that the binding free energies [Formula: see text] for RH = oxygen acids increase with the gas phase acidity of RH. The strongest bonds are formed with strong acids like HCO2H, CH3CO2H, and phenol. Water and alkyl alcohols give much weaker interactions. A simple relationship between gas phase acidity and binding free energy does not occur for RH = carbon acids. Carbon acids like cyclopentadiene, whose high gas phase acidity is largely due to charge derealization by conjugation in the completed anion, do not give Cl− adducts with stability commensurate with the acidity. A relationship between gas phase acidity and binding energy is found for carbon acids with carbonyl groups and for the substituted toluenes. Molecular orbital calculations with the STO-3G basis set provide insights to the bonding occurring in RHCl−. For all cases investigated, hydrogen bonding to Cl− provides the most stable structure. Generally the hydrogen bond occurs through the hydrogen which has the highest net positive charge. The hydrogen bond strength is found approximately proportional to this positive charge. Another proportionality is found between the charge transferred from Cl− to RH, on formation of RHCl−, and the strength of the hydrogen bond.

Bindungskonstanten, Bindungsenthalpien und Entropien für die nicht-kompetitive und die kompetitive Bindung von Acriflavin, Tetramethylacriflavin und Acridinorange an DNA / Binding Constants, Binding Enthalpies and Entropies of the Non-Competitive and the Competitive Binding of Acriflavine, Tetramethylacriflavine and Acridine Orange to DNA

Abstract The binding of the dye cations acriflavine AF, tetramethylacriflavine TMAF and acridine orange AO (scheme of structures) to calf thymus DNA has been investigated by means of absorption spectroscopy, Table I. In order to avoid dye association we used very low dye concentrations and sufficiently high DNA concentrations. In this case we got linear Scatchard isotherms. The formal Scatchard binding constant K strongly depends on the salt concentration Cs (S = NaCl) of the solution and the temperature T (278 - 303 K), K (CS, T). The average value of binding sites per mononucleotide is n = 0.17. It is independent of the dye species and of CS and T. The value of r (bound dye cations per mononucleotide) diminishes with growing salt concentration CS(CS ≲ 1 ᴍ). At sufficiently high salt concentrations r is approximately constant (CS ≳ 1 ᴍ). Obviously there are two types of binding of the dye cations to DNA even in the domain of linear Scatchard isotherms. They can be distinguished experimentally with the competitive salt effect. To describe r(CS,T ) or K (CS, T) we used a simple model with three equilibria: 1. Noncompetitive binding 1 (intercalation) of dye cations to n1 CN binding sites (CN = concentration of mononucleotides), equilibrium constant K1 . 2. Competitive binding 2 (external binding) of dye cations to n2 CN binding sites, equilibrium constant K2. In contrast to type 1 binding, the dye cations in type 2 binding can be replaced by metal cations M of S (M = Na⊕) at sufficiently high salt concentrations CS. 3. Competitive binding 3 of M to the same sites of 2 and the dye cations as competitor, equilibrium constant K3. The model agrees very well with the experiments on the condition n1 = n2 = n. Therefore the dye can be bound to one of the n CN binding sites either non-competitively or competitively. Type 1 and type 2 binding exclude one another at the same binding site in the domain of linear Scatchard plots. The binding constants Ki(i = 1, 2, 3) have been determined by means of the competitive salt effect, Table II. They only are T dependent. From K(T)i we got the binding enthalpies ΔHi 0 and binding entropies ΔSi 0, Table III. AF and AO cations are bound non-competitively and competitively, TMAF only competitively. In comparison with AF or AO the competitive binding of TMAF is much weaker. In the case of AF and AO K1 is approximately one power of ten smaller than K2, K1 ⪡ K2 ! The binding enthalpies of the non-competitive and the competitive binding are nearly equal, ΔH1 0 ≅ ΔH2 0. Therefore the difference in the binding constants K1, K2 can be attributed to the difference in the binding entropies, ΔS1 0 ⪡ ΔS2 0. Thermodynamically type 2 binding (external binding) is preferred to type 1 binding (intercalation). The binding enthalpy of Na⊕ to DNA is in all cases nearly zero, ΔH3 0 ≅ 0. Only the increase of entropy S3 0 &gt; 0 enables binding 3. From the thermodynamic data follows that type 1 and type 2 binding of AF and AO are produced by electrostatic and hydrophobic interaction which are intensified by hydrogen bonding. In contrast to this the weaker competitive binding of TMAF is caused by electrostatic and hydrophobic interaction only. Our investigations agree with former works on ethidium bromide E and tetramethylethidium bromide TME (scheme of structures, Tables II and III). They are consistent with the assignment non-competitive binding = intercalation, competitive binding = external binding.

Electrical properties and defect model of tin-doped indium oxide layers

Tin-doped In2O3 layers were prepared by the spray technique with doping concentrationsc Sn between 1 and 20 at. % and annealed at 500 °C in gas atmospheres of varying oxygen partial pressures. The room-temperature electrical properties were measured. Maximum carrier concentrationsN=1.5×1021cm−3 and minimum resistivities ϱ=1.3×10−4 Ω cm are obtained if the layers are doped withc Sn≈9 at. % and annealed in an atmosphere of oxygen partial pressurep O2 ⋦10−20 bar. At fixed doping concentration, the carrier mobility increases with decreasing oxygen pressure. The maximum obtainable mobility can be described in terms of electron scattering by ionized impurities. From an analysis of the carrier concentration and additional precision measurements of the lattice constants and film thicknesses, a defect model for In2O3:Sn is developed. This comprises two kinds of interstitial oxygen, one of which is loosely bound to tin, the other forming a strongly bound Sn2O4 complex. At low doping concentrationc Sn≲4 at. % the carrier concentration is governed by the loosely bound tin-oxygen defects which decompose if the oxygen partial pressure is low. The carrier concentration follows from a relationN=K 1 ·p O2 −1/8 ·(3 ×1010 × cSn −N)1/4 with an equilibrium constantK 1=1.4×1015 cm−9/4bar1/8, determined from our measurements.

The Correlation of Basicity and Equilibrium Constants Evaluated from Lanthanoid-induced Shifts in the Eu(fod)3-p-Substituted Aniline Systems

Abstract An approximate linear correlation has been found between the basicity of substrate (pKa) and the logarithm of the equilibrium constant K1 for 1:1 adducts evaluated from the least squares analysis of lanthanoid-induced shifts (LIS) for the systems containing Eu(fod)3 and a series of p-substituted anilines in CDCl3. In contrast, both the observed S-values and intrinsic shifts have shown no simple correlation to pKa’s of substrates.

Radical equilibrium studies. II. The thermodynamic parameters of s−butyl

AbstractThe thermal decomposition of azomethane in the presence of propene has been investigated in the range of 568–638°K at reactant partial pressures of up to about 7 torr in the presence of at least 170 torr of argon. The elementary reactions taking place in such conditions are discussed in detail. It is shown that a situation approaching equilibrium is attained between the processes equation image Values are obtained for the equilibrium constant K2, which can be described by the equation Using the best available thermodynamic parameters for methyl and propene, it is concluded that those for s−butyl are in need of adjustment. We recommend the values ΔHf0 (300°K) = 13.8 ± 1.0 kcal/mol and S3000 (1 atm standard state) = 75.6 ± 3.0 cal/mol°K together with group additivity values of the heat capacity. A comparison of measured values of K2 with values calculated from independent measurements of k2 and k−2 shows a discrepancy of about a factor of 3.5.

Studies on the proton magnetic resonance spectra of aliphatic systems. IX. Complex shift and equilibrium constant of association between excess amount of aliphatic alcohol and tris(dipivalomethanato)europium.

From the two step equilibria of the complex formation between the shift reagent Eu (DPM)3 and a large excess of aliphatic alcohol, the two complex shifts Δ1, Δ2 and equilibrium constants K1, K2 are estimated. Δ1 and K1 are comparable with Δc and Kc obtained in an equimolar condition, and the magnitudes of K2 are included within the errors of K1. The infinite concentration shift Δic obtained in the presence of a large excess of the donor is also comparable with Δ1. These results suggest the role of the solvent molecule occupying an overwhelming majority in the sample solution, where the molecular interaction is a time-averaging 1 : 1 donor-acceptor collision in the nuclear magnetic resonance time scale.