Theory of titration curves: Locations of points of maximum slope on potentiometric heterovalent (“asymmetrical”) precipitation titration curves

By a wholly rigorous general treatment of the potentiometric titration curve representing the titration of B^m+ with A^n- to give the precipitate B_nA_m, where n ≠ m, it is shown on taking into account the effect of dilution that: (1) If $\text{n}\text{m}$ > 1, the inflection point must precede the equivalence point, but there is no inflection point if the initial concentration of the ion titrated is smaller than a certain value, which is determined by the values of m, n, and the solubility product of the precipitate. (2) If $\text{n}\text{m}$ < 1, the inflection point may follow the equivalence point — though not by more than a certain definite amount — or may precede it or coincide with it. In every such case there is a concentration of A^n- that will cause the equivalence point to coincide with an inflection point; this concentration depends on the values of m, n, and the solubility product of the precipitate. (3) Unless the difference between the equivalence and inflection points is negligibly small, the traditional treatment in which dilution is neglected gives seriously erroneous estimates of the location of the inflection point.     

The preperation and coordination properties of 1,4-diaza-3-methylbutadiene-2-ylpalladium(II) complexes with different substituents on the imino nitrogen atoms

The complexes trans-[PdCl{$\text{C(=NR)C}$(ME)=NR'} (PPh₃)₂] (R=C₆H₁₁,p-C₆H₄OMe; R$\text{.}\text{?}$=p-C₆H₄OMe, Me) containing a σ-bonded 1,4-diaza-3-menthyl-butadiene-2-yl group with different substituents on the nitrogen atoms have been prepared by two routes. The first involves initial methylation of the mixed isonitrile complex [PdCl₂(CNR)(CNR')]by HgMe₂, followed by reaction with PPh₃ ($\text{Pd}\text{PPh}{}_3$molar ratio $\text{1}\text{2}$). The second method involves condensation of primary aliphatic amines with the carbonyl group of the 1-azabut-1-en-3-one-2-yl moiety of the complex trans-[PdCl{$\text{C(=NR)C}$(Me) = 0} (PPh₃)₂]. The 1,4-diaza-3-methylbutadiene-2-yl derivatives act through their imino nitrogen atoms as chelating ligands towards anhydrous metal chlorides MCl₂ (M = Co, Ni, Cu, Zn). Magnetic moment measurements and the far-infrared and electronic spectra of these adducts indicate an essentially pseudo-tetrahedral configuration at M in the solid and in solution. With the ZnCl₂ adducts, the ¹H NMR pattern for the phenyl protons of the p-methoxyphenyl N-substituents dependss upon the position of the substituent i the 1,4-diazabutadiene chain.     

Analytical applications of azoisoxazoles. III. Complexes of cobalt,copper, and cadmium with 2-(5′-methyl-2′-isoxazolylazo)-4-methoxyphenol

2-(5′-methyl-2′-isoxazolylazo)-4-Methoxyphenol has been synthesized and its ionization constant (pK_a = 7.98 ± 0.08) spectrophotometrically determined in a 4% ($\text{v}\text{v}$) ethanol-water medium at μ = 0.25 M (NaClO₄). The reagent originates water soluble complexes with cobalt (log β₂ = 11.45 ± 0.16), copper (log β₁ = 7.15 ± 0.10), and cadmium (log β₁ = 3.96 ± 0.12), and can be used for the spectrophotometric determination of cobalt and copper as well as metallochromic indicator for copper.     

Nematic—isotropic solution thermodynamics in di(p-methoxyphenyl)-trans-cyclohexane-1,4-dicarboxylate

Solution thermodynamic parameters of selected non-polar solutes have been determined in the nematic and isotropic fluid states of di(p-methoxyphenyl)-trans-cyclohexane-1,4-dicarboxylate. These states have been reported to exert no measurable differential in kinetic medium effects on the Claisen rearrangement¹. Partial molar enthalpies Δ$\text{H}$^soln₂ and entropies Δ$\text{S}$^soln₂ of solution of a series of substituted benzenes in the nematogenic solvent, determined by the gas—liquid chromatographic method of Martire, ^2–4, are reported. Changes in solute excess Gibbs free energy Δ$\text{G}$^E₂ over the nematic—isotropic transition of the solvent, corresponding to the changes in free energy of solution ΔΔ$\text{G}$^soln₂, have been calculated for the series. The results show the nematic and isotropic states of the medium to exhibit distinctly different solvent characteristics and suggest that Claisen reaction kinetics in the nematogenic solvent reflect compensating medium effects on the reactant and its activated state.     

New defect vanadium dioxide phases

Two new monoclinic V₂O₄ phases were prepared at high pressure from the regular monoclinic (M₁) form of V₂O₄. The unit cell dimensions for the unmodified monoclinic (M₂) phase are: a = 9.083, b = 5.763, c = 4.532 Å, and β = 91.30°. The space group $\text{C 2}\text{m}$ is consistent with the crystallographic data. The new vanadium dioxide exhibited a structural transition and an abrupt, reversible change in resistivity (approx. 4 orders of magnitude) at 66°C similar to that observed in M₁-type V₂O₄. This new form of V₂O₄ is believed to be stabilized by chemical and structural defects. Controlled substitution of V⁵⁺ for V⁴⁺ in the structure led to yet another monoclinic (M₃) phase. This phase is closely related to the M₂ phase. The M₃ unit cell dimensions are: a = 4.506, b = 2.899, c = 4.617 Å, and β = 91.79°, having the space group $\text{P 2}\text{m}$. The substitution of V³⁺ yielded only monoclinic (M₁) derivatives. The modified products have varied semiconductor to metal transition temperatures which depend on the type and amount of substitution and defect structure.     

The enthalpies of formation of bis-(benzene)molybdenum and of bis-(toluene)tungsten

Microcalorimetric measurements at 520–523 K of the heats of thermal decomposition and of iodination of bis-(benzene)molybdenum and of bis-(toluene)tungsten have led to the values (kJ mol^?): ΔH^o_f[Mo(η-C₆H₆)₂, c] = (235.3 ± 8) and ΔH^o_f[W(η⁶-C₇H₈)₂, c] = (242.2 ± 8) for the standard enthalpies of formation at 25°C. The corresponding ΔH^o_f(g) values, using available and estimated enthalpies of sublimation, are (329.9 ± 11) and 352.2 ± 11) respectively, from which the metalligand mean bond-dissociation enthalpies, $\text{D}$(Mo—benzene) = (247.0 ± 6) and $\text{D}$(W—toluene) = (304.0 ± 6) kJ mol^?1, are derived.     

Preparation,structure, and magnetic properties of isostructural La3MAlS7 and La3MFeS7 (M = Mg,Mn, Fe,Co, Ni,or Zn)

A series of quaternary metal sulfides of the general formula La₃MM′S₇ (M = Mn, Fe, Co; M′ = Al and M = Mg, Mn, Fe, Co, Ni; M′ = Fe) consisting of linear chains of face shared MS₆ octahedra and isolated M′S₄ tetrahedra has been prepared and studied. The aluminium compounds La₃MAlS₇ (M = Mn, Fe, Co) exhibit linear chain antiferromagnetism. Magnetic behavior of other La₃MFeS₇ sulfides has been examined in detail. The magnetic susceptibility of La₃MgFeS₇ shows that tetrahedral site Fe³⁺ undergoes a transition from $\text{S =}\text{5}\text{2}$ to S = 2 spin state around 150 K.     

The photometric titration of nickel in the presence of cobalt

A spectrophotometric titration of nickel in the presence of cobalt is described using disodium ethylene diaminc tetraacetic acid as a titrant The end-point was obtained by plotting the corrected absorbancy against ml of titrant added Nickel concentrations of 2.5 to 25 mg were determined in the presence of up to 8 mg of cobalt with an error of 1$\text{1}\text{2}$% or less depending upon the concentration of Versenate used A 0.03M and 0.1M versenate was used The effects of pH, concentrations of nickel And cobalt, accuracy of the method, presence of interfering elements, and limitations of the method are discussed.     

Polymérisation cationique du chloro-1 butadiène et copolymérisation avec l'isobutène

The cationic homopolymerization of 1-chlorobutadiene and its copolymerization with isobutene have been carried out in dichloromethane solution. The catalyst-cocatalyst pairs used were AlEt₂Cl-(CH₃)₃CCl and AlEtCl₂-(CH₃)₃CCl. In the latter case, the use of (CH₃)₃CCl was not necessary. According to experimental conditions, high molecular weight copolymers ($\text{M}{}_{\mathrm{n}}\text{= 200,000}$) insoluble in CH₂Cl₂, or soluble low polymers ($\text{M}{}_{\mathrm{n}}\text{= 20,000}$) were obtained. Homopoly-1-chlorobutadienes were soluble low molecular weight polymers ($\text{M}{}_{\mathrm{n}}\text{= 10,000}$). The 1-chlorobutadiene units in the polymers are nearly exclusively 3,4 (mainly trans). Consequently, this method is not convenient to prepare elastomers with a 1,4 structure similar to that of chlorinated butyl rubber.     

Polarographic determination of the stability constants of metal complexes based on the shifts in half-wave or peak potentials of the anodic oxidation of mercury: methylthioacetato- and 2,2′-thiobisacetato complexes

The stability constants of metal-ion complexes, other than those of mercury ions, can be determined from the shifts, caused by an excess of that metal ion, in the anodic waves of mercury oxidation in the presence of the ligand.Let a solution contain L, a ligand that can react with mercury ion from the anodic oxidation of mercury to form the complexes HgL_p. The half-wave potential of the anodic wave will be shifted by the presence of an excess of a metal ion M, which can also react with L forming the complexes M_jL (where j = 1, $\text{1}\text{2}$,…1/N). A general expression is derived relating the half-wave potential shift ΔE_{$\text{1}\text{2}$} to the overall stability constants. If the excess of metal ion M is great enough for the 1:1 complex to predominate in solution (and if HgL₂ is the predominating mercury complex), for reversible, diffusion-controlled processes the general equation can be simplified to:

where c_M is the total concentration of metal ion M.This equation provides an easy and fast method for β₁ determination. The simplified equation is best suited for experimental data obtained from techniques such as DP, AC₁ and AC₂ polarography, whose increased precision in ΔE measurement enables poorly-developed dc-polarographic anodic waves to be used for β₁ determination. Since the metal-to-ligand concentration ratio must be large in order to apply the simplified equation, the determination can be carried out at very small ligand concentrations. This fact renders the new method especially useful when the ligand solubility does not allow the high ligand concentrations needed in the DeFord—Hume method to be reached. The adequacy of the deduced equations when applied to polarographic processes which are irreversible or not controlled by diffusion is discussed.The simplified equation is tested using several metal complexes of methylthioacetate and 2,2′-thiobisacetate ligands and comparing some of the values obtained from experimentally measured ΔE's with known β₁ values taken from the literature. Good agreement is found. For the U(VI)—methylthioacetate complex, which has not been previously reported in the literature, log β₁ = 1.75 ± 0.1.     

Etude à haute pression des tétramétaphosphates du type M2P4O12 (M = Ni,Mg, Cu,Co, Fe,Mn, Cd). Données cristallographiques sur tous les composés M2P4O12

Fe₂P₄O₁₂ has been prepared and identified as an isotype of the other M^II₂P₄O₁₂ tetrametaphosphates (M^II = Ni, Mg, Cu, Co, Mn, Cd). Its monoclinic unit cell:

$\text{a=11.952,b=8.359,c=9.932}\text{A}\text{?}$

$\text{β=118°76}$

contains 4 formula units. The space group is $\text{C2}\text{c}$. For tetrametaphosphates with M^II = Ni, Mg, Cu, Co, and Mn we found a new denser phase induced at 80 kbar and 1000°C. In the case of Fe₂P₄O₁₂ the unit cell of this new form is

$\text{a=9.777,b=8.994,c=4.968}\text{A}\text{?}$

$\text{β=107°22}$

with Z = 2 and two possible space groups Cc or $\text{2C}\text{c}$. This dense phase exists at ordinary pressure for the zinc salt.     

Evolution structurale de monoxydes non-stoechiométriques du type wüstite: Simulations et relations entre paramètres structuraux

For nonstoichiometric monoxides M_1?zO (or MO_x) of the wüstite type, it is possible to forecast the trend of experimental graphs representing the parameters a of the cubic cell or the temperature factor B vs temperature θ or composition z (or x). A criterion for the experimental accuracy allows to justify the existence or not of a curvature on the graphs. The parameter a is calculated a priori for wüstite (M = Fe) vs z. A model gives the law of variation of avs some ionic species and the ratio $\text{? =}\text{(z + t)}\text{t}$; t is the rate of intertitials. The law is $\text{a = a}{}_0\text{[1 ?}\text{1}\text{3}\text{β1z]}$. The calculated value obtained for β1 agrees well with the experimental mean value 〈β〉 = 0.28. This model applies to the monoxide Mn_1?zO for which the calculated value of β1 is close to 〈β〉 = 0.29. In a second model, the cell volume is defined as being the weighted mean of the volumes of distorted and undistorted cells. With knowledge of β1 and ?, it is possible to evaluate the mean radius of a vacancy for each oxide. The factor B is the sum of two contributions B_Th(θ) and B_St(z). This latter varies linearly with z. The coefficient $\text{p = (}\text{?B}\text{?z}\text{)}{}_{\mathrm{\theta }}$ can be calculated a priori from simulations of the shifts resulting from clusters of point defects. Knowing β1, p may be located between 3 and 10 Ų according to the assumptions. The experimental value for the wüstite under equilibrium conditions is p = 4.2 Ų. An empirical relation between B_Th(θ) and a(θ) is discussed from the point of view of Grüneisen's law. When the molar heat C_p is known, it is possible to evaluate the mean force constant D = 0.78 mdyne/Å for the bonds in Fe_1?zO. The compressibility coefficient χ₀ is then obtained. It can be compared with the measured value from the literature, at 25°C under zero pressure.     

Electrochemical oxidation of α-hyponitrate ion and its analytical applications

α-Hyponitrate ion is electrochemically oxidized at mercury electrodes: the reaction proceeds by an initial 1-electron oxidation to give an anion radical which decomposes to give nitrogen oxide and nitrite as the ultimate products. The d.c. polarographic wave of α-hyponitrate (E_{$\text{1}\text{2}$} = -0.325 V vs. SCE) in 0.1 M sodium hydroxide can be used for the determination of α-hyponitrate in the range 0.08–1.3 mM; a.c. polarography (E_p = -0.30 V vs. SCE) is useful in the range 0.075–1.0 mM. Amperometric titration with 0.05 M hexacyanoferrate(III) is suitable for determinations of 5–20 mg of sodium α-hyponitrate. A.c. polarography at pH 11.0 allows α-hyponitrate to be determined in the presence of 50-fold amounts of hydroxylamine.     

Cryogenic degradation of polystyrene in solution

An ultra-high molecular weight and narrow distribution polystyrene ($\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{= 7.3 × 10}{}^6$, M_w/M_n = 1.13) was dissolved in a wide range of solvents. Potential degradation by freezing was studied as a function of solvent type, concentration, cooling rate and number of freezing cycles. Cryogenic experiments were conducted in dioxane, tetrahydrofuran, benzene, dichloroethane, cyclohexanone, p-xylene, methyl methacrylate and styrene. The extent of degradation did not relate to a single solvent parameter, but there seemed to be a tendency towards a limited degradation in solvents with low melting points and/or solubility parameters greatly different from that of polystyrene. A low polymer concentration as well as a high cooling rate promoted chain scission, the latter parameter being the most important. In cyclohexanone and p-xylene, linear relationships were observed between the number of scission per molecule and the number of freezing cycles at high polymer concentrations and at high cooling rates. At lower concentrations and slower cooling, the relationships were non-linear suggesting a different degradation mechanism. The most extensive change in molecular weight distribution was observed on freezing in styrene. After 45 freezing cycles, an $\text{M}$_w of only 2.3 × 10⁶ was observed. The results indicate that chain scission occurred together with polymerization and combination reactions. Freezing of suitable solutions of ultra-high molecular weight polymers can thus be used as a new way of initiating polymerizations by cooling rather than heating.     

Electronic structure and vibrational frequency of Cr2

Cr₂ is produced by pulsed YAG laser vaporization of chromium metal and its fluorescence excitation spectrum is analyzed. The high value of vibrational frequency ΔG″_{$\text{1}\text{2}$} = 452.34 cm^?I (ω″^e ≈ 470 cm^?1) and short internuclear distance r″_e = 1.6788 Å are indicative of a very strongly bound ¹∑⁺_g ground state.     

Phase equilibrium relations in the binary systems LiPO3CeP3O9 and NaPO3CeP3O9

The LiPO₃CeP₃O₉ and NaPO₃CeP₃O₉ systems have been investigated for the first time by DTA, X-ray diffraction, and infrared spectroscopy. Each system forms a single 1:1 compound. LiCe(PO₃)₄ melts in a peritectic reaction at 980°C. NaCe(PO₃)₄ melts incongruently, too, at 865°C. These compounds have a monoclinic unit cell with the parameters: a = 16.415(6), b = 7,042(6), c = 9.772(7)Å; β = 126.03(5)°; Z = 4; space group $\text{C}{}_2\text{c}$ for LiCe (PO₃)₄; and a = 9.981(4), b = 13.129(6), c = 7.226(5) Å, β = 89.93(4)°, Z = 4, space group $\text{P2}{}_1\text{n}$ for NaCe(PO₃)₄. It is established that both compounds are mixed polyphosphates with chain structure of the type |M^I_IM^III_II (PO₃)₄|_∞M^I_I: alkali metal, M^III_II: rare earth.     

An estimation of the temperature dependence of the excluded-volume integral

Lower critical solution temperatures (LCST) of trans-decalin solutions of polystyrene were measured on a newly built electric thermostat, the theta point Θ_L associated with the LCST being determined as 662 K. By use of this result together with the literature data for the ordinary theta point (Θ_U) and the entropy of dilution parameter, the excluded-volume integral B(T) was estimated in terms of the Eichinger method over the temperature range Θ_U to Θ_L. This enabled us to calculate the excluded-volume variable $\text{z}\text{as}\text{0.770 C}{}_{\mathrm{<mtext>M</mtext>}}\text{′ B(T)}\text{M}{}_{\mathrm{<mtext>w</mtext>}}{}^{0.5}$. Here, C_M′ is a numerical factor specific for a given polymer-solvent system and $\text{M}$_w is the weight-average molecular weight. Using the z values calculated from the above expression, we analysed the data on dilute solution properties of polystyrene reported by Berry and by Inagaki et al. It was found that the Domb-Barrett and the Suzuki equations for α_s (the linear expansion factor for the radius of gyration) were in good agreement with Berry's data of light scattering. The first coefficient k₁ in the series α_ν³ = 1 + k₁z + … (α_ν: the hydrodynamic expansion factor) was experimentally evaluated as 1.70. Furthermore, a conversion of the Suzuki equation for α₅ into that for α_ν with this k₁ value was found to account quite satisfactorily for the viscosity behaviour observed by Inagaki et al.     

A thallium(I)-selective electrode based on a liquid ion-exchanger containing 0,0'-didecyldithiophosphoric acid

A liquid ion-exchange electrode containing thallium(I) 0,0'-didecyldithiophosphate in chlorocyclohexane is described. Nernstian behaviour is obtained in the pTI range 1–5.5, the slope of the calibration graph being 57.6 mV/decade change in activity at ionic strength 0.1, Alkali and alkaline earth metal cations do not interfere (K_{$\text{TI}\text{M}$} < 10^?5). Potentials are established rapidly, and are unaffected by pH in the range 5–12. In analytical applications direct potentiometry and potentiometric precipitation titrations with iodide or tetraphenylborate solutions are satisfactory. Various interfering ions can be masked with EDTA.