Quasi-lattice Model Research Articles

Ion association in molten salts. The association of silver(I) with the “Mixed ligand” chloride+bromide in molten sodium nitrate

The quasi-lattice model for quaternary reciprocal systems of molten salts, previously developed for association processes in mixed solvents, has been modified to apply to an association process involving a “mixed ligand” in a pure salt as solvent. The association energies, determined from e.m.f. measurements in the range 620–720 K, for the association of silver(I) with chloride-bromide mixtures in molten sodium nitrate, are in satisfactory agreement with the predictions of the model. The very small, but significant, discrepancies between calculated and experimental association energy values show the same trend as those previously found for the mixed solvent systems.

The quasi-lattice structure in concentrated aqueous solutions

The total neutron diffraction pattern from an aqueous solution of nickel chloride shows a pre-peak at a q value of approximately 1 A −1, which has been identified as the principal peak in the NiNi partial structure factor. In this paper we report an investigation of the position of the pre-peak as the molarity ( C) of the solution is changed. The data show that the peak position is proportional to C 1/3, which argues strongly in favour of the quasi-lattice model for aqueous solutions.

Molecular collisions and self-diffusion in liquids

The velocity autocorrelation function and coefficient of self-diffusion are derived for a hard-sphere fluid. An earlier quasi-lattice model of self-diffusion in liquids is re-examined and a less restrictive expression for the self-diffusion coefficient is derived. The coefficient of self-diffusion of a light or heavy isotope in the normal liquid is considered both for hard spheres and in the quasi-lattice approximation. An experiment is proposed to clarify the nature of the isotope effect in self-diffusion.

Thermodynamic properties of solute molecules at infinite dilution determined by gas-liquid chromatography : I. Intermolecular energies of n-alkane solutes in C 28-C 36n-alkane solvents

Gas-liquid partition chromatography has been used to obtain thermodynamic properties of solute molecules at infinite dilution for n-alkane solutes in three n-alkane solvents ( n-C 28H 58, n-C 32H 66 and n-C 36H 74). Henry's law constants at infinite dilution of n-alkane solutes in n-alkane solvents have been determined from gas-liquid chromatographic retention volume data at five temperatures. From the Henry's law constants, intermolecular energies of n-alkane solute molecules in n-alkane solvents have been estimated by an equation derived from the quasi-lattice model of a liquid mixture of long-chain molecules. The intermolecular energy of solute molecules at infinite dilution varies not only greatly with the chain length of the solute molecules but also with that of the solvent molecules.

Thermodynamic properties of solute molecules at infinite dilution determined by gas-liquid chromatography : II. Interaction energies of contact pairs of methyl and methylene segments

The intermolecular energies of n-alkane solute molecules in n-alkane solvents at infinite dilution have been determined by gas-liquid chromatography. According to the quasi-lattice model, the intermolecular energies of solute molecules can be expressed as the sum of interaction energies of each pair of a segment of the molecules with segments of neighbouring molecules. The interaction energies of contact pairs of CH 3-CH 3, CH 3-CH 2 and CH 2-CH 2 have been estimated by an equation derived from a theory of solute-solvent interactions. A consistent set of the values was found for all of the solute-solvent systems studied without the need to adjust the model parameters.

Thermodynamics of hydrocarbon mixtures using gas-liquid chromatography The determination of activity coefficients of some unsaturated C 5 and C 6 unbranched hydrocarbons in n-octadecane, n-octadec-1-ene, n-hexadecane, and n-hexadec-1-ene

The activity coefficients at infinite dilution for solutes n-hexane, hex-1-ene, trans-hex-2-ene, trans-hex-3-ene, trans-hexa-1,3-diene, trans-hexa-1,4-diene, trans, trans-hexa-2,4-diene, hexa-1,5-diene, cis-hexa-1,3,5-triene, n-pentane, trans-pent-2-ene, and cis-penta-1,3-diene in some of the solvents n-octadecane, octadec-1-ene, n-hexadecane, and hexadec-1-ene have been determined at one or both of the temperatures 308.15 and 323.15 K. The results are discussed in terms of the quasi-lattice model and some results have been fitted to equations generated by factor analysis. Mixed second virial coefficients B 12 of the above solutes and nitrogen have also been determined. The results were obtained from medium-pressure packed-column gas-liquid chromatography.

Silver(I)—ammonia complexes in molten (Li,K)NO3 eutectic

The equilibrium constants for the formation of silver-ammonia complexes in molten (Li, K)NO3 eutectic mixture were determined from e.m.f. measurements. The results are discussed in connection with the quasi-lattice model for the ionic associations in molten salts.

Silver(I)-ammonia complexes in molten (Li,K)NO 3 eutectic

Summary The equilibrium constants for the formation of silver-ammonia complexes in molten (Li, K)NO 3 eutectic mixture were determined from e.m.f. measurements. The results are discussed in connection with the quasi-lattice model for the ionic associations in molten salts.

Self-diffusion coefficients and rotational correlation times in polar liquids. VI. Water

A new model for liquid water is presented. As a first approximation (A) the liquid is considered as a quasi-hard-sphere fluid and the scaled particle theory is employed to calculate the work (w) required to create a vacancy of molecular dimension using the observed density of water. In the second approximation (B) a quasilattice model is invoked which is based on the Ice VII structure and the density and isothermal compressibility of water are computed using the values of w calculated in approximation A. A final approximation (C) is based on the Ice Ic structure. In this approximation the temperature and pressure dependence of self-diffusion, viscosity, and nuclear relaxation times are evaluated. The agreement of the model with experiment is good and only a few parameters enter into the calculation, and these have magnitudes that are physically reasonable. Results of molecular dynamics calculations on water obtained by Rahman are presented which are interpreted to show that molecular rotation in water occurs in rather large excursions of relatively short time duration. For times between the large angular reorientations, librational motions occur which do not result in a large amount of net molecular reorientation. It is proposed that the large amplitude reorientations result from hard molecular collisions. These results confirm the conclusions of earlier work on other liquids. The anisotropy of the rotational correlation time of rank 2 (τ2) in an asymmetric top molecule is derived based on the finite step rotation hypothesis. Available experimental values of τ2 for liquid water are summarized and compared with the results of the model.

Chloride and bromide complexes of zinc(II) and mercury(II) in aqueous ammonium nitrate melts

The stability constants of species HgCl+, HgCl2, in aqueous melts of NH4NO3,xH2O (x= 2–5), and ZnCl+, ZnCl2, ZnBr+, ZnBr2(x= 1–3) have been determined at 55–85 °C from e.m.f. measurements of suitable concentration cells. The results for HgII chlorides are essentially in agreement with a quasi-lattice model of aqueous melts, but the zinc halide species behave anomalously: the chloride complexes are more stable than bromide complexes, and the first consecutive stability constants for ZnCl+ and ZnBr+ increase with temperature, in contrast to the behaviour of other divalent metal halides.

Thermodynamic measurements by electrochemical methods in molten AgCl-LiNO 3-NaNO 3 mixtures

Silver nitrate activities in silver chloride-saturated molten lithium nitrate-sodium nitrate mixtures, between 320 and 410°C, were found to be in good agreement with a quasi-lattice model. Silver chloride solubilities in molten, sodium nitrate lead to the determination of Ag + -Cl − association constants in this melt with a pair formation energy of −4.8±0.1 kcal mol −1 , a constant between 320°C and 410°C, in agreement with the value of Hill et al. 6 , Z being taken as 5. Results in molten lithium nitrate-containing mixtures lead to an estimate of S LiNO 3 0 (298.15)=21.0 cal mol −1 K −1 , and hint at an excess entropy of expression −2.6 x LiCl x NaCl (cal mol −1 K −1 ) in fused (Li-Na)Cl mixtures.

Application of the quasilattice model to association in dilute reciprocal molten salt mixtures. System silver sulfate-potassium nitrate

Application of the quasilattice model to association in dilute reciprocal molten salt mixtures. System silver sulfate-potassium nitrate

Self-diffusion and rotational correlation times in liquid acetylene

Coefficients of self-diffusion have been measured in liquid C2D2; the data are represented by D = (6.37 ± 1.65) × 10−3 exp [− (1.96 ± 0.11)/R T] cm2 sec−1. Deuteron spin-lattice relaxation time data are represented by T1 = (4.04 ± 0.57) × 101 exp [− (1.26 ± 0.08)/R T] sec. The diffusion coefficient data are interpreted by means of a quasilattice model for self-diffusion which yields a pre-exponential factor of 5.2 × 10−3 cm2 sec−1. Rotational correlation times are computed from the T1 data and interpreted in terms of the quasilattice random flight and the dynamically coherent rotation models for molecular rotation. Both models give reasonably good agreement with experiment.

Self-diffusion in liquid ammonia and deuteroammonia

Coefficients of self-diffusion have been measured by the spin-echo technique for neat NH3 and ND3 from 200 to 298°K. The data are well represented by D=(4.5± 0.2)× 10−3exp [−(2.07± 0.02)/RT] for NH3 and by D=(6.0± 0.3)× 10−3exp [−(2.31± 0.02)/RT] for ND3. The difference in activation energy for self-diffusion between NH3 and ND3 is shown to be consistent with the viscosity measurements of Hutchison and O'Reilly. These results are interpreted by means of a quasilattice model for self-diffusion in the liquid state. Values of the work required to create a molecular vacancy are evaluated from liquid density, isothermal compressibility and the scaled particle theory. The quasilattice model yields pre-exponential factors for self-diffusion that are in reasonable agreement with experiment.

Ion association in molten salts. The silver(I)-fluoride association in molten alkali nitrates

Summary The association energy between silver and chromate ions in molten alkali nitrates has been determined from e.m.f. measurements. The results agree with the predictions of the quasi-lattice model for ternary and quaternary reciprocal systems.

Solubility of silver chloride and silver bromide and their complexes in anhydrous calcium nitrate–potassium nitrate (1/1·9) melt

The solubility of silver chloride and bromide as a function of the corresponding halide concentration has been measured in molten Ca(NO3)2,1·925KNO3, in the temperature range 160–200 °C. by use of 110Ag as radioactive tracer. The solubility products and the consecutive stability constants for metal halide complex species were determined and the ΔG°, ΔH°, and ΔS° values of the corresponding equilibria evaluated. The results are compared with data obtained in other nitrate melts and discussed in terms of a quasi-lattice model for reciprocal molten salt systems.

Molecular Rotation in Liquids. Conditional Fast Rotational Diffusion

The theory of finite step rotational Brownian motion is generalized to anisotropic rotators. It is assumed that fast rotational diffusion will occur with the event of a ``hard'' collision between molecules. An expression for the rotational correlation time τ2 is given which is anisotropic and depends on the orientation of the z principal axis of the quadrupolar or dipolar interaction with respect to the principal axes of the rotational diffusion tensor. A general expression for the product of the spin-rotational correlation time (τ1) and τ2 is given. The quasilattice random flight model is generalized with the aid of an expression for the collision frequency given by Einwohner and Alder. The microcanonical conditional rotation model of Atkins et al. is reformulated to the case of rotation upon a hard collision.

Ion association in molten salts. The silver(I)-sulphate and silver(I)-molybdate associations in molten alkali nitrates

Summary The association energy between silver(I) and sulphate ions and between silver(I) and molybdate ions in molten alkali nitrates has been determined from e.m.f. measurements. The results agree with the predictions of the quasi-lattice model for ternary and quaternary reciprocal systems.

Ion association in molten salts. The silver(I)-sulphate and silver(I)-molybdate associations in molten alkali nitrates

The association energy between silver(I) and sulphate ions and between silver(I) and molybdate ions in molten alkali nitrates has been determined from e.m.f. measurements. The results agree with the predictions of the quasi-lattice model for ternary and quaternary reciprocal systems.

Self-Diffusion Coefficients and Rotational Correlation Times in Polar Liquids. III. Toluene

The self-diffusion coefficient of liquid toluene has been measured from 175 to 380°K and is represented by (4.5± 0.6) × 10−3 × Exp[−(3.12± 0.10) / Rt] Cm2Sec−1. Relaxation time data of Woessner and Snowden and the pressure dependence of the ring proton relaxation rates of Parkhurst, Lee, and Jonas are interpreted by means of the quasilattice random flight model of liquids. Root-mean-square angles of reorientation are calculated for the ring and methyl protons from a hindered rotation model of liquid state reorientation. The pre-exponential factor for self-diffusion is calculated to be 2.9 × 10−3 cm2sec−1 from the quasilattice model for the self-diffusion coefficient. Volumes of activation for self-diffusion and the intramolecular relaxation rate are compared with experimental values. It is demonstrated that the microviscosity model of Gierer and Wirtz, which is often invoked to explain the magnitude of rotational correlation times, does not apply to most liquids.