A Simplified Mathematical Model for Calculating the Lattice Energies of Binary Group I and II Ionic Compounds: Using Solver to Estimate the Empirical Constants

Carter, Alan

doi:10.1021/ed077p1081

Cited by 3 publications

(5 citation statements)

References 6 publications

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“…where C is the acyl ascorbate concentration at time t; C 0 is the initial ascorbate concentration; k is the rate constant, the reverse of which is called the scale constant; and n is the shape constant. The kinetic parameters, k and n, were evaluated by fitting the experimental results by nonlinear regression using the Solver of Microsoft Excel for Windows (Microsoft Corp., Redmond, Wash., U.S.A.) (Harris 1998;De Levie 1999;Carter 2000) or the Origin Ver. 6.1 (Microcal Software, Inc., Northampton, Mass., U.S.A.).…”

Section: E: Food Engineering and Physical Propertiesmentioning

confidence: 99%

Stability of Saturated Acyl L-Ascorbates in Aqueous Solution

Kuwabara

Watanabe

Adachi

et al. 2005

Journal of Food Science

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acid, which was formed through the hydrolysis of the ester bond in the ascorbate, was measured at pH decanoic acid, which was formed through the hydrolysis of the ester bond in the ascorbate, was measured at pH decanoic acid, which was formed through the hydrolysis of the ester bond in the ascorbate, was measured at pH decanoic acid, which was formed through the hydrolysis of the ester bond in the ascorbate, was measured at pH decanoic acid, which was formed through the hydrolysis of the ester bond in the ascorbate, The initial concentration of the ascorbate scarcely affected its decomposition at pH 5 and 40 The initial concentration of the ascorbate scarcely affected its decomposition at pH 5 and 40 The initial concentration of the ascorbate scarcely affected its decomposition at pH 5 and 40 The initial concentration of the ascorbate scarcely affected its decomposition at pH 5 and 40 The initial concentration of the ascorbate scarcely affected its decomposition at pH 5 and 40°C. The decompo-°C.The decompo-°C.The decompo-°C.The decompo-°C. The decompositions of acyl ascorbates with acyl chain lengths of 6, 8, 10, and 12 were measured at pH 5 and at different sitions of acyl ascorbates with acyl chain lengths of 6, 8, 10, and 12 were measured at pH 5 and at different sitions of acyl ascorbates with acyl chain lengths of 6, 8, 10, and 12 were measured at pH 5 and at different sitions of acyl ascorbates with acyl chain lengths of 6, 8, 10, and 12 were measured at pH 5 and at different sitions of acyl ascorbates with acyl chain lengths of 6, 8, 10, and 12 were measured at pH 5 and at different temperatures. The temperature dependency of the rate constant for the decomposition of each ascorbate was temperatures. The temperature dependency of the rate constant for the decomposition of each ascorbate was temperatures. The temperature dependency of the rate constant for the decomposition of each ascorbate was temperatures. The temperature dependency of the rate constant for the decomposition of each ascorbate was temperatures. The temperature dependency of the rate constant for the decomposition of each ascorbate was analyzed by the Arrhenius equation, and it was shown that the enthalpy-entropy compensation held for the analyzed by the Arrhenius equation, and it was shown that the enthalpy-entropy compensation held for the analyzed by the Arrhenius equation, and it was shown that the enthalpy-entropy compensation held for the analyzed by the Arrhenius equation, and it was shown that the enthalpy-entropy compensation held for the analyzed by the Arrhenius equation, and it was shown that the enthalpy-entropy compensation held for the decomposition of the ascorbates. decomposition of the ascorbates. decomposition of the ascorbates. decomposition of the ascorbates. decomposition of the ascorbates. K K K K Keywor eywor eywor eywor eywords: acyl ascorbate ds: acyl ascorbate ds: acyl ascorbate ds: acyl ascorbate ds: acyl ascorbate, decomposition, , decomposition, , decomposition, , decomposition, , decomposition, W W W W Weibul...

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Section: E: Food Engineering and Physical Propertiesmentioning

confidence: 99%

Stability of Saturated Acyl L-Ascorbates in Aqueous Solution

Kuwabara

Watanabe

Adachi

et al. 2005

Journal of Food Science

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“…Table I the second and third columns show the lattice enthalpies calculated (a) adding the energies of Table II, a Δ H

_{°}^{italicL}

(∑) = ∑ E i − RT , and (b) from an optimal algorithm, where constants A , B , C , and D , in the equation, b Δ H

_{°}^{italicL}

(∑) = A ∑ n i z

_{2}^{italici}

(1 − B / R 0 )/ R 0 + C / R

_{6}^{0}

+ D , have been adjusted 15, 26. Throughout the fifth column of Table I, in italics, are shown the experimental lattice enthalpy values, Δ H

_{°}^{italicL}

( E ).…”

Section: Resultsmentioning

confidence: 99%

Model of the physical properties of halides with complete graph‐based indices

Pogliani¹

2004

Int J of Quantum Chemistry

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ABSTRACT:Complete graph-based molecular connectivity indices are used to model different theoretical and experimental properties of a class of 20 alkali halides, as well as a theoretical quantum property of a class of fluorides and chlorides. The experimental properties are the lattice enthalpy, the binding enthalpy, and the polarizability in three different media of the alkali halides. The experimental lattice and binding enthalpy are used as training set to evaluate the other sets of theoretical energies, with which the two enthalpies have, finally, been "reconstructed." The theoretical energies are Coulomb energy, polarization energy, van der Waals energy, repulsion energy, and zero-point energy. The lattice enthalpy descriptors are rather good descriptors of its constituent energies: Coulomb, van der Waals, repulsion, and zero-point. The descriptors of the binding enthalpies, instead, fail to model some of its constituent energies: Coulomb, polarization, van der Waals, and repulsion energies. All types of energies are described by basis molecular connectivity indices based on odd complete graph algorithms, which allow an optimal description of the "reconstructed" calculated enthalpies. A common description of the experimental lattice and binding enthalpies with a descriptor trained on the binding enthalpies alone has also been possible. The model of three sets of polarization values of the metal halides with a descriptor trained with one set of polarization values compares positively with a previous study on the polarization of organic compounds. The model of this property requires molecular connectivity basis indices based on a sequential complete graph algorithm. The model of the quantum theoretical property, the electron density at the bond critical point of a class of fluorides and chlorides, allows an interesting comparison with density functional theory calculations.

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“…The repulsive forces were treated in a similar manner. When further van der Waals forces are included by the term C͞R 0 6 and the zero-point energy by D, a generalized equation for the lattice energy is (18,19)…”

Section: Mx(s) Mx(g)mentioning

confidence: 99%

“…In a recent paper, Carter (18) has treated the constants A, B, C, and D in eq 15 as adjustable parameters and fitted this equation to the Born-Haber cycle lattice energies of the group I and II (except for beryllium) halides, oxides, and sulfides, which resulted in…”

Section: Mx(s) Mx(g)mentioning

confidence: 99%

“…The particular situation of this element is rooted in the fact that upon addition of an electron to form the hydride anion the number of electrons is doubled. This leads to strong screening of the nucleus with concomitant tremendous increase in the radius (1.48−1.73 Å, depending on the counter-atom; ref 18,30) on the basis of the relationship R = (n 2 ͞Z eff )a 0 , where n is the value of the valence level, Z eff is the effective nuclear charge on the valence level electron, and the term a 0 is a constant that represents the selection of units for the radius. Because of the closely associated high polarizability, the hydride radius is variable but is always more than twice as large as the bond length of the H 2 molecule.…”

Section: Covalent Bondingmentioning

confidence: 99%

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