Ro-vibrating energy states of a diatomic molecule in an empirical potential

An approximate analytical solution of the Schrödinger equation is obtained to represent the rotational–vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrödinger equation for an empirical potential (EP) V _±(r) = D _e {1 ? (?/δ)[coth (ηr)]^±1/1 ? (?/δ)}² are determined by means of a mathematical method so-called the Nikiforov–Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H₂ and Ar₂.     

Room Temperature Ionic Liquids: Their Cohesive Energies,Solubility Parameters and Solubilities in Them

The cohesive energies of room temperature ionic liquids, RTILs, at the reference temperature T _ref = 298.15 K have been obtained from their molar enthalpies of vaporization. They are ce(298) = ?_v H°(298) ? 298.15R, on regarding the vapors as single ion-paired molecules. The cohesive energy densities, ced = ce/V = δ _H ² are the squares of the (Hildebrand) solubility parameters of the RTIL, which are presented for many RTILs. The solubilities of a variety of solutes in RTILs are discussed in relation to the solubility parameters. It turned out that the δ _H values of RTILs, obtained from the enthalpies of vaporization, may be used for empirical correlations, but are not able to predict the solubilities of solutes in RTILs.     

Modelling of proton and metal exchange in the alginate biopolymer

Acid–base behaviour of a commercial sodium alginate extracted from brown seaweed (Macrocystis pyrifera) has been investigated at different ionic strengths (0.1≤I/mol l^?1≤1.0) and in different supporting electrolytes (Et₄NI, NaCl, KCl, LiCl, NaCl+MgCl₂), with the aim of examining the influence of ionic medium on the proton-binding capacity and of quantifying the strength of interaction with light metal ions in the perspective of speciation studies in natural aqueous systems. Potentiometric ([H⁺]-glass electrode) and titration calorimetric data were expressed as a function of the dissociation degree (α) using different models (Henderson–Hasselbalch modified, Högfeldt three parameters and linear equations). The dependence on ionic strength of the protonation constants was taken into account by a modified specific interaction theory model. Differences among different media were explained in terms of the interaction between polyanion and metal cations of the supporting electrolytes. Quantitative information on the proton-binding capacity, together with the stabilities of different species formed, is reported. Protonation thermodynamic parameters, at α=0.5, are log K ^H=3.686±0.005, ΔG ⁰=?21.04±0.03 kJ mol^?1, ΔH ⁰=4.8±0.2 kJ mol^?1 and TΔS ⁰=35.7±0.3 kJ mol^?1, at infinite dilution. Protonation enthalpies indicate that the main contribution to proton binding arises from the entropy term. A strict correlation between ΔG and TΔS was found, TΔS=?9.5–1.73 ΔG. Results are reported in light of building up a chemical complexation model of general validity to explain the binding ability of naturally occurring polycarboxylate polymers and biopolymers. Speciation profiles of alginate in the presence of sodium and magnesium ions, naturally occurring cations in natural waters, are also reported.     

A family of four-step trigonometrically-fitted methods and its application to the schrödinger equation

In this article we present a singularly almost P-stable exponentially-fitted four-step method for the approximate solution of the one-dimensional Schrödinger equation. More specifically we present a method that is singularly almost P-stable (a concept later introduced in this article) and also integrates exactly any linear combination of the functions {1, x, exp ( ±I v x) , x exp ( ±I v x) , x ² exp ( ±I v x)}. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the approximate solution of resonance problem of the radial Schrödinger equation.     

Synthesis,crystal structure,and thermodynamics of a high-nitrogen copper complex with <Emphasis Type="Italic">N</Emphasis>, <Emphasis Type="Italic">N</Emphasis>-bis-(1(2)H-tetrazol-5-yl) amine

A new high-nitrogen complex [Cu(Hbta)₂]·4H₂O (H₂bta = N,N-bis-(1(2)H-tetrazol-5-yl) amine) was synthesized and characterized by elemental analysis, single crystal X-ray diffraction and thermogravimetric analyses. X-ray structural analyses revealed that the crystal was monoclinic, space group P2(1)/c with lattice parameters a = 14.695(3) Å, b = 6.975(2) Å, c = 18.807(3) Å, β = 126.603(1)°, Z = 4, D _c = 1.888 g cm^?3, and F(000) = 892. The complex exhibits a 3D supermolecular structure which is built up from 1D zigzag chains. The enthalpy change of the reaction of formation for the complex was determined by an RD496–III microcalorimeter at 25 °C with the value of ?47.905 ± 0.021 kJ mol^?1. In addition, the thermodynamics of the reaction of formation of the complex was investigated and the fundamental parameters k, E, n, \( \Updelta S_{ \ne }^{{{\uptheta}}} \), \( \Updelta H_{ \ne }^{{{\uptheta}}} \), and \( \Updelta G_{ \ne }^{{{\uptheta}}} \) were obtained. The effects of the complex on the thermal decomposition behaviors of the main component of solid propellant (HMX and RDX) indicated that the complex possessed good performance for HMX and RDX.     

X-ray and computational structural study of neutral <Emphasis Type="Italic">bis</Emphasis>(<Emphasis Type="Italic">N,N,N</Emphasis>′,<Emphasis Type="Italic">N</Emphasis>′-tetramethylthiophosphoramidoyl)-methylamine

The structure of bis(N,N,N′,N′-tetramethylthiophosphoramidoyl)-methylamine 1 has been determined by single-crystal X-ray diffraction. The compound 1 crystallizes in the monoclinic system, with a space group P2₁/c, a = 11.836(2) Å, b = 11.659(2) Å, c = 12.796(5) Å and β = 95.28(3)°, V = 1758.3(5) Å³ and Z = 4. The X-ray crystallographic data have been assessed by semi-empirical and ab-initio density functional theory and by Hartree–Fock molecular orbital methods. A comparative study of the results of the different methods is given.     

Molecular structure and conformation of nitrobenzene reinvestigated by combined analysis of gas-phase electron diffraction,rotational constants,and theoretical calculations

The molecular structure and conformation of nitrobenzene has been reinvestigated by gas-phase electron diffraction (GED), combined analysis of GED and microwave (MW) spectroscopic data, and quantum chemical calculations. The equilibrium r _e structure of nitrobenzene was determined by a joint analysis of the GED data and rotational constants taken from the literature. The necessary anharmonic vibrational corrections to the internuclear distances (r _e ? r _a) and to rotational constants (B _e ⁽ⁱ⁾  ? B ₀ ⁽ⁱ⁾ ) were calculated from the B3LYP/cc-pVTZ quadratic and cubic force fields. A combined analysis of GED and MW data led to following structural parameters (r _e) of planar nitrobenzene (the total estimated uncertainties are in parentheses): r(C–C)_av = 1.391(3) Å, r(C–N) = 1.468(4) Å, r(N–O) = 1.223(2) Å, r(C–H)_av = 1.071(3) Å, \({\angle}\)C2–C1–C6 = 123.5(6)°, \({\angle}\)C1–C2–C3 = 117.8(3)°, \({\angle}\)C2–C3–C4 = 120.3(3)°, \({\angle}\)C3–C4–C5 = 120.5(6)°, \({\angle}\)C–C–N = 118.2(3)°, \({\angle}\)C–N–O = 117.9(2)°, \({\angle}\)O–N–O = 124.2(4)°, \({\angle}\)(C–C–H)_av = 120.6(20)°. These structural parameters reproduce the experimental B ₀ ⁽ⁱ⁾ values within 0.05 MHz. The experimental results are in good agreement with the theoretical calculations. The barrier height to internal rotation of nitro group, 4.1±1.0 kcal/mol, was estimated from the GED analysis using a dynamic model. The equilibrium structure was also calculated using the experimental rotational constants for nitrobenzene isotopomers and theoretical rotation–vibration interaction constants.     

Structure,bioactivity and theoretical study of 1-cyano-<Emphasis Type="Italic">N</Emphasis>-p-tolylcyclo-propanecarboxamide

A novel cyclopropane derivative, 1-cyano-N-p-tolylcyclopropanecarboxamide (C₁₂H₁₂N₂O, Mr = 200.24) was synthesized and its structure was studied by X-ray diffraction, FTIR, ¹H and ¹³C NMR spectrum and MS. The crystals are monoclinic, space group P2_1/c with a = 7.109 (4), b = 13.758 (7), c = 11.505 (6) Å, α = 90.00, β = 102.731 (8), γ = 90.00 °, V = 1097.6 (9) ų, Z = 4, F(000) = 312, D _c  = 1.212 g/cm³, μ = 0.0800 mm^?1, the final R = 0.0490 and wR = 0.1480 for 1,375 observed reflections with I > 2σ(I). A total of 6,109 reflections were collected, of which 2,290 were independent (R _int = 0.0290). Theoretical calculation of the title compound was carried out with HF/6-31G (d,p), B3LYP/6-31G (d,p), MP2/6-31G (d,p). The full geometry optimization was carried out using 6-31G(d,p) basis set, and the frontier orbital energy. Atomic net charges were discussed, and the structure-activity relationship was also studied. The preliminary biological test showed that the synthesized compound is bioactive against the KARI of Escherichia coli.     

Synthesis,structure and electrochemical properties of some thiosemicarbazone complexes of iridium

Reaction of thiosemicarbazones of salicylaldehyde and 2-hydroxyacetophenone (H₂L¹ and H₂L²) with [Ir(PPh₃)₃Cl] affords complexes of type [Ir(PPh₃)₂(L)(H)] (L = L¹ or L²) in ethanol. A similar reaction carried out in toluene affords the [Ir(PPh₃)₂(L)(H)] complexes along with complexes of type [Ir(PPh₃)₂(L)Cl], where a chloride is coordinated to iridium instead of the hydride. The structure of the [Ir(PPh₃)₂(L²)(H)] and [Ir(PPh₃)₂(L²)Cl] complexes has been determined by X-ray crystallography. Crystal data for [Ir(PPh₃)₂(L²)(H)]: space group, P2₁/c; crystal system, monoclinic; a=12.110(2) Å, b=17.983(4) Å, c=18.437(4) Å, β=103.42(3)°, Z=4; R ₁=0.0591, wR ₂=0.1107. Crystal data for [Ir(PPh₃)₂(L²)Cl]: space group, P2₁/c; crystal system, monoclinic; a=17.9374(11) Å, b=19.2570(10) Å, c=24.9135(16) Å, β=108.145(5)°, Z=4; R ₁=0.0463, wR ₂=0.0901. In all the complexes the thiosemicarbazones are coordinated to the metal center as dianionic tridentate O, N, S-donors and the two triphenylphosphines are trans. The complexes are diamagnetic (low-spin d? ⁶, S=0) and show intense MLCT transitions in the visible region. Cyclic voltammetry on all the [Ir(PPh₃)₂(L)(H)] and [Ir(PPh₃)₂(L)Cl] complexes shows a quasi-reversible Ir(III)–Ir(IV) oxidation within 0.55–0.78 V vs. SCE followed by an irreversible oxidation of the thiosemicarbazone within 0.91–1.27 V vs. SCE. An irreversible reduction of the thiosemicarbazone is also observed within ?1.10 to ?1.23 V vs. SCE.     

A novel angle-dependent potential and its exact solution

The quantum mechanics of a diatomic molecule in a noncentral potential of the type V (r) = V _θ (θ)/r ² + V _r (r) are investigated analytically. The θ-dependent part of the relevant potential is suggested for the first time as a novel angle-dependent (NAD) potential \({V_{\theta}(\theta)=\frac{\hbar^2}{2\mu}\left(\frac{\gamma +\beta \sin^2\theta +\alpha \sin^4 \theta}{\sin^2\theta \cos^2\theta}\right)}\) and the radial part is selected as the Coulomb potential or the harmonic oscillator potential, i.e., V _r (r) =  ? H/r or V _r (r) = Kr ², respectively. Exact solutions are obtained in the Schrödinger picture by means of a mathematical method named the Nikiforov–Uvarov (NU). The effect of the angle-dependent part on the solution of the radial part is discussed in several values of the NAD potential’s parameters as well as different values of usual quantum numbers.     

New hybrids of clozapine and haloperidol and their isosteric analogues: synthesis,X-ray crystallography,conformational analysis and preliminary pharmacological evaluation

Schizophrenia is a debilitating mental disorder which affects approximately 1% of the world’s population. Clozapine is an atypical antipsychotic showing unmatched effectiveness in the control of treatment-resistant schizophrenia. Unlike typical antipsychotics, clozapine does not induce extrapyramidal side effects (EPS), tardive dyskinesia or elevate prolactin levels. However, clozapine can induce a potentially fatal blood disorder, agranulocytosis, in 1–2% of patients, severely limiting its clinical use. The model for antipsychotic activity under investigation is based on obtaining a clozapine-like profile with preferential dopamine D₄ and serotonin 5-HT_2A receptor affinity. Profiled herein are three unique members of a series of prospective antipsychotic agents. Compound (I) originated from the structural hybridization of the commercial therapeutics, clozapine and haloperidol, whilst compounds (II) and (III) possess an alternative tricyclic nucleus derived from JL13; a clozapine-like atypical antipsychotic developed by Liégeois et al. These compounds have been synthesized and characterized by means of elemental analysis, IR, ¹H and ¹³C-NMR spectroscopy, MS and X-ray diffraction. Compound (I) crystallizes in space group P(?1) with a = 10.5032(1), b = 10.6261(2), c = 12.6214(3) Å, α = 81.432(1)°, β = 83.292(1)°, γ = 61.604(1)°, Z = 2, V = 1223.62(4) Å³, C₂₈H₂₉ClN₄O, M _r = 473.00, D _c = 1.284 Mg/m³, μ = 0.185 mm^?1, F(000) = 500, R = 0.0506 and wR = 0.1304. Compound (II) crystallizes in the monoclinic space group P2₁/c with a = 10.8212(2), b = 9.3592(2), c = 22.9494(5) Å, β = 106.471(1)°, Z = 4, V = 2228.88(8) Å³, C₂₅H₂₅ClN₄O₂, M _r = 448.94, D _c = 1.338 Mg/m³, μ = 0.202 mm^?1, F(000) = 944, R = 0.0529 and wR = 0.1129. Compound (III) crystallizes in the monoclinic space group P2₁/c with a = 10.5174(2), b = 9.3112(2), c = 24.2949(5) Å, β = 98.666(1)°, Z = 4, V = 2352.03(8) Å³, C₂₅H₂₄Cl₂N₄O₂, M _r = 483.38, D _c = 1.365 Mg/m³, μ = 0.306 mm^?1, F(000) = 1008, R = 0.0478 and wR = 0.1067. The solid state conformations of (I), (II) and (III) exhibit the characteristic V-shaped buckled nature of the respective dibenzodiazepine and pyridobenzoxazepine nuclei with the central seven-membered heterocycle in a boat conformation. The molecules of (I) form a head-to-tail dimeric motif stabilized by hydrogen bonding. The results of a conformational analysis of compounds (I)–(III) investigating the effect of environment (in vacuo and aqueous solution) are presented. These analogues were tested for in vitro affinity for the dopamine D₄ and serotonin 5-HT_2A receptors and their comparative receptor binding profiles to clozapine and JL13 are reported.     

A New Sandwich Polyoxometalate Constructed from a Zn<Stack><Subscript>6</Subscript><Superscript>12+</Superscript></Stack> Hexagon Cluster Sandwiched by Two B-α-[BiW<Subscript>9</Subscript>O<Subscript>33</Subscript>]<Superscript>9−</Superscript>

A new sandwich polyoxometalate Na₄Zn₂[Zn₂(H₂O)₁₀(ZnCl)₆(B-α- BiW₉O₃₃)₂] · 40.5H₂O (1) has been obtained in aqueous solution and characterized by IR, UV, element analysis, TG and single-crystal X-ray analysis. Polyoxoanion 1 is composed of a Zn ₆ ¹²⁺ hexagon sandwiched by two [BiW₉O₃₃]^9? units, which is firstly observed in tungstobismutate. The crystal data for compound 1: Triclinic, space group P–1, a = 15.426(3) Å, b = 15.467(3) Å, c = 15.526(3) Å, α = 74.24(3)°, β = 64.37(3)°, γ = 60.73(3)°, V = 2905.3(1) ų, Z = 1.     

Two New One-Dimensional Chain-Like Compounds Constructed from the Sandwich-Type Polyoxotungstate Clusters

Two new one-dimensional chain-like compounds, K₄Na₄[Mn₂(H₂O)₈Mn₄(H₂O)₂(GeW₉O₃₄)₂] · 20.5H₂O (1) and K₂Na₄Cu₂(H₂O)₁₂[Cu(H₂O)₂Cu₄(H₂O)₂(SiW₉O₃₄)₂] · 15H₂O (2), constructed from the sandwich-type clusters, have been obtained by the routine synthetic reactions in aqueous solutions, and their structures were determined by X-ray single crystal diffraction analysis. The crystal data is following: for 1, space group, monoclinic, P _21/n, a = 16.693(3) Å, b = 14.935(3) Å, c = 20.090(4) Å, β = 92.23(3)°, V = 5004.7(17) ų, Z = 2; For 2, space group, triclinic, P _?1, a = 11.744(2) Å, b = 13.415(3) Å, c = 17.609(4) Å, α = 73.08(3)°, β = 82.68(3)°, γ = 65.18(3)°, V = 2409.1(8) ų, Z = 1. The crystal structure of 1 shows a 1D ladder-like chain, built up of the sandwich anions [Mn₄(H₂O)₂(GeW₉O₃₄)₂]^12? and the Mn²⁺ ions. Compound 2 is a polymeric chain, composed of the Cu-substituted sandwich-type anions [Cu₄(H₂O)₂(SiW₉O₃₄)₂]^12? linked by the Cu(H₂O)₄ clusters. These extended materials based on the sandwich-type polyoxoanions are rarely reported in the POM chemistry.     

Dye removal using 4A-zeolite/polyvinyl alcohol mixed matrix membrane adsorbents: preparation,characterization, adsorption,kinetics, and thermodynamics

In pursuit of improving performance of the methylene blue adsorption process, the potential of a novel 4A-zeolite/polyvinyl alcohol (PVA) membrane adsorbent was investigated. Adding 4A-zeolite particles to the PVA membrane adsorbent provided an effective structure for the adsorptive membrane in dye removal processes. Effect of zeolite content was also studied via synthesis of different mixed matrix membrane adsorbents (MMMAs) with 5, 10, 15, and 20 wt% 4A-zeolite content. Morphology of MMMAs was analyzed by scanning electron microscope and the intermolecular interactions were determined by Fourier transform infrared spectroscopy. X-ray diffraction was performed to determine the crystal structure of MMMAs. For the sake of finding optimum condition, the adsorption capacity was examined at various operating parameters, such as contact time, temperature, pH, and initial concentration. The maximum value of the adsorption capacity (q _e) of 41.08 mg g^?1 and the highest removal efficiency of 87.41 % were obtained by applying 20 wt% loading of 4A-zeolite. The experimental data were fitted well with the Freundlich adsorption isotherm model (R ² = 0.9917) compared with the Langmuir (R ² = 0.9489) and the Tempkin (R ² = 0.8886) adsorption isotherm models, and the adsorption kinetic data verified the best fitting with the pseudo-second-order model (R ² = 0.9999). The estimated data for Gibb’s free energy (ΔG°) showed that the adsorption process is spontaneous at lower temperature values and non-spontaneous at higher temperature values. Other evaluated thermodynamic parameters such as changing in enthalpy (ΔH°) and entropy (ΔS°) revealed that the adsorption process is exothermic with an increase in orderliness at the solid/solution interface.     

Synthesis of water soluble metalloporphyrin-cored amphiphilic star block copolymer photocatalysts for an environmental application

Two series of water-soluble metalloporphyrin-cored amphiphilic star block copolymers were synthesized by controlled radical polymerizations such as atom transfer radical polymerization (ATRP) and reversible addition fragmentation chain transfer (RAFT), which gave eight amphiphilic block copolymer arm chains consisting of poly(n-butyl acrylate-b-poly(ethylene glycol) methyl ether methacylate) (PnBA-b-PEGMEMA, M_n,GPC = 78,000, M_w/M_n = 1.2, 70 wt% of PPEGMEMA) and poly(styrene-b-2-dimethylamino ethyl acrylate) (PS-b-PDMAEA, M_n,GPC = 83,000, M_w/M_n = 1.2, 67 wt% of PDMAEA), yielding porphyrin(Pd)-(PnBA-b-PPEGMEMA)₈ and porphyrin(Pd)-(PS-b-PDMAEA)₈, respectively. Obtained metalloporphyrin polymer photocatalysts were homogeneously solubilized in water to apply to the removal of chlorophenols in water, and was distinguished from conventional water-insoluble small molecular metalloporphyrin photocatalysts. Notably, we found that the water-soluble star block copolymers with hydrophobic–hydrophilic core–shell structures more effectively decomposed the chlorophenol, 2,4,6-trichlorophenol (2,4,6-TCP), in water under visible light irradiation (k = 1.39 h^?1, t_1/2 = 0.5 h) in comparison to the corresponding water-soluble star homopolymer, because the hydrophobic core near the metalloporphyrin effectively captured and decomposed the hydrophobic chlorophenols in water.     

Synthesis,crystal structure of new linear trinuclear isovalence Co(II)([Co<Subscript>3</Subscript>(H–L)<Subscript>2</Subscript>(L)<Subscript>2</Subscript>]), and visualizing intermolecular interactions with Hirshfeld surface method

S-allyl-β-N-[(2-hydroxyphenyl)methylene]hyrazinecarbodithioate) (1, H₂L), the Schiff base of dithiocarbazate with unsaturated allyl substitution, can act as a new tridentate SNO ligand H₂–L and react with cobalt(II) nitrate hexahydrate to form the novel linear trinuclear isovalence Co(II) complex, [Co₃(H–L)₂(L)₂] 2C₂H₅OH (2). The compounds were characterized by elemental analysis, infrared, and ultraviolet spectroscopy. Compound 2 was also characterized by single-crystal X-ray analysis and crystallizes in the orthorhombic space group, Pbcn, with a = 30.643(1) Å, b = 9.118(4) Å, c = 19.017(7) Å, α = β = γ = 90°, V = 5312.95 Å³, Z = 4, and R ₁ = 0.0790, (wR ₂) = 0.1223. The six-coordinate central Co(II) atom is bonded to two deprotonated metal-containing ligands. The terminal Co(II) atoms are in a square planar SNON four-coordinate environment and connected to the central Co(II) by N-atoms from the ligand backbone. For quantifying the intermolecular interactions in crystal lattice, the new d _norm surface and the breakdown of fingerprint plots have been used for visualizing and exploring the compound 2.     

Synthesis and characterization of a new monophosphate (C<Subscript>6</Subscript>H<Subscript>16</Subscript>N<Subscript>2</Subscript>)(H<Subscript>2</Subscript>PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

Chemical preparation, crystal structure, and NMR spectroscopy of a new trans-2,5-dimethylpiperazinium monophosphate are given. This new compound crystallizes in the triclinic system, with the space group P-1 and the following parameters: a = 6.5033(3), b = 7.6942(4), c = 8.1473(5) Å, α = 114.997(3), β = 92.341(3), γ = 113.136(3), V = 329.14(3) ų, Z = 1, and D_x = 1.565 g cm^?3. The crystal structure has been determined and refined to R = 0.030 and R _w(F ²) = 0.032 using 1558 independent reflections. The structure can be described as infinite [H₂PO₄] _n ^n? chains with (C₆H₁₆N₂)²⁺ organic cations anchored between adjacent polyanions to form columns of anions and cations running along the b axis. This compound has also been investigated by IR, thermal, and solid-state, ¹³C and ³¹P MAS NMR spectroscopies and Ab initio calculations.     

Why is ‘amount of substance’ so poorly understood? The mysterious Avogadro constant is the culprit!

The base quantity ‘amount of substance’ is poorly understood and the name and symbol usually avoided. This is because of its formal interpretation as the number of entities multiplied by the reciprocal of the mysterious Avogadro constant, N _A. If X signifies the kind of entities involved, the number of entities in a sample, N(X), is easily comprehended, and if m _av(X) is the sample-average entity mass, the total mass, m(X) = N(X)m _av(X)—an aggregate of N(X) average entity masses—is also conceptually straightforward. However, the corresponding amount of substance, n(X) = N(X)(1/N _A)—an aggregate of N(X) ‘reciprocal Avogadro constants’—is incomprehensible unless some physical meaning can be attached to 1/N _A. By contrast, the base unit, mole, is thought of by chemists as an aggregate of a particular number of entities: mol = \( {\mathcal N}_{\rm{Avo}} \) ent, where \( {\mathcal N}_{\rm{Avo}} \) is the Avogadro number (equal to g/Da) and ent represents one entity. It makes sense, therefore, to interpret amount of substance as an aggregate of a general number of entities: n(X) = N(X) ent—an easily grasped concept. A ‘reciprocal Avogadro constant’ is thus seen to actually be exactly one entity. One mole then corresponds to setting N(X) = \( {\mathcal N}_{\rm{Avo}} \), for which the total mass is the relative entity mass in grams—conforming to the original mole concept.     

Energetics of lead(II), cadmium(II) and zinc(II) complexes with amino acids

The molar heat capacity and the standard (p ⁰ = 0.1 MPa) molar enthalpies of formation of the crystalline of bis(glycinate)lead(II), Pb(gly)₂; bis(dl-alaninate)lead(II), Pb(dl-ala)₂; bis(dl-valinate)lead(II), Pb(dl-val)₂; bis(dl-valinate)cadmium(II), Cd(dl-val)₂ and bis(dl-valinate)zinc(II), Zn(dl-val)₂, were determined, at T = 298.15 K, by differential scanning calorimetry, and high precision solution-reaction calorimetry, respectively. The standard molar enthalpies of formation of the complexes in the gaseous state, the mean molar metal–ligand dissociation enthalpies, M(II)–amino acid, \( \langle D_{\text{m}} \rangle \)(M–L), were derived and compared with analogous copper(II)–ligand and nickel(II)–ligand.θθ

M(II)–amino acid	\( \Updelta_{\text{f}} H_{\text{m}}^{\text{o}} \)(cr)/kJ mol?1
Bis(glycinate)lead(II), Pb(gly)2	?998.9 ± 1.9
Bis(dl-alaninate)lead(II), Pb(ala)2	?1048.7 ± 1.8
Bis(dl-valinate)lead(II), Pb(val)2	?1166.3 ± 2.5
Bis(dl-valinate)cadmium(II), Cd(val)2	?1243.7 ± 2.7
Bis(dl-valinate)zinc(II), Zn(val)2	?1306.1 ± 2.3