Theoretical studies of electronic structure and structural properties of anhydrous alkali metal oxalates

The theoretical analysis of electronic structure and bonding properties of anhydrous alkali metal oxalates, based on the results of DFT FP-LAPW calculations, Bader’s QTAIM topological properties of electron density, Cioslowski and Mixon’s topological bond orders [reported in the first part of this paper by Kole?yński (doi:10.1007/s10973-013-3126-z)] and Brown’s Bond Valence Model calculations, carried out in the light of thermal decomposition pathway characteristic for these compounds are presented. The obtained results shed some additional light on the origins of the complex pathway observed during thermal decomposition process (two stage process, first the formation of respective carbonate and then decomposition to metal oxide and carbon dioxide). For all structures analyzed, strong similarities in electronic structure and bonding properties were found (ionic-covalent bonds in oxalate anion with C–C bond as the weakest one in entire structure and almost purely ionic between oxalate group and alkali metal cations), allowing us to propose the most probable pathway consisting of consecutive steps, leading to carbonate anion formation with simultaneous cationic sublattice relaxations, which results in relative ease of respective metal carbonate formation.     

Mild route to generate gaseous metal anions

Gaseous metal anions such as Na(-), K(-), Cs(-), and Ag(-) can be generated at ambient temperatures by the collision-induced dissociation of the anions of several dicarboxylic acid salts, including oxalate, maleate, fumarate, succinate, and glutamate salts. The formation of gaseous metal anions in this way is unprecedented because the metal is initially present in its cationic form. The mild process described here could facilitate novel applications of metal anions as selective reagents for gas-phase ion-molecule and ion-ion reactions. Ab initio calculations were used to describe the dissociation process for anions of the oxalate salts. The formation of alkalides occurs via production of a metal-carbon dioxide anion intermediate with a bidentate three-center two-electron bond to the metal. The metal atom acquires a partial negative charge in the intermediate structure.     

Study of sodium interaction with calcium nitrate and carbonate in alkali metal chloride melts by IR and Raman spectroscopy

In the IR and Raman spectra of molten eutectic mixtures of alkali metal chlorides with additions of calcium nitrate and carbonate (without the introduction of sodium), vibrations of NO₃⁻ and CO₃²⁻ groups of symmetry D _3h were detected. After the introduction of sodium metal into the melts of oxygen-containing salts in amounts equal to the stoichiometric content of oxygen-containing groups, the spectra did not show the characteristic frequencies of the NO₂⁻ group or CO₃²⁻ vibrations, which is evidence of the complete oxidation of the alkali metal accompanied by reduction of the nitrate and carbonate groups to nitrogen dioxide and carbon dioxide, respectively. The results of spectroscopic studies are presented.     

Conductivity Studies of Dilute Aqueous Solutions of Oxalic Acid and Neutral Oxalates of Sodium, Potassium, Cesium, and Ammonium from 5 to 35°C

Conductivity measurements of oxalic acid and neutral oxalates (disodium oxalate, dipotassium oxalate, dicesium, and diammonium oxalate) were performed on dilute aqueous solutions, c < 3 × 10^–3 mol-dm^–3, from 5 to 35°C. These data and those available from the literature were analyzed in terms of dissociation steps of oxalic acid, the Onsager conductivity equation for neutral oxalates, the Quint–Viallard conductivity equation for the acid, and the Debye–Hückel equation for activity coefficients, to give the limiting equivalent conductances of bioxalate anion ;(HC₂O₄ ^–) and oxalate anion (1/2C₂O₄ ^2–) and the corresponding dissociation constants K ₁ and K ₂.     

Effect of span 20 concentration on oxalic acid production from post-refining fatty acids by Aspergillus niger XP

Submerged fermentation experiments were carried out to study the stimulating effects of the surfactant Span 20 on the growth of Aspergillus niger XP mutant and oxalic acid production from the post-refining fatty acids. Span 20 concentration of 0.75 g dm⁻³ was found to be the most suitable for oxalic acid production from fatty acids. Using this dose and a fermentation medium containing 30 g dm⁻³ of post-refining fatty acids, the oxalic acid production, oxalate yield, and overall oxalate productivity were the highest. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Kinetics and mechanism of base hydrolysis of chromium(III) complexes with oxalates and quinolinic acid

Base hydrolysis of [Cr(ox)₂(quin)]³⁻ (where quin²⁻ is N,O-bonded 2,3-pyridinedicarboxylic acid dianion) causes successive ligand dissociation and leads to a formation of a mixture of oligomeric chromium(III) species, known as chromates(III). The reaction proceeds through [Cr(ox)(quin)(OH)₂]³⁻ and [Cr(quin)(OH)₄]³⁻ formation. Dissociation of oxalato ligands is preceded by the opening of the Cr-quin chelate-ring at the Cr–N bond. The kinetics of the chelate-ring opening and the first oxalate dissociation were studied spectrophotometrically, within the lower energy d–d band region at 0.4–1.0 M NaOH. The pseudo-first-order rate constants (k _obs0 and k _obs1) were calculated using SPECFIT software for an A → B → C reaction pattern. Additionally, kinetics of base hydrolysis of [Cr(ox)(quin)(OH)₂]³⁻ and cis-[Cr(ox)₂(OH)₂]³⁻ were studied. The determined pseudo-first-order rate constants were independent of [OH⁻]. A mechanism is postulated that the reactive intermediate with the one-end bonded quin ligand, [Cr(ox)₂(O-quin)(OH)]⁴⁻, formed in the first reaction stage, subsequently undergoes oxalates substitution. Kinetic parameters for the chelate-ring opening and the first oxalate dissociation were determined.     

Cluster phase chemistry: collisions of vibrationally excited cationic dicarboxylic acid clusters with water molecules initiate dissociation of cluster components

A homologous series of cationic gas-phase clusters of dicarboxylic acids (oxalic acid, malonic acid, succinic acid, glutaric acid, and adipic acid) generated via electrospray ionization (ESI) are investigated using collision-induced dissociation (CID). Singly charged cationic clusters with the composition (Na(+))(2n+1)(dicarboxylate(2-))(n), where n = 1-5, are observed as major gas-phase species. Significant abundances of singly charged sodiated hydrogen dicarboxylate clusters with the composition (Na(+))(2n)(dicarboxylate(2-))(n)(H+), where n = 1-6, are observed with oxalic acid, malonic acid, and succinic acid. Isolation of the clusters followed by CID results mainly in sequential loss of disodium dicarboxylate moieties for the clusters of succinic acid, glutaric acid, and adipic acid. However, the dimer of sodiated hydrogen succinate, all malonate clusters, and all oxalate clusters, with the exception of the dimer, exhibit complex chemical reactions initiated by the collision of vibrationally excited clusters with water molecules. Generally, water molecules serve as proton donors for reacting dicarboxylate anions in the cluster, initiating dissociation pathways such as the decomposition of the malonate ion to yield an acetate ion and CO(2). The reactivity of several mixed dicarboxylate clusters is also reported. For example, malonate anion is shown to be more reactive than oxalate anion for decarboxylation when both are present in a cluster. The energetics of several representative cluster phase reactions are evaluated using computational modeling. The present results for cationic clusters are compared and contrasted to earlier studies of anionic sodiated dicarboxylic acid clusters.     

The anion binding properties of neutral receptors bearing nitro group,phenanthroline or ruthenium(II) metal

A series of neutral cyclohexadiamine anion receptors containing nitro, phenanthroline or ruthenium(II) have been designed and synthesized. Their u.v.–vis spectroscopy investigations reveal that the receptor bearing nitro group displays the strongest affinities for F⁻, AcO⁻, H₂PO ₄ ⁻ and can be used as an efficient detection tool for the above anions. Results indicate that the anion affinities can be enhanced through appending nitro group and ruthenium(II) metal compared with phenanthroline moiety.     

Metal oxalates in paints: a Raman investigation on the relative reactivities of different pigments to oxalic acid solutions

One degradation phenomenon that occurs in artworks is the formation of metal oxalates on their surfaces. In order to gain insight into the inclination of pigments to produce oxalates, nine pigments including Na, Ca, Fe, Pb and Cu cations were selected to react with oxalic acid solutions at different concentrations (1 M, 0.1 M, 0.01 M and 0.005 M). Micro-Raman spectroscopy was used to detect the different reaction products. Pigments containing calcium (calcite, gypsum and Volterra gypsum) showed a high tendency to form weddellite as well as whewellite, especially at high acidic concentrations; among copper-based pigments (malachite, azurite, verdigris), the formation of moolooite was observed for high concentrations of acid and down to the lowest concentration (0.005 M) in the case of verdigris. Lead oxalate was detected on lead white. No iron oxalates were observed for hematite; the formation of calcium oxalate crystals was observed instead. Ultramarine blue reacted to produce elemental sulfur. According to the results obtained, calcite and verdigris showed the highest reactivity in oxalic acid environments, resulting in a high tendency to form calcium and copper oxalates, even at very low acidic concentrations; this behavior seems to arise from the high solubilities of these pigments in acidic environments.     

Cluster phase chemistry: gas-phase reactions of anionic sodium salts of dicarboxylic acid clusters with water molecules

A homologous series of anionic gas-phase clusters of dicarboxylic acids (oxalic acid, malonic acid, succinic acid, glutaric acid, and adipic acid) generated via electrospray ionization (ESI) are investigated using collision-induced dissociation (CID). Sodiated clusters with the composition (Na(+))(2)(n+1)(dicarboxylate(2-)(n+1) for singly charged anionic clusters, where n = 1-4, are observed as major gas-phase species. Isolation of the clusters followed by CID results mainly in sequential loss of disodium dicarboxylate moieties for the clusters of succinic acid, glutaric acid, and adipic acid (C4-C6). However, all oxalate (C2) and malonate (C3) clusters and dimers (n = 1) of succinate (C4) and glutarate (C5) exhibit more complex chemistry initiated by collision of the activated cluster with water molecules. For example, with water addition, malonate clusters dissociate to yield sodium acetate, carbon dioxide, and sodium hydroxide. More generally, water molecules serve as proton donors for reacting dicarboxylate anions in the cluster and introduce energetically favorable dissociation pathways not otherwise available. Density functional theory (DFT) calculations of the binding energy of the cluster correlate well with the cluster phase reactions of oxalate and malonate clusters. Clusters of larger dicarboxylate ions (C4-C6) are more weakly bound, facilitating the sequential loss of disodium dicarboxylate moieties. The more strongly bound small dicarboxylate anions (oxalate and malonate) preferentially react with water molecules rather than dissociate to lose disodium dicarboxylate monomers when collisionally activated. Implications of these results for the atmospheric aerosol chemistry of dicarboxylic acids are discussed.     

A study of Lux-Flood acid-base reactions in KBr melts at 800°C

The dissociation of CO₃²⁻ (pK = 2.4 ± 0.2) and precipitation of MgO (pL _MgO = 10.66 ± 0.1) in a KBr melt at 800°C were studied potentiometrically with the use of a Pt(O₂)|ZrO₂|(Y₂O₃) membrane oxygen electrode. The direct calibration of the electrochemical circuit allowed only the equilibrium concentration of O²⁻ (of strong bases) to be determined in the melt. The total concentration of oxygen-containing impurities, including CO₃²⁻ and CO₄²⁻ weak bases, can be found by the potentiometric titration of a sample of KBr by adding MgCl₂ (Mg²⁺), a strong Lux-Flood acid, which causes the decomposition of these oxygen-containing anions. This reaction can also be used to remove oxo anions from alkali metal halide melts.     

Structural peculiarities and the possibility of the existence of small water cluster anions (H2O) n − withn≤4

Structures of (H₂O) _n ⁻ anions withn≤4 were optimized at the UHF/4-31++G^** level and their stability was estimated at the MP2/4-31++G^** level. The trimer anion has a chain-like structure while the tetramer anion can exist either in a chain-like or a cyclic configuration. In the dimer anion and in the chain-like anions, the excess electron density is localized on the terminal water molecule, an acceptor of the H-bond proton. In the cyclic anion, it is uniformly distributed over the free hydrogen atoms. All considered anions have energy values higher than those of the corresponding neutral oligomers. The detachment of an electron from the anions should proceed with the liberation of energy. However, trimer and larger anions are stable against dissociation into individual water molecules and a free electron. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 41–46, January, 1997.     

The structure of deprotonated tri-alanine and its <Emphasis Type="Italic">a</Emphasis><Stack><Subscript>3</Subscript><Superscript>−</Superscript></Stack> fragment anion by IR spectroscopy

We present the first infrared spectra of a mass-selected deprotonated peptide anion (AlaAlaAla) and its decarboxylated fragment anion formed by collision induced dissociation. Spectra are obtained by IRMPD spectroscopy using an FTICR mass spectrometer in combination with the free electron laser FELIX. Spectra have been recorded over the 800–1800 cm⁻¹ spectral range and compared with density functional theory calculated spectra at the B3LYP/6-31++G(d,p) level for different isomeric structures. These experiments suggest a carboxylate anion for [M-H]⁻ and an amide deprotonated (amidate) structure for the a ₃ fragment anion [M-H-CO₂]⁻. The frequency for the amidate carbonyl stretch occurring around 1555±5 cm⁻¹ has been confirmed by additional spectroscopic studies of the conjugated base of N-methylacetamide, which serves as a simple model system for the deprotonated amide linkage in a peptide anion.     

Effects of carbon nanofiber composites on electrode processes involving liquid|liquid ion transfer

Composite electrodes were prepared from chemical vapor deposition grown carbon nanofibers consisting predominantly of ca. 100 nm diameter fibers. A hydrophobic sol–gel matrix based on a methyl-trimethoxysilane precursor was employed and composites formed with carbon nanofiber or carbon nanofiber—carbon particle mixtures (carbon ceramic electrode). Scanning electron microscopy images and electrochemical measurements show that the composite materials exhibit high surface area with some degree of electrolyte solution penetration into the electrode. These electrodes were modified with redox probe solution in 2-nitrophenyloctylether. A second type of composite electrode was prepared by simple pasting of carbon nanofibers and the same solution (carbon paste electrode). For both types of electrodes it is shown that high surface area carbon nanofibers dominate the electrode process and enhance voltammetric currents for the transfer of anions at liquid|liquid phase boundaries presumably by extending the triple-phase boundary. Both anion insertion and cation expulsion processes were observed driven by the electro-oxidation of decamethylferrocene within the organic phase. A stronger current response is observed for the more hydrophobic anions like ClO₄⁻ or PF₆⁻ when compared to that for the more hydrophilic anions like F⁻ and SO₄²⁻. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, March 13–16, 2005     

Simultaneous determination of oxalate, thiosulfate, and thiocyanate in urine by ion-exclusion chromatography with electrochemical detection

Summary A sensitive ion-exclusion chromatographic method has been developed for determination of oxalate, thiosulfate, and thiocyanate. The method is based on separation of these anions on a polymethacrylate-based, weakly acidic cation-exchange resin (TSKgel OApak-A) and detection by means of a glassy carbon (GC) electrode electrochemically modified with polyvinylpyridine (PVP), palladium, and iridium oxide (PVP/Pd/IrO₂). The electrochemical behavior of oxalate, thiosulfate, and thiocyanate at this chemically modified electrode (CME) have been investigated by cyclic voltammetry. The results indicated that electrocatalytic oxidation of these anions by the electrode was efficient and that the sensitivity, stability, and lifetime of the electrode were relatively high. Combined with ion-exclusion chromatography the PVP/Pd/IrO₂ electrode was used as the working electrode for amperometric detection of these anions. All linear ranges were over two orders of magnitude and detection limits, defined asS/N=3, were 9.0×10⁻⁷ mol L⁻¹ for oxalate, 6.7×10⁻⁷ mol L⁻¹ for thiosulfate, and 5.6×10⁻⁷ mol L⁻¹ for thiocyanate. Correlation coefficients were all>0.998. Coupled with microdialysis sampling the method has been successfully applied to the determination of oxalate, thiosulfate, and thiocyanate in urine.     

Preparation of supported metal catalysts starting from hydrotalcites as the precursors and their improvements by adopting “memory effect”

Hydrotalcite-like compounds (HTlcs) can be used as the catalysts as it is since they contain various transition metal cations as the catalytically active species well dispersed on the basic support materials. Moreover, increasing numbers of the applications of HTlcs after the heat treatment have been found since the oxides with very small crystal size, stable to thermal treatments, are obtained after the calcination. The oxides possess interesting properties such as high surface area, basic properties and further form small and thermally stable metal crystallites by reduction. Moreover, the calcined oxides show a unique property, i.e., “memory effect,” which allows the reconstitution of the original hydrotalcite structure. We have developed the catalytic applications of hydrotalcites as it is and moreover the mixed oxides derived from hydrotalcites for various catalytic reactions, i.e., oxidation, dehydrogenation and reforming of hydrocarbons, and even for the reforming of methanol and the CO shift reaction. Aerobic oxidation of alcohols, Baeyer−Villiger oxidation of ketones and O₃ oxidation of oxalic acid have been successfully carried out with the Mg−Al hydrotalcites containing Ni, Fe and Cu, respectively, as the catalysts in liquid phase. In the O₃ oxidation of oxalic acid, the catalytic activity was enhanced by the “memory effect,” i.e., Mg(Cu)–Al hydrotaclite was reconstituted on the surface of Mg(Cu,Al)O periclase particles and oxalic acid was incorporated as anions in the hydrotalcite layer, resulting in an enhanced oxidation of oxalic acid. As the catalysts in the vapor phase reactions, Mg/Fe/Al mixed oxides prepared from Mg–Al(Fe) hydrotalcites and effectively catalyzed the dehydrogenation of ethylbenzene. Supported Ni metal catalysts have been prepared from Mg(Ni)–Al hydrotalcites and successfully used in the steam reforming and the oxidative reforming of methane and propane. Moreover, the Ni catalysts have been improved by combining a trace amount of noble metals by adopting the “memory effect” and used in the production of hydrogen for the PEFC under the daily startup and shutdown operation. Also starting from aurichalcite or hydrotalcite precursor as the precursor, Cu/Zn/Al catalysts with high Cu metal surface area have been prepared and successfully applied in the steam reforming of methanol and dimethyl ether, and moreover in the CO shift reaction.     

Determination of oxalate in black liquor by headspace gas chromatography

This study demonstrated a headspace gas chromatographic method (HS-GC) for the determination of oxalate content in black liquor (alkaline aqueous solution of inorganic chemicals and dissolved wood species from the alkaline pulping of wood). The method described in this paper is based on the reaction between oxalic and manganese dioxide in an acidic medium, in which oxalic acid is converted to carbon dioxide that is measured with a GC using a thermal conductivity detector. The challenge in developing this method was ensuring complete conversion of oxalic acid while minimizing the contribution of side reactions between carbohydrates, lignin and manganese dioxide to the carbon dioxide measured. It was found that a complete conversion of oxalate to carbon dioxide can be achieved within 3 min at a temperature of 70 degrees C; a MnO(2):C(oxalate) (concentration of H(2)C(2)O(4)+HC(2)O(4)(-)+C(2)O(4)(2-)) mole ratio of 60 and H(2)SO(4) concentration of 0.005-0.01 mol/L in the headspace vial. The method can detect concentrations as low as 0.39 microg of oxalate. The standard deviation was found to be 7% while recovery experiments with black liquor showed recoveries of 93-108% which were deemed acceptable for analysis of oxalate in an industrial sample such as black liquor.     

Re-evaluation of the First and Second Stoichiometric Dissociation Constants of Oxalic Acid at Temperatures from 0 to 60 °C in Aqueous Oxalate Buffer Solutions with or without Sodium or Potassium Chloride

Equations were developed for the calculation of the first stoichiometric (molality scale) dissociation constant (K _m1) of oxalic acid in buffer solutions containing oxalic acid, potassium hydrogen oxalate, and potassium chloride from the determined thermodynamic values of this dissociation constant (K _a1) and the molalities of the components in the solutions. Similar equations were also developed for the second stoichiometric dissociation constant (K _m2) of this acid in buffer solutions containing sodium or potassium hydrogen oxalate, oxalate and chloride. These equations apply at temperatures from 0 to 60 °C up to ionic strengths of 1.0 mol⋅kg⁻¹ and they have been based on single-ion activity coefficient equations of the Hückel type. For the equations for K _m1, the activity parameters of oxalate species and the K _a1 values were determined at various temperatures from the Harned cell data of a recent tetroxalate buffer paper (Juusola et al., J. Chem. Eng. Data 52:973–976, 2007). By using the resulting equations for K _m1, the activity parameters of oxalate species for K _m2 and the K _a2 values were then determined from the new Harned cell data and from those of Pinching and Bates (J. Res. Natl. Bur. Stand. (U.S.) 40:405–416, 1948) for solutions of sodium or potassium oxalates with NaCl or KCl. The resulting simple equations for calculation of K _m1 and K _m2 for oxalic acid were tested with all important thermodynamic data available in the literature for this purpose. The equations for ln (K _a1) and ln (K _a2) are of the form ln (K _a)=a+b(t/°C)+c(t/°C)². The coefficients for ln (K _a1) are the following: a=−2.8737, b=0.000159, and c=−0.00009. The corresponding coefficients for ln (K _a2) are −9.6563, −0.003059, and −0.000125, respectively. The new activity coefficient equations were used to evaluate the pH values of the tetroxalate buffer solution (i.e., of the 0.05 mol⋅kg⁻¹ KH₃C₄O₈ solution) for comparison with the pH values recommended by IUPAC at temperatures from 0 to 60 °C and to develop a new two-component oxalate pH buffer of 0.01 mol⋅kg⁻¹ KHC₂O₄+0.05 mol⋅kg⁻¹ Na₂C₂O₄ for which pH values are given from 0 to 60  °C. Values of p(m _H) calculated from these equations are tabulated for these buffers as well as for buffer solutions with KCl and KH₃C₄O₈ as the major component and minor component, respectively. Tables of p(m _H) are also presented for 0.001 mol⋅kg⁻¹ KHC₂O₄+0.005 mol⋅kg⁻¹ Na₂C₂O₄ solutions in which KCl is the supporting electrolyte.     

Kinetics of the thermal dehydrations and decompositions of some mixed metal oxalates

Both isothermal and programmed temperature experiments have been used to obtain kinetic parameters for the dehydrations and the decompositions in nitrogen of the mixed metal oxalates: FeCu(ox)₂·3H₂O, CoCu(ox)₂·3H₂O and NiCu(ox)₂·3.5H₂O, [ox=C₂O₄]. Results are compared with those reported for the thermal decompositions of the individual metal oxalates, Cuox, Coox·2H₂O, Niox·2H₂O and Feox·2H₂O. X-ray photoelectron spectroscopy (XPS) was also used to examinee the individual and the mixed oxalates. Dehydrations of the mixed oxalates were mainly deceleratory processes with activation energies (80 to 90 kJ·mol⁻¹), similar to those reported for the individual hydrated oxalates. Temperature ranges for dehydration were broadly similar for all the hydrates studied here (130 to 180°C). Decompositions of the mixed oxalates were all complex endothermic processes with no obvious resemblance to the exothermic reaction of Cuox, or the reactions of physical mixtures of the corresponding individual oxalates. The order of decreasing stability, as indicated by the temperature ranges giving comparable decomposition rates, was NiCu(ox)₂>CoCu(ox)₂>FeCu(ox)₂, which also corresponds to the order of increasing covalency of the Cu−O bonds as shown by XPS. In celebration of the 60^th birthday of Dr. Andrew K. Galwey     

Reactions of atomic metal anions in the gas phase: competition between electron transfer, proton abstraction and bond activation

Bare metal anions K(-), Rb(-), Cs(-), Fe(-), Co(-), Ni(-), Cu(-), and Ag(-), generated by electrospray ionization of the corresponding oxalate or tricarballylate solutions, were allowed to react with methyl and ethyl chloride, methyl bromide, nitromethane, and acetonitrile in the collision hexapole of a triple-quadrupole mass spectrometer. Observed reactions include (a) the formation of halide, nitride, and cyanide anions, which was shown to be likely due to the insertion of the metal into the C-X, C-N, and C-C bonds, (b) transfer of H(+) from the organic molecule, which is demonstrated to most likely be due to the simple transfer of a proton to form neutral metal hydride, and (c) in the case of nitromethane, direct electron transfer to form the nitromethane radical anion. Interestingly, Co(-) was the only metal anion to transfer an electron to acetonitrile. Differences in the reactions are related to the differences in electron affinity of the metals and the Δ(acid)H° of the metals and organic substrates. Density functional theory calculations at the B3-LYP/6-311++G(3df,2p)//B3-LYP/6-31+G(d) level of theory shed light on the relative energetics of these processes and the mechanisms by which they take place.