Cp*MCpMoFe(CO)7(μ3-S), Cp*MoCpMFe(CO)7(μ3-S) (M = W,Mo) and Cp*WCp*MoFe(CO)7(μ3-S). Crystal structure of CpMoCp*WFe(CO)7(μ3-S)

CpMoFeCo(CO)₇(₃-S) reacts with Cp^*M(CO)₃Cl or CpM(CO)₃Cl (M=W, Mo) to gave the mixed-metal clusters Cp^*WCpMoFe(CO)₇(₃-S) (1), Cp^*MoCpMoFe(CO)₇(₃-S) (2), CpWCp^*MoFe(CO)₇(₃-S) (3), CpMoCp^*MoFe(CO)₇(₃-S) (4) and Cp^*WCp^*MoFe(CO)₇(₃-S) (5). The title clusters have been characterized by i.r., ¹H/¹³C-n.m.r. spectroscopy and their compositions have been confirmed by elemental analyses. The X-ray crystal structure analysis shows the two independent enantiomeric molecules of clusters (1) in one crystal structure unit.     

Redox Properties of Rhodium(III) Oxo-Bridged Carboxylate Complexes

Chemical and electrochemical oxidation of rhodium (III) oxo-bridged carboxylate complexes was studied. The chemical [with O₃ and Ce(IV) salts] or electrochemical (at potentials of 1.00-1.20 V) oxidations of the binuclear complexes [Rh₂(-O)(-O₂CCH₃)₂(H₂O)₆]^{2 +} and [Rh₂(-O)(-O₂CCF₃)₂(H₂O)₆]^{2 +} leads to the superoxo complexes [Rh₂(-O)(O₂-)(-O₂CCH₃)₂(H₂O)₅]⁺ and [Rh₂(-O)(O₂ ^-)(-O₂CCF₃)₂(H₂O)₅]⁺ with terminal coordination of O₂-. The trinuclear acetate [Rh₃(₃-O)(-O₂CCH₃)₆(H₂O)₃]⁺, unlike its trifluoroacetate analog [Rh3(₃-O)(-O₂CCF₃)₆(H₂O)₃]⁺, is oxidized only electrochemically at a potential of 1.38 V. The oxidation of [Rh₃(₃-O)(-O₂CCH₃)₆(H₂O)₃]⁺ is reversible and involves formation of an unstable superoxo group O₂ ^- between two Rh₃III(₃-O) cores.     

Controlled-potential coulometric studies on fluoride and sulphate complexes of neptunium (VI)

Fluoride and sulphate complexing of Np(VI) has been studied by controlled-potential coulometry at a constant ionic strength. The values of ₁ ^* and ₂ ^* for fluoride complexes were found to be 9.4 and 8.9, respectively, at an ionic strength =0.5. At an ionic strength =1.0, ₁ ^* and ₂ ^* obtained were 6.6 and 10.5, respectively. Sulphate complexing of Np(VI) was studied only at an ionic strength =0.5. The value of ₁ ^* obtained was 5.6.     

μSr studies of free radicals in the gas phase

Muonium (Mu=₊+e^-) is the bound state of a positive muon and an electron. Since the positive muon has a mass about 1/9 of the proton, Mu can be regarded as an ultra light isotope of hydrogen with unusually large mass ratios (MuHDT=1/9123). The muon spin rotation technique (SR) relies on the facts that (1) the muon produced in pion decay, ^{+ +} + , is 100% spin polarized and (2) the positron from muon decay is emitted preferentially along the instantaneous muon spin direction at the time of the muon decay.In transverse field SR (TF-SR), the precession of the muon spin in muonium substituted radicals is directly observed by detecting decay positrons time differentially. From observed radical frequencies, the hyperfine coupling constants (A ) of C₂H₄Mu, C₂D₄Mu,¹³C₂H₄Mu, C₂F₄Mu, and C₂H₃FMu are determined. In the longitudinal field avoided level crossing (LF-ALC) technique, one observes the resonant loss of the muon spin polarization caused by the crossing of hyperfine levels at particular magnetic fields. The LF-ALC method together with the information onA obtained from TF-SR allows one to determine the magnitude and sign of the nuclear hyperfine constants at - and -positions. Results are compared with hydrogen substituted ethyl-radicals and isotope effects are discussed.     

Photometric detection of cyclodextrins in liquid chromatography by using iodine generated electrochemically in-situ

A method has been developed for photometric detection of cyclodextrins (CD) in liquid chromatography using iodine (I₂) generated electrochemically in-situ. Iodide ion in the mobile phase was electrochemically oxidized to I₂ which was subsequently reacted with I^–, in an electrochemical flow cell, forming I₃^–. The absorbance of I₃^– was found to be greatly enhanced when CD were present in the mobile phase. The absorbance enhancement was caused by the change in the mole fraction of I₃^–, because of the inclusion reaction of I₃^– with CD. On the basis of this phenomenon, CD were detected by means of a photodiode-array UV–visible detector positioned downstream of the electrochemical flow cell. The signals were found to be linearly dependent on CD concentration. Because the formation constants of I₃^– with CD decrease in the order -CD>-CD>-CD, -CD was most detectable by the method. Detection limits were 1.0 mol L^–1 for -CD, 65 mol L^–1 for monoG1--CD, 100 mol L^–1 for -CD, and 200 mol L^–1 for -CD.     

C-C bond formation at polynuclear metal centers

Studies on C-C bond formation between simple hydrocarbon species such as CH₂, C=CH₂, CH=CH₂, CH₂=CH₂, CH₂=C=CH₂ and CHCH at a diruthenium center suggest that the process is promoted when the dimetal center can readily compensate for the two electrons lost in the formation of the new C-C bond. Thus, whereas -CH₂ and ethene combine only under forcing conditions, the combination of -CH₂ with allene or ethyne, which have additional -electrons available for coordination, occurs readily at room temperature. Likewise, the availability of uncoordinated -electrons in -C=CH₂ allows vinylidene to link rapidly with ethene at room temperature. Alkyne complexes [Ru₂(CO)(-RCCR)(-C₅H₅)₂] (R=CF₃ or Ph) react only under vigorous conditions with additional alkyne to give [Ru₂(CO)(-C₄R₄) (-C₅H₅)₂], but give these same species at room temperature in the presence of acid, shown to be due to the intermediacy of highly reactive 30-electron -vinyl cations. Thermally, alkyne linking proceedsvia three-alkyne species [Ru₂(-C₆R₆)(-C₅H₅)₂] to a four-alkyne complex [Ru₂(-C₈R₈)(-C₅H₅)₂], containing an unprecedented C₈ ligand composed of a C₆ ring with a C₂ tail. Treatment of [Ru₂(CO)(-RCCR)(-C₅H₅)₂] with unsaturated metal fragments gives trimetal complexes such as [Ru₃(CO)₅(₃-CF₃CCCF₃) (-C₅H₅)₂]. The MeCN derivative of this species undergoes unusual linking processes on reaction with additional alkyne to giveinter alia [Ru₃(CO)₃(₃-CCF₃){₃-C₃(CF₃)₃}(-C₅H₅)₂], arising from alkyne cleavage, and [Ru₃(CO)₃{₃-C₄(CF₃)₂(CO₂Me)₂}(-C₅H₅)₂], a closo-pentagonal bipyramidal Ru₃C₄ cluster.     

Diacetylenic Derivatives of Fe2(CO)6(μ-EE′): Spectroscopic Investigations of Fe2(CO)6{μ-EC(H) = C(C≡ CMe)E′} (E = E′, E ≠ E′; E, E′ = S, Se, Te)

The diacetylenic adducts, Fe₂(CO)₆{-EC(H) = C(C CMe)E} (E = E, E E; E, E = S, Se, Te) (1–8) have been obtained from the room temperature stirring of Fe₂(CO)₆(-EE) with HC CC CMe in methanol solvent containing sodium acetate. Compounds 1–8 have been characterized by IR and multinuclear NMR (¹H, ¹³C, ⁷⁷Se, and ^l25Te) spectroscopy. Trends in the chemical shifts of ⁷⁷Se and ¹²⁵Te NMR spectra of Fe₂(CO)₆{-EC(H) = C(C CMe)E} with a variation of EE are discussed.     

Chemistry on the rhomboidal Ru4 faces of the clusters RU4(CO)13(μ-PR2)2: Novel small molecule,ligand, and skeletal transformations

Tetrametal clusters such as Ru₄(CO)₁₃(-PPh₂)₂ and Ru₄(CO)₁₀(-PPh₂)₄ are 64-electron systems and, with five metal-metal interactions, are formally electron rich. In fact these clusters have unusual rhomboidal (or flat butterfly) structures with three or four elongated Ru-Ru bonds. With molecular orbitals antibonding with respect to metal metal interactions occupied in such clusters, facile two electron oxidation or ligand dissociation processes should occur, giving electron precise molecules. The molecule Ru₄(CO)₁₃(-PPh₂)₂ 1a undergoes a remarkable, reversible transformation upon loss of CO affording (-H)Ru₄(CO)₁₀(-PPh₂)[₄-¹(P),¹(P),¹(P),¹,²-{C₆H₄}PPh]3 a cluster which contains a five coordinate phosphido bridge and an orthometallated ² arene ring. This conversion is reversible under CO. These and other results which will be discussed confirm that M₄ clusters with electrons in excess of the expected EAN rule count may exhibit unusual reactivity. The solid-state CP/MAS and static powder³¹P NMR spectra of some of these clusters exhibit^99/101Ru-³¹P couplings, values of which have been measured for the first time.     

The electronic structure and spectrum of the silver(I)perchlorate-pyridine complex

The absorption spectrum of the silver perchlorate-pyridine system was measured in acetonitrile and ethanol in the wavelength region of 180 m to 400 m. It was found that the solution exhibits a new shoulder in the 210 m region characteristic for the 11 complex, in addition to the absorption maxima at 196 m and 253 m which correspond, respectively, to the L _a and L _b bands of pyridine. From the concentration dependence of the absorption intensity of this shoulder, the equilibrium constant for 11 complex formation was determined to be 108 l/mole at 26 °C. Furthermore, we studied theoretically the electronic structure of this complex by the method of the localized orbital model, the effect of the solvation energy upon the charge-transfer configurations being taken into account. The theoretical results show that the new absorption band at 207.5 m has to considerably great extent the character of a charge-transfer type excitation.

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Zusammenfassung Das Absorptionsspektrum des Systems AgClO₄-Pyridin in Acetonitril- und Äthanol-Lösung wurde im Bereich von 400-180 m vermessen. Es treten Absorptionsmaxima bei 196 und 253 m auf, die der L _a -bzw. L _b -Bande des Pyridins entsprechen; daneben eine Schulter bei 207 m als Charakteristikum des 11-Ag⁺-Pyridin-Komplexes. Aus der Konzentrationsabhängigkeit der Intensität dieser Schulter folgt als Gleichgewichtskonstante der Komplexbildung k=108 l/Mol (26 °C), aus der Temperaturabhängigkeit H=4,5 kcal/Mol, S=–6 Cl in guter Übereinstimmung mit polarographischen Ergebnissen. Weiterhin wurde die Elektronenstruktur mit der Methode der Moleküle in Molekülen unter Berücksichtigung von Solvatationseinflüssen untersucht. Danach ist die neue Schulter als Ladungsübergangsbande zu klassifizieren.

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Résumé Mesure du spectre d'absorption du système AgClO₄-Pyridine en milieu acétonitrile ou éthanol dans le domaine 400-180 m. On obtient des maxima d'absorption vers 196 et 253 m correspondant aux bandes L _a et L _b de la pyridine; un épaulement vers 207 m est caractéristique du complexe 11-Ag⁺-Pyridine. D'après la variation de l'intensité de cet épaulement avec la concentration on obtient comme constante d'équilibre du complexe k=100 l/Mol (26 °C), et à partir de la variation avec le température H=4,5 kCal/Mol, S=–6 Cl, en bon accord avec les résultats polarographiques. De plus la structure électronique est étudée à l'aide de la méthode des molécules dans les molécules en considérant les effets de solvatation. On en déduit le caractère de bande de transfert de charge de cet épaulement.

     

Excited Π states of divinyl chalcogenides and chalcophenes

Electron transitions in divinyl chalcogenides (CH₂=CHXCH=CH₂, where X is S, Se, or Te) have been analyzed using UV absorption spectra of dialkyl and alkyl vinyl chalcogenides. The following relations for the orbital energies are found: ^* < ^* < ^* < ^* for Te and ^* < ^* < ^* < ^* for S and Se. For chalcophenes, a correlation between the energy of the excited state (E ^*) of specific symmetry, the ionization potential (I) and the electron affinity (EA) is obtained:E ^*=const+(I+EA)/2. The electron affinity of divinyl chalcogenides is estimated. The correlation between the excited ^* states of divinyl chalcogenides and chalcophenes is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 831–835, May, 1994.     

Mono and dinuclear cationic rhodium(I) and iridium(I) complexes with sulphur donor and group Vb ligands

Summary Rhodium(I) and iridium(I) mixed complexes of the formulae [M(diolefin)LL]ClO₄, [M(diolefin)L₂L]ClO₄, [(diolefin)LIr(-L)₂IrL(diolefin)](ClO₄)₂, [(diolefin)LM(-L-L)ML'(diolefin)](ClO₄)₂, [(diolefin)Rh{-(L-L)}₂Rh(PPh₃)₂](ClO₄)₂ and [(diolefin)LIr{-(L-L)}₂IrL (diolefin)](C1O₄)₂, (L=monodentate sulphur ligand, L-L=bidentate sulphur ligand, L=group Vb ligand; M=Rh, diolefin=1,5-cyclooctadiene (COD) or 2,5-norbornadiene (NBD); M=Ir, diolefin=COD) are described.Author to whom all correspondence should be directed.     

Thermoanalytical investigation of the guest-release process in aromatic-guest clathrates of three-dimensional metal complex hosts

The guest-release process was investigated in terms of the activation energy evaluated by thermogravimetry for the en-Td-type clathratescatena--[catena--(ethylenediamine)cadmium(II) tetra--cyanocadmate(II) or -mercurate(II)]-benzene(1/2), -benzene-d ₆(1/2), and -pyrrole(1/2), the Hofmannen-type clathratescatena-[catena--(ethylenediamine)cadmium(II) tetra--cyanonickelate(Il)]-benzene (1/2) and -pyrrole(1/2), the Hofmann-pn-type clathratecatena-[catena--(dl- orl-propylenediamine (cadmium(II) tetra--cyanonickelate(II)]-pyrrole(2/3), and the pn-Td-type clathratescatena-[catena--(dl-propylenediamine) or -(l-propylenediamine)cadmium(II) tetra--cyanocadmate(II)]-benzene(2/3). Values of the activation energy are correlated with the structural change in the metal complex host accompanied by the release of the guest molecules. The crystal structure ofcatena-[ethylenediaminecadmium tetra--cyanonickelate(II)], the residual host of the Hofmann-en-type, has been analyzed to elucidate the correlation.     

Spectrophotometric Determination of the Polyiodohalides of Organic Nitrogen-Containing Cations

The following biologically active diiodohalides of organic cations were studied: N-cetylpyridinium, trimethylbenzylammonium, triethylbenzylammonium, and N,N-dimethylmorpholinium diiodochlorides; N-cetylpyridinium, tetramethylammonium, tetrabutylammonium, and N,N-dimethylmorpholinium diiodobromides; and N,N-dimethylmorpholinium and butyroylcholinium triiodides. A simple and rapid procedure was proposed for the determination of the above compounds; it is based on the conversion of organic diiodohalides into the corresponding triiodides (_{300 nm} 4 × 10⁴; _{370 nm} 2 × 10⁴) in the presence of excess potassium iodide (RSD 2%). An extraction–spectrophotometric method was developed for the quantitative determination of the biologically active compounds in pharmaceutical dosage forms based on their ion associates with anionic dyes, erythrosine (m _min = 1.25–3.30 g; RSD 3%) and Bromothymol Blue (m _min = 3.85 g; RSD = 3%), or a cationic dye—1,3-dimethyl-2-(4-morpholinophenyl)azobenzimidazolium phenylsulfate (m _min = 2.32–8.26 g; RSD 4%). The developed procedures were used for monitoring drug substances in model pharmaceutical preparations (RSD 4%).     

Synthesis of Osmium–Palladium Mixed-Metal Clusters with 2-(diphenylphosphino)Pyridine as a Bridging Ligand

Reaction of the pentanuclear cluster [Os₅C(CO)₁₄(PPh₂py)] in CH₂Cl₂ with 1.2 equivalents of Pd(MeCN)₂Cl₂ led to the high-yield synthesis of the new osmium–palladium carbonyl cluster [Os₅PdC(CO)₁₄(-Cl)Cl(-PPh₂py)] 1. Cluster 1 is thermally unstable and converts slowly in refluxing CHCl₃ to [{Os₄C(CO)₁₀(-Cl)(-PPh₂py)}(₄-Pd){Os₄C(CO)₁₂(-Cl)}] 2 and [{Os₄ (₅-C)(CO)₁₂(-Cl)}₂(-Pd₂Cl₂)] 3 in 4% and 67% yield, respectively. Reaction of 1 with iodine gave [Os₅PdC(CO)₁₄(-Cl)I(-PPh₂py)] 4 and [{Os₄(₅-C)(CO)₁₂(-I)}₂(-Pd₂I₂)] 5 in moderate yields. All complexes have been characterized by spectroscopic and single-crystal X-ray diffraction analysis.     

The Quest for Single-Source Precursors for BaTiO3 and SrTiO3

The reactions between titanium alkoxides Ti(OR)₄ (R = Et,i Pr) and strontium -diketonates Sr(-dik)₂ (-dik = thd, acac) were investigated. The various Sr-Ti species, Sr₂Ti₂(-dik)₄ (OR)₈, have a 1:1 Sr:Ti stoichiometry and were characterized by elemental analysis, FT-IR and by single-crystal X-ray diffraction for Sr₂Ti₂(₃-OiPr)₂ (-OiPr)₄ (OiPr)₂(thd)₄ (1). The hydrolysis-polycondensation reactions of the various species were investigated and the resulting powders analyzed by light scattering and XRD. While acetone was found to have little influence on the hydrolysis reactions of the Sr-Ti species, polycondensation of Ti(OiPr)₄ in neat acetone offers a trinuclear enolate Ti(₃-O)₂(OCMe=CH₂)₃ (OiPr)₅(iPrOH) (4). Comparisons between the Ba-Ti and Sr-Ti systems are given.     

The determination of tin in explosive materials by thermal neutron activation analysis

A method, based on the measurement of the -photopeak at 332 keV arising from a¹²⁴Sn(n, )^125mSn reaction, has been developed for the rapid measurement of Sn at concentrations of 20 g g^–1, present as the cross-linking agent, in explosive charges. The method is comparative, and has a limit of detection of 0.6 g g^–1 and a precision of 5% RSD. The method requires no sample preparation and is economical in effort.     

An upper bound to bond electric dipole moments

An upper bound can be set to the dipole moment of the X-H bond (with X+H^– polarity) for symmetrical molecules of XH₄ and XH₃ type from the experimental values of the g factor and bond length. The following upper bounds have been found to the bond dipole moments: CH₄ (C+H^–<0.902 D, SiH₄, (Si+H^–)<4.21 D, GeH₄+ (Ge+H^–)<3.59 D, NH₃ (N+H^–)<0, PH₃ (P+H^–)<2.74 D. These results enable one to rule out certain published data on the dipole moment of the C-H bond in methane as certainly incorrect. In the case of the ammonia molecule, the possibility of N+H^– polarity is ruled out.Translated from Teoreticheskaya i Éksperimental'naya Khitniya, No. 3, pp. 346–350, May–June, 1985.     

New cobalt trimethylacetate complexes with pyridine

The reaction of the tetranuclear trimethylacetate complex Co₄(₃-OH)₂(-OOCCMe₃)₄(²-OOCCMe₃)₂(EtOH)₆ with pyridine in acetonitrile was studied. Two new compounds, viz., the hexanuclear cobalt(ii) complex Co₆py₄(₃-OH)₂(-OOCCMe₃)₁₀ (25% yield) and the unusual ionic compound [Co₃py₃(₃-O)(-OOCCMe₃)₆]⁺[Co₄py(₄-O)(-OOCCMe₃)₇]^– (5% yield), were prepared. The structures of the new compounds were established by X-ray diffraction analysis.     

Komplexbildung im System Ni2+—o-Methylbenzamidoxim

Zusammenfassung Die Komplexe des Ni²⁺ mit o-Methylbenzamidoxim wurden in neutraler und in alkalischer Lösung spektrophotometrisch untersucht. Die Bildungskonstanten sindK ₁=40 für 11 undK ₂=1,7·10² für 12 in neutraler Lösung und ₁ = =(3,92 ±0,2) · 10⁴für 11 und lgK = lg ₁ + lg ₂ = 3,45 ± ±0,15 für 12 bei 25° und =1 in alkalischer Lösung.

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Complex formation in the systemeNi ²⁺—o-methylbenzamide oxime

The complexes of Ni²⁺ with o-methylbenzamide oxime were investigated spectrophotometrically in neutral as well as in alkaline solution. The formation constants areK ₁=40 for 11 andK ₂=1.7·10² for 12 in the neutral solution and ₁ = =(3.92 ±0.2) · 10⁴ for 11 and lgK = lg ₁ + lg ₂ = 3.45 ± ±0.15 for 12 at 25° and =1 for the alkaline solution. *** DIRECT SUPPORT *** A3615139 00007

     

Statistical evaluation of the influence of several sample pretreatment methods on the mercury content detectable by chemical analysis of contaminated soil samples under practical conditions

The estimation of the environmental risk of contaminated sites caused by hazardous components may be obtained, for instance, by means of a soil survey. There unavoidable errors by sampling, sample preparation and chemical analysis occur. Furthermore, in case of mercury contaminations, the mercury content detectable by chemical analysis can be falsified, if between sampling, on the one hand, and sample preparation and sample decomposition for chemical analysis, on the other hand, volatile components or elementary metallic mercury escape from the sample. Thus, in these cases, handling of samples such as air drying, storing in plastic bags or thermal evaporation, generally termed sample pretreatment, is a further source of error in evaluating a material. However, the measuring results are influenced not only by sampling, sample pretreatment, sample preparation by homogenization and splitting, and chemical analysis; they must also reflect the intrinsic properties of the soil sample subject to both global fluctuations and local heterogeneities. The present work shows by example of a non-uniformly contaminated site to what extent the analytically detectable mercury content is changed by the method of handling of soil samples in the period between sampling and chemical analysis. A hierarchical experimental design was realized in order to separately quantify the different sources of variation of the measured mercury contents, which are caused by global variations, local heterogeneities, sample preparation, sample pretreatment as well as chemical analysis. As turned out by variance analysis, the variance portion contributed to the total variance by sample pretreatment is highly significant and lies in the same order of magnitude as the variance caused by local heterogeneities of the soil. That means that the type of sample pretreatment influences the analytical results essentially. In order to quantify the effect of a definite pretreatment method in comparison with the mercury content of the unchanged original soil sample, the probable systematic error of a method was introduced. Investigations were only carried out at two sampling locations of the contaminated site because of the relatively high labour; the mean values and variances obtained cannot be immediately transferred to other sites. However, the general knowledge can be used as methodical basis for further investigations. Particularly, the consequence arises that the regulations existing for the treatment of mercury-contaminated samples between sampling and chemical analysis must be revised to obtain comparable criteria of evaluation.Symbols used level of error in statistical tests, - _i random effect of the i-th sampling location with respect to the mercury content, effect of global fluctuations - _ij random effect of the j-th primary sample (composite sample) at the i-th sampling location, effect of local heterogeneity, sampling error - _ijk random effect of the k-th subsample within the respective j-th primary sample (composite sample) at the i-th sampling location, sample preparation error - _ijkl random effect of the l-th pretreated sample belonging to the respective k-th subsample of the j-th primary or composite sample at the i-th sampling location, sample pretreatment effect - _1– probable relative systematic error of a pretreatment methods as compared with the original material at the coverage probability 1– - overall expected mercury content of the sampling results - _i expected mercury content of the i-th pretreated composite sample at a fixed location - û_{1.1 –} lower limit of a confidence interval for the unknown expected mercury content of unchanged original material at the confidence probability 1– - _i intraclass correlation coefficient - ² , ² , ² , ² , _Z ² variance components caused by global variability, local heterogeneity, sample preparation, sample pretreatment and analytical error, respectively - _total ² total variance of mercury content - D² operator of the variance of a random variable - E operator of the mathematical expectation of a random variable - F_i mean squared sum quotient of the Fisher's F-distribution - F_1–/2(fg_i, fg_j) critical value of the F-distribution at fg_i and fg_j degrees of freedom, respectively - fg_i degree of freedom of a (mean) sum of squared deviations - H_i hypothesis regarding a statistical law - I_1– confidence interval for the unknown expected value difference of two methods compared at the probability 1–, probable systematic error of a pretreatment method as compared with the unchanged original material at the coverage probability 1– - MQ_i, mq_i mean squared deviations as explained in the context - n_i number of sampling locations, primary samples per location, subsamples per primary sample, pretreatment methods and measuring values per pretreated sample, respectively - S _i ² , s _i ² variance estimation obtained by chemical analysis - SQ_i, sq_i sum of squared deviations - S(|Y₁–Y_i|) mean error of the absolute mean value difference |Y₁–Y_i|) - t_1–/2;m critical value of the Student's t-distribution at m degrees of freedom and the probability 1–/2 - Y_ijklm mercury content obtained on the m-th final sample of the l-th pretreated sample belonging to the k-th subsample of the j-th primary sample at the i-th sampling location - Y_i, y_i,... mean values obtained by sampling and chemical analysis - Z_ijklm random error of the ijklm-th measuring value (final sample value) Y_ijklm.