Abstracts

Vol. 17, No. 2, 1998

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 77–88 (1998)

GHTMDD – 309 ISSN 0350 – 0136

Received: September 20, 1998 UDC: 678.6.02

Accepted: November 23, 1998

To{ko A. Mi{ev¹, Rolf A. T. M. van Benthem² and Theo J. G. Zwartkruis²

Due to the specific polymer architecture, dendridic polymers offer unique rheological properties making them very interesting materials for various applications. Unfortunately, in most cases, perfect dendritic molecules can not be produced from commercially available monomers in one single production step. Recently, a number of synthetic methods have been developed where monomers available on large scale can be used. The products made in this way, often called hyperbranched polymers, lack the perfect structure of a dendritic molecule, retaining however a number of properties typical for dendrimers. In this paper two calculating techniques are described that can be used in the experimental design for synthesis of hyperbranched polycondensates in general, and hyperbranched polyesteramides based on diacid anhydrides, amino diols and monocarboxylic acids in particular. The first method makes it possible to calculate the resin compositions as a function of number average molecular weight, the percentage of free hydroxyl groups, the amount of the monoacid used as modifier of the polymer properties, and the acid value of the resin during the polycondensation process. The second method is based upon the stochastic theory of branching combined with a kinetic approach. The method uses the composition of the resin already calculated as input and delivers as output morphology related molecular characteristics such as the number average molecular weight, weight average molecular weight and the degree of branching. In addition, it can be also used with necessary refinements to determine the crosslinking density in the case of thermosetting systems.The combination of these two methods will constitute a powerful tool in the hands of the resin chemist in his experimental design.

Keywords: hyperbranched polymers; polyester amides; calculating methods; dendrimers; molecular weights, morphology, degree of branching; diacid anhydrides; amino alcohols; experimental design

To{ko A. Mi{ev¹, Rolf A. T. M. van Benthem² i Theo J. G. Zwartkruis²

Blagodarej}i na specifi~nata polimerna arhitektura, dendrimerite poseduvaat unikatni reolo{ki svojstva {to gi pravat mnogu interesen materijal za razli~ni primeni. Za nesre}a, vo najgolem broj slu~ai dendrimeri so perfektna struktura ne mo`at da bidat sintetizirani koristej}i komercijalno dostapni monomeri. Neodamna se razvieni nekolku metodi koi ovozmo`uvaat koristewe na monomeri dostapni vo golemi koli~estva. Proizvodite napraveni na ovoj na~in, ~esto nare~eni hiperrazgraneti polimeri, ne ja poseduvaat perfektnata struktura na dendrimerite, no sepak zadr`uvaat odreden broj od svoite izvonredni svojstva. Vo ovaa statija se opi{ani dva metoda koi mo`at da se koristat vo eksperimentalniot dizajn pri sinteza na hiperrazgraneti polikondenzati, a posebno hiperrazgraneti poliesteramidi bazirani na anhidridi na dikarboksilni soedinenija, aminodioli i monofunkcionalni organski kiselini. Prviot metod ovozmo`uva presmetka na sostav na smola kako funkcija od srednata broj~ena molekulska masa, procentot na slobodni hidroksilni grupi, sodr`inata na monofunkcionalni kiselini kako modifikatori na polimernite svojstva i kiselinskiot broj vo tekot na polikondenzacioniot proces. Vtoriot metod e baziran na stohasti~kata teorija na razgranuvawe kombinirana so kineti~ki priod. Ovoj metod ja koristi ve}e presmetanata kompozicija na smolata kako vlezna varijabila i kako rezultat gi dava karakteristikite koi se naso~eni na polimernata morfologija kako sredna broj~ena molekulska masa, sredna masina molekulska masa i stepenot na razgranuvawe. U{te pove}e, so potrebni usovr{uvawa ovoj metod mo`e da se koristi za presmetuvawe na stepenot na vmre`uvawe vo slu~aj na termoreaktivni sistemi. Kombinacijata na ovie dva metoda mo`e da bide od zna~ajna pomo{ za istra`uva~ite pri olicetvoruvawe na eksperimentalniot dizajn.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 89–96 (1998)

GHTMDD – 310 0350 – 0136

Received: October 10, 1998 UDC: 678.746

Accepted: November 11, 1998

Maria Bercea, Silvia Ioan, Simona Morariu and Bogdan C. Simionescu*

The paper deals with polystyrene (M_w = 4.37× 10⁵ – 1.91× 10⁷ g/mol) in dilute solutions of different solvents. The Mark-Houwink dependences and the unperturbed dimensions of polystyrene determined by different methods were discussed. Also, the perturbed dimensions of macromolecules over a large domain of concentrations and molecular weights were determined.

Keywords: polystyrene; Mark-Houwink dependences; perturbed and unperturbed dimensions

Maria Bercea, Silvia Ioan, Simona Morariu i Bogdan C. Simionescu*

Predmet na interes vo trudot e polistiren (M_w = 4,37× 10⁵ ‡ 1,91× 10⁷ g/mol) vo razredeni rastvori na razli~ni rastvoruva~i. So pomo{ na razli~ni metodi se opredeleni i diskutirani Mark-Houwink-ovite zavisnosti i nenaru{enite dimenzii na verigite. Opredeleni se, isto taka, i naru{enite dimenzii na makromolekulite i molekularnite masi vo {iroko koncentracisko podra~je.

Klu~ni zborovi: polistiren; Mark-Houwink-ovi zavisnosti; naru{eni i nenaru{eni dimenzii

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 97–104 (1998)

GHTMDD – 311 ISSN 0350 – 0136

Received: May 15, 1998 UDC: 547.751 : 543.422.6

Accepted: October 23, 1998

Blagoja Andonovski^*, Lidija Šoptrajanova and Ilinka Spirevska

The protonation of indole, indolyl-3-acetic acid, indolyl-3-propionic acid and indolyl-3-butyric acid in sulfuric acid was studied by ultraviolet (UV) spectroscopy in the 400–190 nm region. The position of the additional protons in the protonated compounds was discussed. The absorbance values were measured at several selected short wavelengths and the molar absorptivities were estimated. From these values, using Hammett’s equation, the pK_a values for indole, indolyl-3-acetic acid, indolyl-3-propionic acid and indolyl-3-butyric acid: –3.6 (± 0.1); –5.6 (± 0.4); 5.3 (± 0.1) and 4.9 (± 0.3), were obtained, respectively. The pKa values (and the solvent parameter m*) were estimated using the Excess Acidity Method as well.

Keywords: indole; indole derivatives; protonation; dissociation constants; solvent parameter; Excess Acidity Method; UV spectroscopy

Ispitano e protoniraweto na indol, indolil-3-ocetnata kiselina, indolil-3-propionskata kiselina i indolil-3-buternata kiselina vo sulfurna kiselina so primena na metodite na ultravioletova spektroskopija (UV), vo podra~jeto na branovi dol`ini od 400 do 190 nm. Diskutirana e i polo`bata na adiranite protoni kaj protoniranite soedinenija. Vrednostite na apsorbancata se mereni na nekolku selektirani branovi dol`ini i od niv se opredeleni molarnite apsorpcioni koeficienti. Od ovie vrednosti, so primena na Hammett-ovata ravenka, presmetani se pK_a-vrednostite za indol, indolil-3-ocetnata kiselina, indolil-3-propionskata kiselina i indolil-3-buternata kiselina i tie se: ‡3,6(± 0,1); ‡5,6(± 0,4); 5,3(± 0,1) i 4,9(± 0,3), soodvetno. So primena na metodot na zgolemena kiselost se opredeleni pKa-vrednostite i solvatacioniot parametar m*.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 105–111 (1998)

GHTMDD – 312 ISSN 0350 – 0136

Received: February 3, 1998 UDC:546.79 : 543.552

Accepted: November 20, 1998

Verica Jakimovi}, Simka Petrovska-Jovanovi} and Kornelija Stojanova

The square-wave voltammetry (SWV) is a technique that can be used for determination of tungsten in microamounts. The method is based upon a quasi-reversible reduction reaction of W(V) to W(III) in hydrochloric acid (c(HCl) = 6 mol dm^–3), which was chosen by our measurements as the best supporting electrolyte. The best results were achieved at the following experimental conditions: initial potential of –0.550 V, final potential of –0.850 V, frequency of 100 Hz, square-wave amplitude of 0.04 V and potential increment of 2 mV. The well-defined cathodic peak, which occurs at a potential of approximately –0.700 V, can be used to determine the tungsten in the range of 2.0.10^–6 mol dm^–3 to 8.3.10^–5 mol dm^–3. In order to apply the proposed method for the determination of tungsten in some samples, the influence of several potentially interfering ions (Pb, Cd, Cu, Ni, Co, Zn and Fe) is investigated. The experimental results showed that it is necessary to eliminate the interference by Pb(II) and Cd(II) ions when they are present in large quantities (higher or equal to the W(VI) concentration in the cell).

Keywords: tungsten; SWV; electroanalytical investigation

Razvien e nov elektroanaliti~ki metod za opredeluvawe na volfram so primena na SWV. Metodot e baziran na sledewe na pik na potencijal od ‡0,700 V, koj se dol`i na odvivawe na kvazireverzibilna elektrodna reakcija na redukcija vo hlorovodorodna kiselina kako osnoven elektrolit. Ispituvawata poka`uvaat deka najdobri rezultati se dobivaat ako merewata se vr{at pri slednive uslovi: po~eten potencijal: ‡0,550 V, kraen potencijal: ‡0,850 V, frekvencija: 100 Hz, amplituda: 0,04 V i potencijalen inkriment: 2 mV. Za osnoven elektrolit e odbrana hlorovodorodna kiselina so c = 6,0 mol dm^–3. Pri ovie uslovi linearna zavisnost e zabele`ana vo granici od 1,96 10^–6 mol dm^–3 do 8,30 10^–6 mol dm^–3. Za da se primeni metodot za odreduvawe na volfram vo primeroci, neophodno e prethodno da se otstrani vlijanieto na Pb(II) i Cd(II), koga tie se prisutni vo pogolemi koli~estva.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 113–118 (1998)

MHK "Zletovo", 91400 Veles, Republic of Macedonia

Leaching rates of copper and indium from copper dross, arising from thermal lead refining in sulphuric acid solutions, were studied. The effects of temperature and acid concentration were investigated. The kinetics of copper leaching over the temperature range of 323 to 373 K obeyed the equation for the rate of a surface chemical reaction, occurring on a shrinking particle. However, the calculated apparent activation energy of only 14.1 kJ mol^–1 clearly indicates the opposite. Lead sulphate, the major solid product of the leaching process, was not an impediment to copper dissolution.

The dissolution of indium was limited to about 25 to 40 % depending on the temperature and the sulphuric acid concentration. The very fast decrease of the reaction rate indicated that the rate of indium dissolution was most probably controlled by diffusion of either the reactants or the product through a layer of lead sulphate. However, it was not possible to prove this by using any of the diffusion-controlled leaching models available so far. A formal kinetic equation of the type a = t/(a+b·t) has been suggested instead, on the basis of which an activation energy of 39.6 KJ mol^–1 was calculated for the initial stage of the process of indium leaching.

Keywords: Indium; copper; leaching rate; heterogeneous reaction kinetics; formal kinetics

Prou~uvana e brzinata na lu`ewe na indium i bakar od bakaren dros koj se sozdava pri plamenata rafinacija na olovoto. Ispituvano e vlijanieto na temperaturata i na koncentracijata na sulfurnata kiselina. Vo temperaturen interval od 323 do 373 K procesot na lu`ewe na bakar ja zadovoluva ravenkata za brzina na hemiska reakcija koja se odviva na povr{inata na ~esti~ka koja se smaluva. Presmetanata vrednost na aktivacionata energija od samo 14,1 kJ mol^–1 e daleku pomala od voobi~aenite vrednosti za hemiski kontrolirani procesi i jasno uka`uva deka lu`eweto na bakarot e difuzno kontrolirano. Olovniot sulfat, najgolemiot del od cvrstiot produkt, ne pretstavuva{e prepreka za lu`ewe na bakarot.

Rastvoraweto na indiumot be{e limitirano na okolu 25 do 40%, zavisno od temperaturata i koncentracijata na sulfurnata kiselina. Golemiot pad na brzinata na reakcijata uka`uva deka brzinata na rastvoraweto na indiumot e kontrolirana so difuzija na reaktantite ili produktot niz slojot od oloven sulfat. Me|utoa, ova ne mo`e{e da se potvrdi so primena na nitu eden od poznatite kineti~ki modeli za difuziono kontrolirani reakcii. Predlo`ena e neformalna kineti~ka ravenka od tipot a = t/(a+b·t), vrz osnova na koja e presmetana aktivaciska energija od 39.6 kJ mol<sup>–1</sup> za po~etniot stadium na procesot na lu`ewe na indium.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 119–123 (1998)

GHTMDD – 314 ISSN 0350 – 0136

Received: October, 4, 1998 UDC: 615.451.23

Accepted: October 23, 1998

Short communication

Release rate of Lidocaine HCl incorporated in both aqueous phases of multiple W/O/W emulsion was measured as a function of two formulation variables – the volume ratio of primary W/O in the W/O/W emulsion and the concentration of hydrophilic emulsifier in the external aqueous phase. By changing the formulation parameters, differences in dispersion status of the emulsions were obtained, which affected the drug release rate. Increase of the volume ratio of primary W/O emulsion and decrease of the hydrophilic emulsifier concentration in the external aqueous phase of multiple W/O/W emulsion resulted in decrease of the drug release rate. Changes of those two parameters could be used for achieving the different drug release rates from the emulsions.

Keywords: multiple emulsions; water/oil/water; W/O/W; formulation; drug release

Klu~ni zborovi: pove}ekratni emulzii; voda/maslo/voda (V/M/V); formulacija;
osloboduvawe na lekovita materija

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 125–128 (1998)

GHTMDD – 315 ISSN 0350 – 0136

Received: March 25, 1998 UDC:665.637.3.094.3-926.217(549.4)

Accepted: November 20, 1998

Pavle I. Premovi}, Branislav N. [uhartovi}, Miroslav P. Premovi},
Dejan T. Dulanovi} and Dragan M. \or|evi}

Kerogen-like material was generated during a laboratory heating experiment with asphaltenes in the presence of air oxygen. Asphaltenes were extracted from a Heimar (A recent seep) and IPRG sandstones (Dead Sea Basin, Israel) impregnated by heavy/asphaltic crudes and heated at 50–200^oC for 1–12 days. These results suggest the possible occurence of low temperature (£ 100^oC) kerogenization by air oxygen of the Dead Sea (DS) asphaltenes as (B old petroleum seepage location) impregnated with a heavy crude.

Keywords: kerogenization; asphalt; oxygen

R e z i m e

KEROgEnIZACIJA NA ASFALTENITE SO KISLOROD OD VOZDUHOT:
PESO^NATA KARPA HEIMAR (STARO NAO\ALI[TE NA NAFTA B)
OD BASENOT NA MRTVOTO MORE (IZRAEL)

So zagrevawe na asfaltenot vo vozdu{na atmosfera, vo laboratoriski uslovi, se dobiva materija sli~na na kerogenot. Asfaltenite se ekstrahirani od peso~ni karpi impregnirani so te{ka nafta od Heimar (novo nao|ali{te A) i od IPRB (basen na Mrtvoto More, Izrael), so zagrevawe na 100‡200 ^oS, vo tekot na 1‡12 dena. Kerogenizacijata na asfaltenite so kislorodot od vozduhot ja sledi kinetika od prv red, a presmetanoto vreme na polu`ivot (t<sub>1/2</sub>) za asfaltenite od Mrtvoto More iznesuva 2000 do 3 dena na 0‡100 <sup>o</sup>S. Ovie rezultati sugeriraat mo`nost za niskotemperaturna (£ 100 ^oS) kerogenizacija na asfaltenite od Mrtvoto More, a so toa i mo`nost na toj na~in da se formira materijal sli~en na kerogenot vo peso~nite karpi vo Heimar (staro nao|ali{te na nafta B), impregnirani so te{ka nafta.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 129–134 (1998)

GHTMDD – 316 ISSN 0350 – 0136

Received: July 13, 1998 UDC: 665.3.061.3 : 634.8.076

Accepted: November 20, 1998

Slav~o Aleksovski¹, Helena Sovová², Beti ]urapova¹ and Filimena Poposka¹

1Department of Chemical and Control Engineering, Faculty of Technology and Metallurgy,
The "Sv.Kiril & Metodij" University, 91000 Skopje, Republic of Macedonia
²Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic,
Prague, Czech Republic

Supercritical fluid extraction with carbon dioxide (SFE) and Soxhlet extraction of grape seeds oil was examined. Supercritical fluid extraction was performed in a 13 cm³ laboratory extractor, at 28 MPa and 40 ^oC with a flow rate 0.9 g CO₂/min. During 2 hours of extraction, 61 to 69 % of oil was extracted from 8 g of the ground grape seeds of mean particle size 0.35 mm. A simulation of the extraction curves for several grades of grinding was performed to point out the effect of particle size.

Solvent extraction was performed with 10 – 40 g of ground seeds in a standard Soxhlet apparatus of 500 cm³ volume, using hexane (hexane-fraction, 68 – 72 ^oC), ethanol and petroleum ether as solvents. The extraction time was 10 – 15 h and the phase ratio ranged from 1/15 and 1/100. Hexane was shown as a more selective solvent, while ethanol as a safer solvent.

Comparison of the applied methods confirms that the quality of oil obtained by the SFE is better because of its authentic composition and because of the absence of any traces of organic solvents. Also the initial extraction rate is considerably higher for the SFE. On the other hand, the total yield of the oil obtained by the SFE is lower than that of the oil obtained by the Soxhlet extraction.

Keywords: grape seed oil; supercritical fluid extraction; solvent extraction; supercritical carbon dioxide; hexane; ethanol; petroleum ether; simulation

R e z i m e

SUPERKRITI^NA EKSTRAKCIJA SO JAGLERODDIOKSID
I SOXHLET-EKSTRAKCIJA NA MASLO OD SEMKI OD GROZJE

Superkriti~nata ekstrakcija e izveduvana vo laboratoriski ekstraktor so volumen od 13 cm³, pod slednive operacioni uslovi: pritisok vo ekstraktorot 28 MPa, temperatura 40 ^oC, protok na superkriti~niot jagleroddioksid 0,9 g CO₂/min. Vo tekot na ekstrakcijata od 2 ~asa, se ekstrahiraat 61 do 69% maslo od 8 g someleni semki so sreden dijametar od 0,35 mm. Izvedena e simulacija na ekstrakcioni krivi za nekolku stepeni na somelenost na semki so cel da se poka`e efektot od goleminata na ~esti~kite.

Ekstrakcijata so rastvoruva~i e izveduvana vo standardna Soxhlet-aparatura od 500 cm³ so heksan (heksanska frakcija, 68 – 72 ^oC), petroleter i etanol, so odnos na fazite od 1/15 i 1/100 i vreme na ekstrakcija 10 ‡ 15 ~asa. Heksanot se poka`uva kako poselektiven rastvoruva~, dodeka etanolot kako pobezbeden.

Sporedbata na dvete primeneti postapki potvrduva deka kvalitetot na masloto dobieno so superkriti~nata ekstrakcija e podobar poradi negoviot avtenti~en sostav i poradi otsustvoto na kakva bilo traga od rastvoruva~. Isto taka, po~etnata brzina na ekstrakcija e zna~itelno povisoka pri superkriti~nata ekstrakcija. Od druga strana, vkupniot prinos na maslo dobien so superkriti~nata ekstrakcija e ponizok otkolku prinosot na maslo dobien so Soxhlet-ekstrakcijata.

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 135–140 (1998)

GHTMDD – 317 ISSN 0350 – 0136

Received: October 9, 1998 UDC: 546.74 : 543.422

Accepted: November 23, 1998

Marina Stefova¹, Traj~e Stafilov¹ and Elisaveta Stikova²

In this work a determination of nickel in urine and blood serum samples by electrothermal atomic absorption spectrometry is performed using the IUPAC reference method with several modifications. These modifications refer to the concentration of the sample and to the instrumental parameters. Nickel is extracted as bis-(1-pyrrolidinecarbodithioato)nickel(II) complex in 4-methyl-pentane-2-one (methyl isobuthyl ketone, MIBK) as a solvent. Samples are first digested with mixture of acids (HNO₃, H₂SO₄, HClO₄) up to 200 °C to remove the organic matter. The residue is then adjusted to pH 7 and ammonium pyrrolidine dithiocarbamate (APDC) solution is added. The bis-(1-pyrrolidinecarbodithioato)nickel(II) complex is extracted in MIBK. The concentration of nickel extracted in MIBK is measured by electrothermal atomic absorption spectrometry. The method was tested with standard additions of nickel to samples of urine and serum and satisfactory results were obtained for the recovery values. Determinations of nickel concentration performed on 70 samples of urine and 68 samples of serum from workers exposed to nickel compounds showed that in the most cases nickel concentrations are slightly higher than the ones found in the control group. This fact indicates the need of permanent control and action to protect the workers from the acute or chronic intoxication with nickel and its compounds.

Keywords: nickel; blood serum; urine; determination; electrothermal atomic absorption spectrometry

R e z i m e

OPREDELUVAWE NA NIKEL VO URINA I KRVEN SERUM SO ELEKTROTERMI^KA ATOMSKA APSORPCIONA SPEKTROMETRIJA

Vo trudov se prezentirani rezultatite od opredeluvaweto na nikel vo primeroci od urina i serum so elektrotermi~ka atomska apsorpciona spektrometrija, koristej}i go referentniot metod od IUPAC so nekolku modifikacii. Ovie modifikacii se odnesuvaat na koncentriraweto na obrazecot i na instrumentalnite parametri. Nikelot e ekstrahiran kako bis-(1-pirolidinkarboditioato)nikel(II) kompleks vo 4-metil-pentan-2-on(metil izobutil keton, MIBK) kako rastvoruva~. Primerocite se zagrevaat so smesa od kiselini (HNO₃, H₂SO₄, HClO₄) do 200 °C za otstranuvawe na organskite materii, a ostatokot potoa se neutralizira do pH = 7. Potoa se dodava rastvorot od amoniumpirolidinditiokarbamat (APDC) i formiraniot bis-(1-pirolidinkarboditioato)nikel(II) kompleks se ekstrahira vo MIBK. Koncentracijata na nikel vo ekstraktot se opredeluva so elektrotermi~ka atomska apsorpciona spektrometrija. Postapkata e proverena so metodot na standardni dodatoci, pri {to se dobieni zadovolitelni rezultati za analiti~kiot prinos. Izvr{eni se opredeluvawa na zastapenosta na nikel vo 70 primeroci od urina i 68 primeroci od serum zemeni od rabotnici izlo`eni na soedinenijata na nikel. Dobienite rezultati vo pove}eto slu~ai imaat malku povisoki vrednosti od onie vo kontrolnata grupa, {to ja nametnuva potrebata za postojana kontrola i prezemawe merki za za{tita na rabotnicite od akutni ili hroni~ni truewa so nikel i negovite soedinenija.

Klu~ni zborovi: nikel; serum; urina; opredeluvawe; elektrotermi~ka atomska apsorpciona spektrometrija

Bulletin of the Chemists and Technologists of Macedonia, Vol. 17, No. 2, pp. 141–145 (1998)

GHTMDD – 318 ISSN 0350 – 0136

Received: July 9, 1998 UDC: 542.941

Accepted: October 23, 1998

There are quite a number of methods for balancing chemical equations. A variant of the oxydation number method is proposed for fast and easy balancing of complex redox equations. The principal aid are formal balance numbers (FBN). These have been introduced as an alternative to the conventional/traditional values of the oxydation numbers. The values of the FBNs are chosen in such a way, to ensure that only two elements change their state, in which case the original oxydation number technique for balancing equations may be employed. The method is probably the fastest of all possible methods that rely on ‘chalk and blackboard’.

Keywords: chemical equation balancing; graduate education research; teaching/learning aids

Poznat e golem broj metodi za izramnuvawe hemiski ravenki. Vo trudov e predlo`ena varijanta na metodot na oksidacioni broevi, koja ovozmo`uva brzo i lesno izramnuvawe na kompleksni redoks-ravenki. Klu~no e voveduvaweto na poimot formalni broevi za izramnuvawe (formal balance numbers, FBN). Ovie broevi se vovedeni kako alternativa za konvencionalnite vrednosti na oksidacionite broevi. Vrednostite na FBN se izbiraat taka {to da ovozmo`uvaat promena na sostojbata na samo dva elementa. Vo takov slu~aj mo`e da se upotrebi originalniot metod na oksidacioni broevi za izramnuvawe na ravenkite. Predlo`eniot metod e, verojatno, najbrziot od site {to ne vklu~uvaat upotreba na smeta~i.

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