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溶質（成分1）と溶液（成分2）からなる二成分系溶液を溶媒で希釈しても、体積は保存されない。モル濃度（物質量濃度）はある成分の物質量と溶液の体積の比で表される。それゆえ、溶液を希釈して正確なモル濃度を算出するには、体積の非加成性を考慮しなければならない。しかし、高校化学の教科書には、体積の加成性の成立を前提とした見かけのモル濃度が登場する。厳密には見かけのモル濃度は溶液と溶媒の密度が同一の場合にのみ有用である。本研究では希釈後の溶液の正確なモル濃度の算出方法を提案した。そして、この方法を、14.000mol/L および 5.000mol/L の水酸化ナトリウム（NaOH）水溶液の希釈に適用して、希釈後の正確な濃度および見かけの濃度を算出した。その結果、両者の間に不一致が認められ、特に14.000mol/L のNaOH水溶液を希釈する際、溶液と溶媒の体積比が1.000mL:0.500mLの場合に、モル濃度とみかけのモル濃度との間に約3％の相違が認められた。本方法を用いれば、希釈後の水溶液のモル濃度を容易に推算することが可能であり、高校化学の教材として有用である。, When a binary solution, which is composed of a solute (component 1) and solvent (component 2) is diluted with its solvent, is not conserved. Molarity (Amount concentration) is the ratio of the chemical amount of a component to the total volume of the solution, and therefore, the nonadditivity of volumes should be considered in order to obtain the accurate molarity of a diluted solution. However, the apparent molarity of a diluted solution computed under the assumption that the additivity of volumes lolds appears in some Japanese high school chemistry textbooks. Strictly, the apparent molarity is only valid if the density of an original solution is equal to that of an added solvent. In this paper, the method of estimating the accurate molarity of a diluted binary solution is first derived. Secondly, this method is applied to diluting sodium hydroxide (NaOH) aqueous solutions, and the accurate and apparent molarities of the diluted NaOH aqueous solution are estimated from the concentrated 14.000 and 5.000 mol/L aqueous ones. There is a discrepancy between the accurate and apparent molarities, and this is most significant (ca.3%) when the volume ratio of the 14.000 mol/L NaOH aqueous solution to water is 1.000 mL:0.500 mL. Using this method, it is easy to estimate the accurate molarities of the diluted aqueous solution and improve the teaching material for high school chemistry.

The effects of hydrogen bonds on the molecular structure of water-tetrahydrofuran (H2O&ndash, THF), water-dimethyl sulfoxide (H2O&ndash, DMSO), and water-tetrahydrofuran-dimethyl sulfoxide (H2O&ndash, THF&ndash, DMSO) in binary aqueous solutions and ternary aqueous solutions were studied using Raman spectroscopy. The results indicate that in the binary aqueous solution, the addition of THF and DMSO will generate hydrogen bonds with water molecules, resulting in changes in the peak positions of S=O bonds and C&ndash, O bonds. Compared with the binary aqueous solutions, the hydrogen bonds between DMSO and THF, and the hydrogen bonds between DMSO and H2O in the ternary aqueous solutions are competitive, and the hydrogen bond competition is susceptible to water content. In addition, the formation of hydrogen bonds will destroy the fully hydrogen-bonded water and make it change to the partially hydrogen-bonded water. By fitting the spectra into the three Gaussian components assigned to water molecules with different hydrogen bonding (HB) environments, these spectral features are interpreted by a mechanism that H2O in different solution systems has equal types of water molecules with similar HB degrees-fully hydrogen-bonded H2O (FHW) and partially hydrogen-bonded H2O (PHW). The ratio of the intensity transition from FHW to PHW is determined based on Gaussian fitting. Therefore, the variation of hydrogen bond competition can be supplemented by the intensity ratio of PHW/FHW ((IC2 + IC3)/IC1). This study provides an experimental basis for enriching the hydrogen bonding theory of multivariate aqueous solution systems.

Ispitan je proces uklanjanja kadmija i cinka postupkom u koloni iz binarne ekvimolarne vodene otopine ukupne početne koncentracije c o (Cd+Zn) ≈ 1 mmol/L pri protocima od Q = 1, 2 i 3 mL/min. Provedena su tri radna ciklusa i tri ciklusa regeneracije na istom uzorku zeolita visine sloja od 8 cm. Iz eksperimentalnih rezultata nacrtane su krivulje proboja i krivulje regeneracije, izračunati su karakteristični parametri te je utvrđena učinkovitost procesa. Povećanjem protoka otopine proboj i iscrpljenje se pojavljuju ranije, smanjuje se kapacitet zeolita i efikasnost kolone. Prirast ukupne količine (Cd+Zn) iona vezanih na zeolitu linearno raste od početka eksperimenta nakon čega se počinje smanjivati (točka infleksije) što ukazuje na promjenu mehanizma koji kontrolira ukupnu brzinu procesa. Primjenom Advekcijsko-disperzijsko-reakcijskog modela (ADR) izračunat je koeficijent aksijalne disperzije, D L , pomoću kojega je izračunat koeficijent prijenosa tvari, k f kroz difuzijski granični sloj čestice zeolita. Utvrđeno je da je utjecaj aksijalne disperzije izraženiji za veće protoke otopine kroz sloj jer otopina zaobilazi dio čestica u zeolitnom sloju zbog nedovoljnog kontakta između otopine i zeolita. Najveća vrijednost k f utvrđena je u točki proboja, a zatim opada prema točki iscrpljenja uslijed povećanja debljine difuzijskog graničnog sloja. Do područja infleksije brzinu procesa kontrolira prijenos tvari konvekcijom u tekućoj fazi, a nakon infleksije prijenos tvari difuzijom kroz česticu. Povećanjem protoka može se obraditi veći volumen otopine u kraćem vremenu, međutim protok postaje ograničavajući faktor jer uslijed njegova povećanja dolazi do pojave aksijalne disperzije koja dovodi do smanjenja efikasnosti kolone. Removal of cadmium and zinc from equimolar binary aqueous solution of total initial concentration of c o (Cd+Zn) ≈ 1 mmol/L has been investigated using the column process at the flow rates of Q = 1, 2 and 3 mL/min. Three service and three regeneration cycles were performed on the same zeolite bed with height of 8 cm. The experimental results are shown by breakthrough and regeneration curves, and the characteristic parameters have been calculated as well as removal efficiency. By increasing in flow rate, the breakthrough and exhaustion points occured earlier, while zeolite capacity and column efficiency decreased. The quantity of (Cd+Zn) ions increases linearly from the beginning of the experiment, after that decrease (inflection point) indicating a change in mechanism which controls the overall process rate. The Advection-Dispersion-Reaction (ADR) model was applied for calculation of the axial dispersion coefficient, D L from which the mass transfer coefficient, k f , through the diffusion boundary layer has been calculated. The impact of axial dispersion is more pronounced for higher flow rates because of the solution bypassing some of the zeolite particles due to insufficient contact between the solution and the zeolite layer. The highest value of k f is observed in the breakthrough point, and then decreases to the exhaustion point due to increase in thickness of diffusion boundary layer. Up to inflection, the mass transfer by convection through the liquid phase controls the overall procces rate, and after that the mass transfer by diffusion through the boundary layer of the zeolite particle. By increasing in flow rate a larger volume of the solution can be treated in a shorter time, but the flow of the solution becomes a limiting factor because with its increase, an axial dispersion occurs which consequently results in a reduction of column efficiency.

著者はこれまでに二成分系溶液の希釈後の体積の（Ｖм）の推算式を誘導し、種々の水溶液に応用した。本研究では、この式を用いて、20℃で炭酸ナトリウム（Na2CO3)および炭酸カリウム（K2CO3)水溶液を水で希釈した場合のＶмを算出した。希釈前のNa2CO3およびK2CO3水溶液の濃度は、溶質の質量分率でそれぞれ0-0.1500、0-0.5000とした。希釈前の水溶液と加えた水の体積比は、1.000mL:9.000mL、3.000mL:7.000mL、5.000mL:5.000mL、7.000mL:3.000mL、9.000mL:1.000mLとした。いずれの水溶液も、希釈前の溶液の濃度の増加とともに体積は減少した。混合の体積比が5.000mL:5.000mLの場合に体積は最小値を示し、Na2CO3水溶液では9.959mL、K2CO3水溶液では9.753mLであった。このように、希釈後に有意な体積変化が認められた。本手法を用いれば、実験を行うことなく容易にＶмを推算できるので、高校理科の教材として有用である。, The author has already derived the method of estimating the volume of a diluted binary solution (VM), and applied it to various aqueous solutions. In this paper, the method is applied to sodium carbonate (Na2CO3)and portassium carbonate (K2CO3) aqueous solutions in order to examine volume changes in diluting these solutions with water at 20℃ using their density data. The concentration ranges of original Na2CO3 and K2CO3 aqueous solutions are 0-0.1500 and 0-0.5000 mass fractions of solutes respectively. The volume ratios of the original aqueous solution to the added water are 1.000mL:9.000mL, 3.000mL:7.000mL, 5.000mL:5.000mL, 7.000mL:3.000mL, and 9.000mL:1.000mL. For both solutions, as the concentrations of the original solution are increasing, the values are decreasing, and their minimums are 9.959mL for the Na2CO3 aqueous solution and 9.753mL for the K2CO3 aqueous one at the ratio 5.000mL:5.000mL. The obvious volume decreases are recognized after diluting original solutions. Using this method, the VM alues can be simply estimated without performing experiments, and therefore it is useful as teaching material for high school science.

一般に、溶液の希釈に伴い体積の加成性は破綻する。二成分系溶液の希釈後の体積の推算式に関してはすでに誘導した。本研究では、この式を用いて、２０℃で水酸化ナトリウム（NaOH)および水酸化カリウム(KOH)水溶液を水で希釈した場合の体積を算出した。希釈前のNaClおよびKCl水溶液の濃度は、溶質の質量分率でそれぞれ0-0.400、0-0.500とした。希釈前の溶液と溶媒の体積比は、1.000mL：9.000ｍL、3.000mL:7.000ｍL、5.000mL:5.000ｍL、7.000mL:3.000ｍL、9.000mL:1.000ｍLとした。いずれの水溶液も、希釈前の溶液の濃度の増加とともに体積は減少した。混合の体積比が5.000mL：5.000mLの場合に体積は最小値を示し、NaOH水溶液では9.649mL、KOH水溶液では9.753mLであった。このように、希釈後に有意な体積変化が認められた。本手法を用いれば、実験を行うことなく容易に体積推算することが可能であり、高校理科の教材として有用である。, In general, the additivity of volume does not hold when a solution is diluted with a solvent. The method of estimating the volume of a diluted binary solution (VM) has been already derived. In this paper, our method is applied to sodium hydroxide (NaOH) and potassium hydroxide (KOH) aqueous solutions in order to examine volume changes in diluting these solutions with water at 20℃ using their density data. The concentration ranges of original NaOH and KOH aqueous solutions are 0-0.4000 and 0-0.5000 mass fractions of solutes respectively. The volume ratios of the original solution to the added solvent are 1.000 mL: 9.000 mL, 3.000mL: 7.000ｍL, 5.000mL: 5.000mL, 7.000mL:3.000mL, and 9.000mL: 1.000mL. For both solutions, as the concentrations of the original solution are increasing, the values are decreasing, and their minimums are 9.649 mL for the NaOH aqueous solution and 9.753 mL for the KOH aqueous one at the ratio 5.000mL: 5.000mL. The obvious bolume decreases are recognized after diluting original solutions. Using our method, the VM values can be simply estimated without performing experiments, and therefore it is useful as teaching material for high school science.

一般に、希釈前の溶液と溶媒の体積の和は、希釈後の溶液の体積の値にはならない。すなわち、溶液の希釈に伴い体積の加成性は破綻する。二成分系溶液の希釈後の体積(ＶM)の推算方法に関してはすでに誘導した。本研究では、これを用いて、20℃で塩化ナトリウム(NaCl)および塩化カリウム(KCl)水溶液を水で希釈した場合のVMの値を推算した。希釈前のNaClおよびKCl水溶液の濃度は、溶質の質量分率でそれぞれ0-0.2600. 0-0.2400とした。希釈前の溶液と溶媒の体積比は、1.000mL:9.000mL、3.000mL:7.000mL、5.000mL:5.000mL、7.000mL:3.000mL、9.000mL:1.000mLとした。いずれの水溶液も、希釈前の溶液の濃度の増加とともにVMは減少した。混合の体積比が5.000mL:5.000mLの場合に、VMは最小値を示し、その値は、NaCl水溶液では9.959mL、KCl水溶液では9.975mLであった。これらの体積変化はいずれも微小であり、マイクロスケール実験でも検出できない程度であったが、希釈に伴う有意な体積の減少が認められた。本手法は単純かつ容易であり、高校理科（物理・化学）の教材として有用である。

Ispitano je uklanjanje Cd i Zn iona postupkom u koloni iz binarne vodene otopine ukupne početne koncentracije c o (Cd+Zn) ≈ 1 mmol/L, a koncentracijskog omjera kadmija i cinka Cd/Zn = 1,93. Radni ciklus proveden je propuštanjem otopine s vrha prema dnu kolone kroz nepomičan sloj zeolita visine H = 8 cm pri stalnom protoku od Q = 1 mL/min. Tijek radnog ciklusa pratio se određivanjem koncentracije Cd i Zn iona te pH vrijednosti u efluentu. Nakon radnog ciklusa provedena je regeneracija sloja zeolita otopinom NaNO 3 c = 176,5 mmol/L, uz iste radne uvjete. Rezultati su prikazani krivuljama proboja i krivuljama regeneracije, iz kojih su određene točka proboja, točka iscrpljenja, završetak regeneracije te su izračunati karakteristični parametri: kapacitet u točki proboja, kapacitet u točki iscrpljenja, efikasnost kolone te stupanj regeneracije. Proboj je postignut nakon ≈ 44 h pri čemu je obrađeno ≈ 2,7 L binarne otopine, a do točke proboja Cd i Zn ioni vezali su se istovremeno. Iscrpljenje je postignuto nakon ≈ 65 h do kada je obrađeno ≈ 3,9 L binarne otopine. Koncentracija Cd u efluentu neznatno prelazi njegovu koncentraciju u influentu, dok je koncentracija Zn znatno veća od one u influentu, što ukazuje na efekt istiskivanja već vezanih Zn iona iz strukture zeolita ionima Cd iz otopine. Ovo nije očekivano budući da Cd i Zn ioni imaju slična fizikalna svojstva kao hidratizirani ionski radijus, elektronegativnost i energiju hidratacije. Razlog istiskivanja može se pripisati većoj koncentraciji Cd iona u početnoj otopini, u odnosu na koncentraciju Zn iona, što znači da se promjenom koncentracije iona u influentu može utjecati na količinu vezanih iona u radnom ciklusu. Prema rezultatima ciklusa regeneracije veća je količina eluiranih Cd nego Zn iona, što potrđuje da se u strukturi zeolita vezalo više Cd. Potpuna regeneracija sloja zeolita završena je već nakon ≈ 5 h pri čemu je utrošeno svega 0,31 L otopine NaNO 3 . Visoki stupanj regeneracije α R ukazuje na uspješno provedenu regeneraciju čime je omogućeno ponovno korištenje istog sloja zeolita u novom radnog ciklusu, što je od izuzetne važnosti za primjenu u praksi. The removal of Cd and Zn ions by column method from binary aqueous solution with total initial concentration c o (Cd+Zn) ≈ 1 mmol/L, and with concentration ratio Cd/Zn = 1.93 has been investigated. Service cycle has been performed by passing the feeding solution from the top to the bottom of the column through the fixed zeolite bed of height H = 8 cm at a constant flow rate of Q = 1 mL/min. After service cycle, the regeneration of zeolite bed has been performed at the same experimental conditions with NaNO 3 solution of c = 176.5 mmol/L. The progress of the service and regeneration cycles was tracked by measuring the Cd and Zn concentrations and pH values in the effluents. The results are shown by breakthrough and regeneration curves from which the breakthrough and exhaustion points and the end of regeneration have been determined, as well as the characteristic parameters have been calculated: breakthrough and exhaustion capacities, removal efficiency, and the degree of regeneration. The breakthrough has been obtained after ≈ 44 h when ≈ 2.7 L of binary solution has been treated, and until breakthrough the Cd and Zn ions bound simultaneously. The exhaustion has been achieved after ≈ 65 h when ≈ 3.9 L of binary solution has been treated. The concentration of Cd in the effluent slightly exceeds its influent concentration, while Zn concentration is considerably higher than its influent concentration. This indicates the displacement of already bound Zn in zeolite structure by Cd from the feeding solution. This behaviour has not been expected since Cd and Zn ions have similar physical properties such as hydrated ionic radius, electronegativity and energy of hydration. The reason of displacement can be attributed to the higher inlet Cd concentration, compared to Zn. This means that changing the inlet concentration can affect the amount of bound ions in the service cycle. According to the results of the regeneration cycle the amount of eluted Cd is greater compared to Zn, which confirms that the zeolite structure bound more Cd. The regeneration of zeolite layer has been completed after ≈ 5 h wherein only 0.31 L of NaNO 3 solution was spent. The high degree of regeneration α R indicates a successfully performed regeneration. This enables for reuse the same zeolite layer in a new service cycle, which is extremely important for practical application.

When the binary solution, whichi is composed of a solute and a solvent, is diluted with its solvent, volume is not conserved; the total volume of an original solution and an added solvent is not equal to that of its diluted solution. This phenomenon is well known, however, it has been never quantitatively discussed from the viewpoint of science education. In this paper, the method of estimating the volume of a diluted binary solution is first derived. The volume of a diluted solution is obtained from volumes and densities of an original solution and an added solvent and from the density of the diluted solution. Densities of the original and diluted solutions are calculated using an empirical equation, which is a power function of the mass fraction of a solute. Successively, our method is applied to D-glucose and sucrose aqueous solutions in order to examine volume changes in diluting these solutions with water at 20℃, The concentration ranges of original D-glucose and sucrose aqueous solutions are 0-0.6000 and 0-0.8000 mass fractions of solutes respectively. The volume ratios of the original solution to the added solvent are 1.000 mL: 5.000mL, 2.000mL:4.000mL, 3.000mL:3.000mL, 4.000mL:2.000mL, and 5.000mL:1.000mL, For both aqueous solutions, volumes decrease over the 0.2500 solute mass fraction range, and they reach minimum values (5.983mL for D-glucose and 5.963mL for sucrose aqueous solution) at the ratio 3.000mL: 3.000mL. Although these volume changes are too small to be detected using our microscale experiments, the obvious volume decreases are recognized after diluting original solutions Estimating volumes of diluted aqueous solutions is very simple and easy, and it is concluded that our method is useful as teaching material for high school science.

Ispitan je proces uklanjanja olova i cinka postupkom u koloni iz binarnih vodenih otopina ukupnih početnih koncentracija co(Pb+Zn) ≈ 1 mmol/l, a uz mijenjanje omjera co(Pb)/co(Zn) od 0,18 do 2,15. Eksperimenti su provedeni izotermno u staklenim kolonama s nepomičnim slojem prirodnog zeolita klinoptilolita visine 4, 8 i 12 cm. Tijek radnog ciklusa i ciklusa regeneracije pratio se određivanjem koncentracije Pb i Zn iona, te pH vrijednosti u efluentu i regeneratu. Monitoringom pH vrijednosti može se pouzdano i brzo procijeniti točka proboja i završetak regeneracije, što je za praktičnu primjenu od velikog značaja. Rezultati su prikazani krivuljama proboja i krivuljama regeneracije iz kojih su izračunati karakteristični parametri: kapacitet u točki proboja i iscrpljenja, efikasnost uklanjanja, simetrija krivulje proboja, visina zone prijenosa tvari, vrijeme kontakta, količina eluiranih iona, stupanj regeneracije i koncentracijski faktor. Uzastopnim ponavljanjem 12 radnih ciklusa i ciklusa regeneracije postignuto je višestruko iskorištenje zeolita bez smanjenja njegova kapaciteta. Do točke proboja Pb i Zn ioni vežu se istovremeno i razmjerno njihovoj koncentraciji u ulaznoj otopini, a u točki iscrpljenja udio vezanog Pb je veći zbog istiskivanja već vezanih Zn iona Pb ionima iz ulazne otopine. Ovaj je efekt potvrđen regeneracijom zeolita pri kojoj su omjeri količina eluiranih iona nR(Pb)/nR(Zn) značajno veći od Pb/Zn omjera, kao i SEM snimkama čestica zeolita te elementarnom EDS analizom. Regeneracijom zeolita postignuto je potpuno eluiranje iona, a volumeni regenerata su i do 10 puta manji od volumena izvorne otopine. To je od osobitog značaja za primjenu prirodnih zeolita u obradi otpadnih voda. Eksperimentalne krivulje proboja testirane su prema Thomasovu i ADR modelu. Utvrđeno je dobro slaganje eksperimentalnih s modelnim krivuljama proboja, te se dobio uvid u kinetiku i mehanizme prijenosa tvari tijekom procesa izmjene. Removal of lead and zinc from binary aqueous solutions with total initial concentrations co ≈ 1 mmol/l, at different ratios of co(Pb)/co(Zn) from 0,18 to 2,15 has been examined using the column method. Experiments were carried out isothermally in glass columns filled with natural zeolite up to bed depths of 4, 8 and 12 cm. Service and regeneration cycles were studied by monitoring of the Pb and Zn concentrations and pH values in the effluent and regenerate solutions. The measurement of pH values allows efficient determination of the breakthrough point and the end of regeneration. The results are shown by breakthrough curves and regeneration curves and the following characteristic parameters have been calculated: breakthrough and exhaustion capacities, removal efficiency, symmetry of breakthrough curves, height of the mass transfer zone, empty bed contact time, quantity of eluted ions, degree of regeneration, and the concentration factor. Twelve successful service and regeneration cycles were carried out without reducing zeolite capacity. Up to breakthrough, Pb and Zn ions were bound simultaneously according to their concentrations in the influent, while at the exhaustion point the quantity of bound Pb was higher. This is due to the displacement of bound Zn by Pb from the feeding solution. This effect has been confirmed by regeneration of zeolite where the ratio of quantities of eluted ions nR(Pb)/nR(Zn) was much higher than the Pb/Zn ratio in the influent. The displacement effect has also been confirmed by SEM images of zeolite particles and elemental EDS analysis. The regeneration of zeolite provides for complete elution of bound ions and the volumes of regenerates were up to 10 times lower compared to the volume of solutions in service cycles. This contributes to the application of natural zeolites in wastewater treatment processes. The experimentally obtained breakthrough curves have been tested according to the Thomas and the ADR models. The modelled curves showed very good agreement with the experimental ones, and were helpful in estimation of kinetic parameters and mechanisms of mass transfer during the overall process.

The mathematical equation for Separation of the binary aqueous solution is developed by using the Spiegler- Kedem theory. The characteristics of a B-9 hollow fibre module of Du Pont are determined by using these equations and their results are compared with the experimental results of Ohya et al. The agreement between these results is found to be excellent., {"references":["M.W.Vonk and J.A.M.Smit, Thermodynamics of Ternary Systems in\nReverse Osmosis,Desalination,48(1983)105-119.","Sharad K Gupta, Design and Analysis of a Radial - Flow Hollow - Fiber\nReverse - Osmosis System, Ind.Engg. Chem. Res.26(1987) 2319-2333.","D.spiegler and D.Kedem, Thermodynamics of hyperfiltration(reverse\nosmosis)criteria of efficient membranes,Desalination 1(1966)311.","H.Ohya, H.Nakajima,K.Tagaki,S.Kagawa and Y.Negishi, An analysis of\nreverse osmosis characteristics of B-9 hollow fibre module,\nDesalination, 21(1977)257.","Masahide Tanguchi, Shoji Kimura. Estimation of Transport parameters\nof RO membranes for seawater Desalination, AICHE Journal,10, 46(\n2000).","Nakao S and S. Kimura, \"Analysis of Solutes Rejection in\nUltrafiltration\", J. of Chemical Engg. Japan,14, 1 (1981) 32-37.","Sekino M. and N. Fujiwara, \" Analysis of Hollow-Fibre Reverse\nOsmosis Modules,\" Kagaku Kogaku Ronbunshu, 17, 1088-1095(1991).","Masaaki Sekino, Mass Transfer Characteristics of Hollow Fibre RO\nmodules, Journal of Chemical Engineering of Japan, 28(1995)843-846."]}