3." i. \ 1 p x}: .f ‘ ,. ‘3," <. v "'- A, CC Pi... \‘ ts .9.» {-an ‘ 0’, (I ". (k. a ,1 M0 .. 7-7.“ s a. - u ~s‘.-’ \ . . . . l . _ . I ' -~-. ’, . .0 ELECTROHETRIC TITRATION CF OXIDIZING AND REDUCING SUBSTANCES A Thesis Submitted to the Faculty of the Michigan State College of Agriculture and Applied Science in Partial Fulfillment of the Requirements for the Degree of Kaster of Science BY Charles Henry Spurway 1926 H~~v V v v ‘T C12..?.”"~”' ”l . -.-- L‘R‘l - A , )1. VV 1 i " ._/| a v“- ,. t t) 7 V" r‘ " ' >—J ‘ n i'l’. i i N -A_—————-—__4 _, Dwight T. Ewing, Ph.D. Associate Professor of Chemistry Major Professor II II. III. IV. V. VI. VII. III TABLE OF COHTENTS Introduction General Theory Methods and Apparatus Special Points Taken from the Literature of the Subject Concerning the Electrometric Titration of Several Chemical Substances Electrometric Titration Curves Curve Data and Discussion Bibliography I Introduction Electrometric titration methods of chemical analysis, particularly for the determination of small quantities of several of the elements combined in some oxidisable or reduceable form, are coming into general use in laboratories devoted to teaching, research. and the process control of many industries. In addition to the work already done on these methods, there are still many possibilities and some Opportunities for applying them to the qualitative and also to the quantitative determination of other elements, and to the control of other industrial processes. These methods are valuable to chemists because of their case of Operation, accuracy, and time saving qualities. Not only are electrometric titration methods serviceable for analytical procedures, but because they deal with quantity and movement of electrons, or charges of negative electricity, they are applicable to problems involving chemical hypotheses, and theories relating to the state or preperties of matter in solution. As is-the case with practically any division of a general science. the literature dealing with the theory and the problems of electrometric titration is scattered through a large number of scientific and industrial Journals; and hence. is buried from the sight of the average student and investigator in chemical science largely because of the time and labor found I‘D necessary to assemble, arrange, and mentally digest the contents of the many papers extant on the subject. Collecting and cataloging the knowledge on any subject, interesting in itself,and also applicable to the study of various scientific problems is considered advisable. because by this means such knowledge is placed within easy reach of students and other interested persons; and in addition. complete bibliOgraphies of the subject may be maintained. This thesis has for its object, then. four main divisions of effort: (1) An exposition of the general theoretical and practical principles upon which electrometric titration methods are based, more particularly with respect to oxidation and reduction effects; (2) A description of the several analytical methods now in use; (3) A search for possible new correlations that might be exposed by a study of the titration curves found in the literature; and, (4) A complete, up-to-date bibliography of the subject. . O . . e . In a ‘ s Oi ‘ 1 r I o . s n V! e t \. . I. O t o i . . . O V ‘ I o . . II General Theory The theoretical basis for electrometric methods dealing with oxidation and reduction phenomena lies chiefly in the work of the Swedish physicist Arrhenius tn establishing the electrolytic dissociation theory of substances in solution (177;); and lies also in the second law of Faraday which states that the valence of an ion is a function of the number of electrical charges it carries C127).Acids, bases. and salts when in water solution are dissociated into ions (electrically charged particles) and the number of these electrical charges are preportional to the valence of the elements involved. This phenomenon may be graphically illustrated as follows: NaCl -—+ Na+4k Cl- Monovalent dissociation. IgSO4 —+ lg”+ SOZ- Divalent dissociation. A1013 -+ A1”; 013‘" Trivalent dissociation. SnCl4 ~€P antF 012'"! Tetravalent dissociation. Some of the chemical elements may exist in combination in more than one state of valence, and dissociate electrolytically in accord with this valence state, thus, - Ferrous Sulfate - Pe804 «eh-Pektk»80;"’ ++F Ferric Sulfate - Fe2{304)3 —e— 3’9 4‘ 530;“- We can change the valence of iron and some of the other chemical elements by adding or subtracting electrical charges - electrons. The valence of iron from two in the ferrous state ' V e ‘ Q . 4—..— o c. -. can be raised to three in the ferric state by subtracting one electron(adding a positive charge), or from the ferric to the ferrous state by adding one electron(subtracting a positive charge). Pe'H' -- Q = Fe+*+ Fem-q- @ :: Fe++ 'hen an electron, or electrons, are taken from an element in solution the.element is said to be oxidized; and when the Opposite change takes place, the element is said to be reduced. These changes are accompanied by electrical effects which can be observed and measured. The common method of measuring these electrical effects is by comparing them with a normal or a standard electrode which gives a definite electromotive force. The calomel standard cell is the one most commonly used. If an electrode of a noble metal such as a piece of platinum foil or wire is placed separately into solutions of ferric and ferrous ions, a definite potential difference will be set up between the electrode and the ions in each solution, and the value of this potential difference will depend upon the concentration of the iron ions of these solutions. There will be a tendency for the ferrous ions to give up electrons to the platinum wire, charging it negatively, and for the ferric ions to take up electrons from the platinum wire charging it positively. But, if the platinum wire dips into one solution containing a mixture of ferric and ferrous ions, and is connected externally with a normal calomel electrode which in turn makes contact with the ferrous-ferric solution by means of a salt arm making a liquid-liquid Junction, a potential difference is established which is determined by the ratio of the ferrous to the ferric ions in the solution. In the measuring process this potential difference is compared to that of the normal calomel cell. The relationship is expressed by Peter's equation.(6). RT (reduction product) a? (oxidation product) observed potential difference a constant applying to this particular case (reduction product) and is equal to B when 4 ------------------ =-l (oxidation product) the gas constant =volts X coulombs absolute temperature valence of the metal Faraday =-. 96,540 coulombs When applied to the case under consideration, the formula becomes,- Subtracting numerical values and changing to common logarithims, we have,- E - - 0.46 4- 0.058 leg I ..... E, or the potential difference, then becomes a measure of the relative concentration of the ferric and ferrous ions. As the ratio of these ionic concentrations gradually changes, due to the addition of oxidizing or reducing reagents, B will also show a gradual and corresponding change in value until one of the ionic concentrations becomes vanishingly small as compared with the other, when E will show an abrupt change of comparatively great magnitude which may be taken as the end- point of the reaction. The theory may-be applied to all oxidation and reduction reactions, but the constant, C, is different in value for the different chemical elements that may be oxidized or reduced. Some of these constants are given by LeBlanc (17?). The potential at the beginning and end of the reaction depends upon the nature and concentrations of other ions which may be present as well as the concentrations of the ferrous or ferric ions, but the changes in potential due to the addition of reagents are always slight in magnitude until the end-point of the reaction is reached when a great change takes place. It is possible to determine quantitatively two or more substances present in the one solution providing they can be oxidized or reduced by the same reagent, and that their oxidation or reduction potentials are far enough apart in values to give separate end-points within the voltage range obtainable. The oxidation or reduction reaction must progress quite rapidly for the electrometric method to be of value. 0‘ ‘9. e‘ V a )‘1: I a (l 't I? III METHODS A classification of the different systems used in the methods of electrometric titration has been made by Kolthoff (Chem. Weekblad 50,559(1920). Three systems are given by Kelthoff, to which a fourth may be added. 1. The common system, consisting of a stable electrode, unattacked in an acid solution, used with a constant half-cell such as the calomel cell or a similar electrode. 2. The Pinkhof system (Chem. Weekblad 16,1163-7,1919) in which a compensating electrode replaces the calomel half-cell, the potential of the compensating electrode being equal to the stable electrode at the end of the titration. A reversal of polarity marks the end-point in this case. The common disadvantages of this system is that each titration requires a different compensating electrode, and the concentration of substances foreign to the titration may interfere with the compensating effects. 3. The Treadwell system (Helv. Chim. Acta 2,680,1919) is composed of a half-cell replacing the standard electrode which contains an electrolyte having the same composition at the titrated solution at the end-point of the reaction. This system has the same disadvantages as the Pinkhof system being specific for each titration. 4. The bimetallic system of Willard and Fenwick (J.A.C.S. 44,2504,l922) may be mentioned as a fourth system of electrometric titration. In this system the standard half-cell is replaced with an inactive metal or a metal-alloy electrode which shows no great change in potential at the end-point of the reaction. Some of the metals used are tungsten, and alloys of the platinum group of metals. Another form of this system consists of two inactive metallic electrodes, one of platinum, upon which in imposed an e.m.f. equal to the hydrogen overvoltage of the platinum electrode. Some data regarding the specific use of these systems are discussed in connection with the methods used for the several elements that may be determined quantitatively by means of electrometric titration. ESSENTIAL APPARATUS I —,II) . (a) ‘3? I— C. Figure 1. Diagram of the apparatus. P - Potentiometer. A Leeds and Northrup Students' potentiometer is suitable for a great variety of determinations. Ba - Battery. Two dry cells, or a four volt accumulator may be used. R - Resistance for adjusting the electric current in in the (a) circuit. A plug resistance of 11, 110 ohms capacity works well with two dry cells. 3 - A current reversing, double pole, double throw switch. The reversing feature of this switch aids in making voltage readings if the voltage should become negative during a titration. By reversing the (a) circuit current, the potentiometer may be read directly. G - Galvanometer. A sensitive, dead beat, galvanometer is very good for the purpose, although a too sensitive galvanometer is not to be desired for some work. 3.0. - A standard cell, used for calibrating the potentio- meter as a diredt reading voltmeter. r - A high resistance used to protect the standard cell. This high resistance may also be used in the titrating cell circuit to prevent drawing a current from it. C - Titrating cell. These titrating cells may be of a variety of forms depending upon the nature of the work to be done. K1 and K2 - are key-switches used to momentarily close their respective circuits when calibrating or reading the potentiometer. The apparatus illustrated and described belongs to the commonly usedwcompensating system devised by Poggendorf for the measurement of voltages. It consists, essentially, of two electrical circuits, one of which (a) may be set at a 10 known value through the potentiometer, and the value of the other unknown circuit (b) measured by comparison with the circuit (a). Titrating Cells.- Various forms of titrating cells are in general use. If in any particular case it is unnecessary to protect the solutions being titrated from oxidation by the oxygen of the air, or from possible contamination by carbon dioxide gas, or any other laboratory gas or fume; an epen beaker, or other cpen dish of suitable size and shape is all that will be required. On the other hand, a closed container, or cell, is necessary for the titrating of solutions that oxidize readily in the air, or that require elimination of the adsorbed oxygen by eleutration with an inert gas passed through the solution preliminary to the titration, or that need to be protected from gas injury by maintaining constantly an atmosphere of an inert gas over them during the titration procedure. Two common forms of closed containers for electro- titration work are; 1. the titrating head described by Hostetter and Roberts (45), and 2. the closed container used by Ewing and Eldridge (75). Burette tips, electrodes, stirrers, or the delivery points of other pieces of apparatus, or gas inlets and outlets are sealed into the cells in some suitable manner a In the earlier electrometric titration work, a capillary electrometer was used in place of the galvonometer; and for 11 end-point determination only, a common sliding resistance, of the proper value, took the place of the potentiometer. In this case, the end~point readings were taken by constantly adjusting the resistance to hold the electrometer at zero as the titration progressed, and the end-point was shown by a marked deflection of the electrometer. This arrangement is now used sometimes in laboratories where rapid work is required, but the galvanometer has practically replaced the capillary electrometer as a null-point instrument in the electrometric titration work. Titration curves may be plotted from the readings taken in the above manner when the resistance is first calibrated and provided with a scale for interpreting the results. Calibration of the potentiometer.- In calibrating the potentiometer to read as a voltmeter, the potentiometer is first set at its voltage reading corresponding to the exact voltage of the standard cell. The resistance R is then adjusted until by slight tapping of the key K2 the galvanometer shows no deflection. Practically no current should be taken from the standard cell, hence, for accurate work, a rough standard cell should first be used while the preliminary resistance adjustments are being made, and the final adjust- ment then made with the accurate standard cell. For accurate work this calibrating of the potentiometer should precede each titration, especially if titration curves are to be plotted from the voltage readings. 12 Special kinds of electrometric titrating apparatus made in compact, portable forms and adapted to different types of analytical work are new on the market. The vacuum tube generally used in radio sets has also been used in place of the potentiometer for making e1ectro~ metric titrations. For references see Geode(93), Calhane a Cushing(134b), Treadwe11(l68), and Gardner(176). Method of making electrometric titrations.- The actual method of Operation used will depend somewhat upon the nature of the work; certain precautions being necessary in most cases. It is the plan of the writer to give only a general outline of the methods used at the present time. The common technis adapted by investigators for making electrometric titrations is to place a known quantity of a certain oxidisable or reducible solution into the titrating vessel, usually in an acid solution, although some titrations require an alkaline solution, and then titrating this solution with a reducing or oxidising reagent, as the case may require, and the voltage readings taken in a manner that allows for the plotting of a curve with the voltage readings plotted against cubic centimeters of the reagent used, This procedure is known as direct titration. An indirect method of titration is used in cases where a sharp end-point can not be obtained by means of the direct method. The indirect method consists of adding an excess of reagent to the solution to be titrated and then 13 titrating this excess with a reagent that does give a sharp end-point with the first solution used in excess. In making a first study of a reaction, known solutions are used in order to prove the accuracy or advantage of the method before the method is applied to unknown solutions. As stated before, if the end-point alone is desired in a titration it is only necessary to determine the point in the titration where the greatest deflection of the galvanometer takes place. It is advisable to know just about the quantity of titrating reagent that will be required for a determination, and as the end- point is approached, tO add the reagent, drOp by drOp, until the end-point is exactly reached. It must be remembered that in making titrations by the electrometric method the voltage changes are caused by the changing concentrations Of the ions in the solutions, and that any ionic concentration change will cause a corresponding change in voltage. This being the case, the Operator must know, in order to do accurate work, that the only concentra- tion changes taking place are due to the additions of the reagent used, and not due to changes at the electrodes, or to oxidation or reduction effects not due to the reagent added, or to side reactions that may take place under the conditions of the titration. This means that the electrodes should not be attacked by the original solutions, or by the products formed during the reaction; and that the oxygen of the air must be excluded when easily oxidiaable solutions are being used; and 14 also, that possible side reactions do not interfere with the main determination. It is also necesarry to know that the reaction is completed when the end-point deflection occurs . The common method of protecting a titration against air oxidation is to bubble an inert gas through the solution preliminary to the titration Operation in order to remove absorbed oxygen, and then during the titration to maintain an atmosphere of the gas over the solution in the titrating cell. Carbon dioxide, hydrOgen and nitrogen are the inert gases ordinarly used. However, bubbles of the gas should not be allowed to adhere to the metallic electrode, as this tends to form a gas electrode and causes a change in e.m.f. of the cell; hence, the adsorbed oxygen, or other gas, should be removed before the metallic electrode is inserted into the solution. The metallic electrode generaly used is platinum. Some workers prefer platinum foil of a certain size for the metallic electrode, while others have found platinum wire best, at least for certain determinations. The shape and size of the platinum electrode is probably specific for some titrations, but this point seems to have been little investi- gated. These platinum electrodes must be kept clean and bright by washing in acids, cleaning solutions, ignition, scouring, or by electrolyzing deposited substances from them; the most 15 suitable method in any case depends upon the nature of the deposit on the electrode. Mechanical stirring of the solution during the titration process is practically always need. Temperature control is Lunimportant for reduction or oxidation reactions that take place rapidly at room tempera- ture. Where heating is required to hasten the reaction, the usual method is to heat the solution to the required tempera- ture and then titrate rapidly for the end-point. Some workers have found, however, that by cooling the solutions to a low temperature, better results could be obtained. The prOper temperature for a reaction, at least within a certain range, is important for reactions that require heating in order to increase the speed at which they take place. The advantage of using the electrometric end-point in a titration method is its high degree of accuracy, and to make the fullest use of the delicacy of these methods, all standard solutions used for making electrometric titrations should be standardized by the most accurate methods possible for each particular solution. When a high degree of accuracy can be attained in the standardization of the titrating reagents, the electrometric titration method is exceedingly accurate, and very small quantities of a substance may be determined by means of it if sharp end-points may be obtained. 16 So great is the accuracy attainable as compared with the common volumetric analysis, by means Of these methods that many workers in this field recommend that the standard reagents be made up by weight instead of by volume, and that the titrating additions of reagents be made by weight also instead Of being measured from a burst. The degree of accuracy required or desired will probably be a determining factor in this connection with many Operators Of the electrometric titration methods. Another important factOr in electrometric titration is the kind of acid used to acidify the solution being titrated, and the degree or quantity of this acidity necessary for best results. This factoris specific for each titration, within certain limits, and when not known, or can not be determined from the literature on the subject, it must be experimentally determined. Breaking the circuit while taking the voltage readings is sometimes done in order to prevent deposition of metals on the electrodes. The magnitude of the end-point voltage deflection depends upon the intensity Of the reduction or oxidation processes and may be used as a measure of them. 0'! 17 IV SPECIAL POIKTS TAKEK F? n EYE TERATUFE OF TPE SUBJECT COKCERE HG T3? 333 TROLETRIC TITRLTICK OF SEVERAL C3EMICAL ELEAEKTS In the folloWing discussion the several elements and substances that have been investigated by means Of the electrometric titration methods are listed alphabetically. The numbers in parentheses given in connection with the subjects and paragraphs refer to the numbers of the refer- ences in the bibliography appended to this thesis. The "*" were not found in the Michigan references marked with a State College library (Decehber 51, 1925.) This list of subjects with the reference numbers will serve as a cross reference to the bibliography. Antimony.- (107), (147) Antimonous sul hate mav be titrated with potassium p c} A. bromate in various concentrations of hydrochloric acid, 3-20 percent. (107) (C.A. 17, 1604) Antimony in the form of antimonous chloride may be tit- rated with potassium dichronate in the.presence of hydro- chloric acid, 100 cc. of the solution containing 15 cc. of hydrochloric acid (d. 1.18), at room temperature, and with constant stirring. lntimonous chloride and stannous chloride may be titrated together in one sample, but mercuric chloride should be present in the solution in excess when antimony is titrated in the presence of tin. (147) (0.3. 19, 451) 18 Arsenic.- (137), (151) Arsenic lay also be titrated by means of potassium bronate in a 5-20 percent hydrochloric acid solution. ’107) (C.A. 17, 1604) A sodium arsenite solution, 0.0222d, was prepared as recommended by the AmeriCan Society of T sting haterials for steel analysis, and titrated against an iodide solution which had been standardized against potassium bromate. The sodium arsenite was titrated electrometrically with a potassium -permanganate solution, 0.115N, standardized by means Of sodium oxalate. 25 cc. of the permanganate solution was titrated in 100 cc. of nitric acid (d. 1.13) with the arsen- ite solution. A tungsten electrode was used in place of the calomel electrode, as in the presence of potassium chloride in the solution, the theoretical end-point was not obtained. The potassium chloride causes a more complete reduction of the This reaction was also carried out in a 2.5K sulfuric acid solution with 0.0964N sodium arsenite. in the nitric acid solution the'manganese is reduced from a valence of 7 to an average valence of 3.5.-’65n041+ lng.»‘-.s0§+l5 H§+2L~flvff4il$11msogf But in the sulfuric acid solution, the valence is reduced to an average of 2.5;- Mn04? 9 .u. is 054 14 ngzfliv'ii'sffiiemsog.‘ In the electrometric titration of arsenic attention should be paid to details especially acid concentration, 19 teaperature, presence of halide or mangan(us salt, and to standardize the solutions used under the same conditions as they are to be used in the method of analysis. (151) (C.A. 17, 2687) A20 dyes.- (94) The azo dyes were reduced by means of a 0.25N titanous chloride solution in excess and the excess titrated with a 0.05N ferric alum solution. The titrations were carried out in an atmosphere of carbon dioxide. Thiocyanate was not satisfactory as an outside indicator, because of the presence f carton dioxide, and becaus the solutions the selves were 0 sometimes either pink, blue, or green in color. The reaction flask consisted of a 250 cc. Tyrex extraction flask with a a ”1 ne salt- E-hole stepper to accomodate a platinum electrode, t arm of the calomel half-cell, and a buret. Trocedure.- 0.5 to 1.0 gram, f the finely pondered dye, sufficient in quantity to require 50 to 40 cc. of the titanous chloride solution for reduction, was placed into the reaction ' I‘J flask; and 25 cc. of distilled water was then added, the flas- covered loosely, and placed on a steam bath for about 10 min- utes to dissolve or suften the particles. next, 25 cc. of 40 percent sulphuric acid was added, the flask stoppered, and a current of carbon dioxide was passed through for five min; utes. Then the required amount of the titanous chloride solution was added, at least five co. more tha was required for reduction. The liouid was then boiled for five minutes and then cooled to 300 C. in a water bath, and titrated. (94) {0...}... 16, 11:):)‘. 2O Bromine.-l(ll)*, (61), (105), (116), (120)* A known weight of potassium.iodide solution was titrated with a potassium bromate solution in the presence of enoush su furic acid to make the solution about 2H at the end of the experiment, and until about 10 percent of the iodide remained undecomposed. Then the voltage became constant, the titration was completed with potassium permanganate. Experiments in- dicated that in this titration the presence of small anounts of chlorate nad no influence. The iodide solution was also successfully titrated with the bromate solution. The last drops of the bromate solution were added very slowly to avoid running by the end-point, and the whole titration re- quired at least 15 minutes for end-point, and much lonser to \- acquire the data for plotting a curve. Hydrochloric acid may not be present in Quantities in excess of 0.2N. (61) (0.3. 15, 5793) Dutoit and von Weisse used the electrometric method for the titration and separation of the halides, and recommended precipitation With a silver salt or some other suitable precipitant. They call attention to the suitability of the method for determining the halides in very dilute concen- trations as 10-20 milligrams of chloride per liter, or smaller quantities of bromide or iodide. Two end-points are obtained in a mixture of the three halides, the first one is. J. the iodide prec'pitation, and the second one occu s when all r“ the halides are precipitated. -heoe authors claim.t?at 21 iodide may be determined in this way in the presence of a great excess of bromide or chloride. (11) (C.A. 6, 722) Eronate may also be titrated with titanous chloride at a concentration of 0.05N x 1.4663, and protecting the solution by means of carbon dioxide gas. 50 cc. of a sol- ution of potassium bromate, 0.05N, in 200 cc. of boiled water, and 10 cc. of ION sulfuric acid were used for the titration. Uydrochloric acid may be used in place of the sulphuric acid, but should not exceed a concentration of 0.5N ‘ at the end of the titration. The chanse of bromide in hydro- cyanic acid solution to bromine cyanide by titrating with potassium permanganate is too slow for the bimetallic elec- trode system to be used; but the end-point in this reaction may be deternined by means of the usual mononetallic system 'if the titration curve is plotted. This oxidation reouires the theoretiCal equivalent of oxygen, and the oxalate factor of the permanganate may be used. (105‘, (116),(C.A. 17, 397) (C.A. 17, sseex By means of the mercury electrode, chlorides and brom- ides may be titrated electrometrically with mercurous nit- rate, but not in the presence of each oth r. (126) (C.A. 18, 1793) COPPGT-- (10)*. (ee)*, ( 20)‘. (157)* W? Dutiot and von .eisse made a detailed study of the prin- ciples of concentration cells as applicable to voluuetric analysis by precipitation. They produced polarization in 22 the cell by means of a feeble, imposed current and used revolving electrodes to prevent this current from setting Up concentration differences. The several points studied are: (1) Speed of stirring. .2) Effect of foreign substances. (5) Effect of dilution. (4) Influence of the auxillary current. (5) Duration of the titration. Cepper was titrated with a solution of potassium ferrIDQACI’ ~ -.oc4940- . . ’..-.-. o . ‘ . .... . 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Titration of potassium iodide -- 0.25584 grams in 100 cc. of 10 percent sulfuric acid solution. -- 5. lith potassium permanganate —- 3.161 grams per liter. 6. With potassium dichromate -- 4.903 " H n 7. With potassium brcmate —- 2.785 " H 8. With potassium iodate -- 5.567 " " " Titration of potassium ferrocyanide -- 0.8448 grams in 100 cc. of 10 percent sulfuric acid solution. -- 9. With potassium permanganate -- 5.161 grams per liter. 10. With potassium bromate -- 2.783 " n n 11. With potassium dichromate -- 4.903 " " " Titration with potassium permanganate -- 5.161 grams per liter.-- 12. Of potassium ferrocyanide -- 0.8448 grams in 100 cc. of 10 percent sulfuric acid solution. 13. 14. 15. 16. 17a, 18a, 19. 20. 21a, 22a, 25a, 24. 25. 26. 79 0f ferrous sulfate -- 0.556 grams in 100 cc. of 10 percent sulfuric acid solution. 0f potassium iodide -- 0.25384 grams in 100 cc. of 10 per- cent sulfuric acid solution. Titration with potassium bromate -- 2.785 grams per liter. 0f potassium ferrocyanide -- 0.8448 grams in 100 cc. of 10 percent sulfuric acid solution. 0f potassium iodide -- 0.25384 grams in 100 cc. of 10 percent sulfuric acid solution. Titration with potassium permanganate. -- 17b. 0f vanadium and iron. 18b. 0f vanadium and uranium. 0f iron. Of iron, vanadium, and uranium in 700. sulfuric acid. 21b,210. 0f iron, vanadium, and uranium in two additions of sulfuric acid of 4 cc. each during the titration. Titration with potassium dichromate. -- 22b. 0f iodate in sulfuric acid. 23b. 0f bromate in sulfuric acid. 0f chlorate in hydrochloric acid. Titration with potassium permanganate. -- 0f iodide and bromide in the presence of chloride. 0f iodide in the presence of chloride. 27. 80 0.021 grams of chromium titrated with ferrous sulfate. 28a,28b. Ferrous and titancus ion titrated with potassium permanganate. 29a,29b. Ferrous and titanous ion titrated with potassium dichromate. 50a,50b. Reverse of curves 28a and 28b. Ferric ion and perman- ganate titrated with titanous ion. 51a,5lh. Reverse of curves 29a and 29b. Ferric ion and dich- 32. 34. 35. romate titrated with titanous ion. 75 cc. of 0.055 ferrous sulfate in a high concentration of hydrochloric acid titrated with 0.1N potassium dichromate. Electrodes -- platinum; 0.1N potassium chloride calomel electrode. 25 cc. of 0.1N ferrous sulfate, 20 percent sulfuric acid, titrated with 0.1M potassium permanganate. Electrodes -- platinum; tungsten. ferrous sulfate in 55 percent hydrochloric acid solution titrated With 0.1K potassium dichromate. Electrodes -- platinum; standard silver chloride half-cell. Ferrous sulfate in 55 percent hydrochloric acid solution titrated with 0.1N potassium dichromate. Electrodes -- platinum; silver chloride platinum. 81 Terrous sulfate in 20 percent sulfuric acid titrated with 0.1K potassium permansanate. Electrodes -- platinum; silver chloride platinum. 250 cc. of solution containing 75 cc. of a 0.05m pot- assium dichromate solution titrated with 0.1K ferrous sulfate in different concentrations of hydrochloric acid. 0.4M hydrochloric acid. 0.8M hydrochloric acid. 2.0M hydrochloric acid. Titration with potassium permanganate -- (a) Uranium solution -- 1 cc. equals 0.0151 grams. (b) Permansanate solution -- 0.1011N. (c) Ferrous solution -~ 0.1001N. 10 cc. of uranium solution, 40 cc. of 2 cc. concentrated sulfuric acid in so of solution, 80-900 -- reduced. 0a,40b. Uranium titrated with permanganate. 41a,4l‘b. H H H H 42a,42b,42c. Uranium plus 1 cc. of ferrous sulfate solution titrated with permanganate. Uranium titrated with permanganate in various concentrat- ions of sulfuric acid. -- 45a,45b. 20 cc. sulfuric acid in 100 cc. total volume. 44. 45. 10 H " H H H '1 H H 5 7' H I? 'Y H H H H 468. , 46b 0 2 H " " N H n n n 47. 48. 49. 50. 51. 52. 55. 54. 55. 56. 57. 58. 59. 60. 61. 82 Potassium biniodate treated with excess iodide and the excess iodide titrated with potassium permanganate - 0.02N iodate in 150 cc. with sulfuric acid. 0.05N " " 250 " " ” " iodate titrated with permanganate in sulfuric acid. 4.1 mg. ferrous iron in 70 percent hydrochloric acid titrated with 0.01 potassium dichromate. 4.24 mg. ferrous iron titrated with 0.01m potassium dichromate. In 67 percent sulfuric acid. H 33 n n u n 17 n n u ' 50 " hydrochloric acid. Effect of adding ferric iron -- No ferric iron. 500 ppm. of ferric iron. 1500 ppm. of ferric iron. 2500 ppm. of ferric iron. 0.558 mg. ferrous iron and 1660 mg. ferric iron. Ferric iron titrated with 0.005N stannous chloride. Stannous chloride titrated with-0.01N potassium dichromate. Ferric iron reduced with stannous chloride in excess and both titrated with 0.01 potassium dichromate.-- 85 62a,62b. In 40 percent hydrochloric acid. 5a,65b. " 50 " n n 64a,64b. " 60 " " n 65a,65b. " 70 " vv n 66a,66b. " 90 " n n Ferrous iron titrated with 0.01N potassium permanganate - 67. 2.87 mg. ferrous iron in 17 percent sulfuric acid. 68. 2.87 mg. ferrous iron in 10 percent sulfuric acid with 28.7 mg. of ferric sulfate. 69. 2.87 mg. ferrous iron in 2.5 percent of 85 percent phos- phoric acid with 57.5 mg. of ferric sulfate. 70. 2.87 mg. ferrous iron in 2.5 percent of 85 percent phos- phoric acid with 57.5 mg. of ferric sulfate and 5 percent sulfuric acid. 71. 2.87 mg. ferrous iron and 6 percent of the phosphoric- sulfuric acid mixture with 250 mg. of iron as ferric chloride. 72. 2.87 mg. ferrous iron and 6 percent of the phosphoric- sulfuric acid mixture with 250 mg. of iron as ferric chloride, and 5 percent of hydrochloric acid. Ferrous iron titrated with potassium dichromate in various concentrations of hydrochloric acid. -- 75. 50 cc. concentrated hydrochloric acid, 100 cc. water, 1.4 gm. ferrous ammonium sulfate. 74. 50 cc. concentrated hydrochloric acid, 100 cc. water, 1.05 gm. ferrous ammonium sulfate. 84 75. 100 cc. concentrated hydrochloric acid, 50 cc. Water, 1.05 gm. ferrous ammonium sulfate. 76. 10 cc. 0.1N potassium bromide titrated with approximately O.lN mercurous nitrate. 77. 10 cc. 0.1N potassium chloride titrated with approximately 0.1N mercurous nitrate. A general consideration of these electrcmetric titration curves shows that it is quite impossible to obtain from them distinct theoretical correlations of first importance. Nearly all of the investigational work pertaining to them has been done from the standpoint of analytical chemistry alone; and the chief aims of the investigators seems to have been, to discover suitable reagents for the titrations, to obtain well-marked end-points, and to determine small quantities of unknowns. In general, it may be stated that the end sought was rapidity and refinement of analytical methods. To this end, various kinds of electrodes, various concent- rations of reactants and of acid solutions, and different mechanical operations have been employed; all of which is contrary in principle to the systematic research necessary in this kind of work in order to establish fundamental chem- ical concepts. Some of the points taken under consideration are as follows: 85 l. The end-point placement on the graph with reference to the zero e.m.f. and the magnitude of the deflection of the curves. . 2. is there a "neutral point"? 5. Correlation with the Periodic Law. 4. Slope of curve deflections or Speed of the reactions with reference to kind and strength of acid used. 5. Energy relationships. 6. Chemical activities. 7. Summary of rules for electrometric titration. 8. Scope and Opportunities in the field of electrometric titration. A cursory examination of the curves will suffice to show that no distinct relationship exists between the mag- nitude of their end-point deflections and their position on the graphs with respect to the zero e.m.f. point. However, from the standpoint of their position on the graphs alone, the curves can be classified, roughly, into three groups: 1. Those ranging from 400 millivolts up. 2. Those occupying ‘the intermediate position of O to 400 millivolts. 5. Those having the e.m.f. range of 0 down to the lowest negative voltage obtained. A list of the reactions of class 1. -- Curves l to 4 -- oxidation of ferrous iron. curves 5 to 8 -- oxidation of potassium iodide. UUI‘VGS Curves 12 to 16 -- oxidation of ferrocyanide, Curve 210 9 to 11 -- oxidation of 86 ferrocyanide. ferrous iron, and potassium iodide. -- oxidation of uranium. Curves 22b to 25b -- reduction of iodate and bromate. Curves 25 to 26 -- oxidation of iodide and bromide. Curve 27 -- reduction of chromium. Curves 28b and 29b -- oxidation of ferrous iron. Curves 50b and 51b -- reduction of ferric iron. Curves 52 to 56 -- oxidation of ferrous iron. Curves 40b, 41b, and 420 -- oxidation of uranium and ferrous iron. Curves 47 to 49 -- oxidation of iodide. Curves 50 to 59 -- oxidation of ferrous iron. Curves 62b to 66b -- oxidation of ferrous iron. Curves 67 to 75 -- oxidation of ferrous iron. A list of the reactions of class 2. -- Curves 20 to 21b -- oxidation of vanadiun. Curves 17b, 18b -- oxidation cf vanadium. Curve 19 -- oxidation of ferrous iron. Curves 28a, 29a -- oxidation of titanium. Curves 50a, 51a -- reduction of titanium. Curve 55 -- oxidation of ferrous iron. Curves 57 to 59 -- reduction of dichromate. Curve 60 reduction of ferric iron. 87 oxidation of tin. Curve 61 - Curves 62a, 66a reduction of ferric iron. Curve 76 bromide and mercurous chloride. Curve 77 - chloride and mercurous chloride. A list of the reactions of class 5. -- Curves 17a, 18a, 21a -- oxidation of vanadium. Curves 40a, 41a, 42a -- oxidation of uranium. Curves 44, 45, 46a -- oxidation of uranium. The basis for the above classification is apparent, and can be referred to the initial and final electrode potentials of the several substances used in the titrations. The high- est voltage is obtained with permanganate, and the lowest with uranium in a low state of oxidation. From these data we can conclude that permanganate is a strong oxidizer and uranium a strong reducer. metals with two or more states of oxidation, or valences, will give end-points for these differ~ ent states, and the end—point curves will occupy different positions on the graph, the lowest oxidation state correspond- ing to the lowest position on the graph. The electrode pot- ential may be negative for a low state of oxidation and pos- itive for a higher state of oxidation. The electrode potential of a solution measures 'ts oxid- izing or reducing power. Therefore, in general, the greater the difference in electrode potential between an oxidizing solution and a solution to be oxidized, the greater the act- 88 ivity of the oxidizing reaction and hence the greater the 'speed of reaction and the sharper the end-point deflection of the measuring potentiometer. The same conditions apply to reducing reactions. in both cases, however, the strength of the acid titrating solution is an important factor, as is also the kind of acid used to acidify the titrating solution. The disturbing influences are the electrode potentials of the products of the reaction, and the kind of electrodes used in the determinations. The titration of uranium with permanpanate may be taken as illustration of the consideration. Curves 43a and 43b represent this titration in 20 percent sulfuric acid solution. In this case the change in potential is great being from about -530 to +1150 millivolts for both stages of oxidation of the uranium compound; but the endpoint deflect- ions are not sharp. in a 2 percent solution of sulfuric acid, however, as illustrated by curves 46a and 46b, about the ' same change in voltage is observed while the two end-points are very distinct. Another illustration of this same phenomenon may be 'found in the titration of stannous and ferrous ion with dich-' romate - curves 61 to 66. The influence of kind of acid is illustrated in the titration of ferrous iron with dichromate - in both sulfuric and hydrochloric acid solution - curves 51 to 54 - in which ease the hydrochloric acid solution gives the best end-point. 89 ‘In case certain reactions do not give suitable end-points, these end-points may be improved by reversing the reaction. Curves 28 to 31 illustrate a case of this kind. Ferrous and titanous ion titrated with permanganate or dichromate do not give suitable curves; but when ferric ion and dichromate or permanganate is titrated with titanous ion, sharp end-points are obtained in case of the ferric ion and permanganate, and for the ferric ion alone in case of the dichromate. This eXperiment shows, also, that titanous ion will reduce ferric ion, or that one metal ion will satisfactorily reduce or oxidize another metal ion provided that the values of elec- trode potentials are far enough apart. For slow oxidation or reduction reactions, or in cases where sharp end-points may not be obtained, it is often ex- pedient to add a known excess of the oxidizing or reducing reagent, and after sufficient time has elapsed for the re- action to be completed, this excess of reagent is titrated by means of another quickly acting reagent that does give a sharp end-point, and the unknown ion calculated from the difference between the ouantity of reagent first added and the excess found by titration. Again, the oxidation process may be easier applied to a certain metal than the reduction process in titration. in this case, the metal is first reduced by some knoun efficient proéess after which it is titrated with an oxidizing reagent, or this process may be reversed. 90 in only one case does the end-point e.m.f. approximately coincide with O e.m.f.; that is in the reduction of perman- ganate with titanous ion in the presence of ferrous ion. The number of elements investigated is too small to provide a means of correlation with the periodic law. More- over, oxidizine or reducing power may be only relative; for instance, ferrous iron may reduce permanganate and oxidize a stannous salt. A metal in a low state of oxidation may be caused to reduce the same metal in a higher state of oxidation. The formula eXpressing change in free energy for an electrometric reaction change is ~45F — E.N F. While the change in-energy accompanying a change in valence for 1 gram mole is l Farady, it is now known if this value Can be eXperimental y realized. The difficulties enco‘ntored in electrometric titration processes are the unknown liquid- liquid potential values, and the unknown values of chemical activities of electrolytes in the presence of other electro- lytes - acids or salts. The data at hand give no values that may be used to calculate energy changes from a theor- etical standpoint. The magnitude of the curve deflections is, however, an effect of this free energy.change. From an examination of the data on electrometric tit- ration methods, with special reference to oxidation or re~ duction reactions, some rules and precautions may be evolved 91 as follows: 1. Choose active oxidizinr and reducing reagents. 2. Suitable metallic electrodes are of importance. 5. Select chemical reactions that are complete. 4. Slow reactions may be used if an excess of reasent is added and this excess back-titrated or titrated With a third substance. 5. A pro- per temperature is important for some reactions. 6. The interaction of components should not disturb the titration process. 7. A certain strength and kind of acid will be found necessary for sharp end-points. 8. Avoid substances that interfere with the reaction -- external oxidizing or reducing substances. 9. Weighing the solutions is more accurate than measurino them, especially for the determin- ation of small quantities of unknowns. 10. All reasents should be accurately standardized by the best known methods, and by applying the electrometric titration method, in the same manner as the resular titration is to be conducted, when possible. Only a limited number of elements and chemical com- pounds have been studied by means of the electrometric titration methods, and an opportunity exists to study those elements that have not already been employed in these methods. very little work has been done on phoSphates, carbonates, sulfides, chromates, and oxalates, and the formation of colloids by means of oxidation or reduction methods. Another possible field for the use of these methods lies in a study 92 of the effects of catalyzere on chemical reactions and the energy changes involved. Almost no work has been done with these methods in the field of organic analyses, except on aldehydes and reducing sugars. ...] VII BIETIOJRAPUY 1892 Oxidniion cells. 13, EE7-408. 1835 leotronetric Chef]. , 11. 4.36.910 9 The potential of hydrofo neuman. Z. physig. Chem., 1937 ihe use of the eloctronoter as of 7. “016° -‘- 1r“ hunec‘ u \L- 90-“. kafi‘ k. . 53- :01. r Lad A gaannoneter titrition Oxidation nnn reduction cells, plex ions Z. physik. Chen., 25, 195- 2 6. 190? Stvdies on oxidation potentials. Chem., 24, 2? 5- -62. W. D. Eencroft. Z. Robert and several Bottfer. notk(d. nnd on *Veir e1 eotroitlotive phfi’si}; .3 "J Tehrei . Z P 14,1JoJ-2500 indicator in "o . 1' I (‘1' \Jllx.‘ I Z. pk Salomon. 3 force. Ru metals. th e inflrunune 95 rw. . b:](:"—A1. , Bernhard tho titration -\ f‘ t blflleijo , L1. . tilelctrcwflfcx1., of com- CO dolph Feter 9b. 10. 11. ‘4. 1'7 1‘. 14. 15. 94 1902 The theory of oxidation and reduction cells. Carl 0 Fredenhngen. Z. anorg. Chem., 49, 538-463- 1911 m 1 ine employment of the electrometric method for the ~ estimation of the acidity of tan liquors. H. c. Qand Lind U0 ('0 T131137. . :0 SOC. Chcji'lo lnlo , 3"), 30 III. Frecipitation followed ty change of potential. 1?. Determination of copper and silver. 7. Titration and separati(n of the halides. Dntoit and ”9 q C I n , 7 ‘ fir:- sse. .. Chen. phgs. 9, 516 all H. C ‘64'... (COA. 6, 722‘ The titration of potass'um cyanide in the presence of potassium ferrocynnide. 7. D. Treadwell. u. anorf. Chem.. 71, 219-225. ’C.A. 5, 55911 1913 Gene applications of the hydrogen electrode in analysis, \ 7v 3 research and teaching. Joel i. Hildebrand. J.n.C.S., :5, £347-71. ‘ (0.31. 7' £307"), The increase in the oxidizing potential of the dichromate ion on platinum Caused ty certain reducing aren s. an improved method for the electrometric determination of ti] ferrrvs salts. 1. 3. Forbes and . P. ?artlett. J.A.C.S.. I . 35 1527-58. (C.A. 7 5v ()1 a) . Separation of chlorides and hronides by silver nitrate accordine to the conductivity method._P. Dutoit and Reeb. 463. (C.A. 8, 472i 9 17. 18. 19. F; ‘9 0 ‘5 ‘u ‘J. (‘7) ()1 (“D 95 1914 Automatic titrations. 1. Automatic electrometric tit- ration of dichromate and ferrous iron. E. Tierel. Z. anal. Chem., 53, 755-62. (C.A. 9, 838) The electro-titrametric method and its application to general analytical chemistry. T. P. Vesselink van Vuchtelen & Arno ltano. J.A.C.W., 36, 1795-1805. (Co-(A10 8, 341““) 1916 conductivity cell for electro~titration. H.E.Rohhins. An. Cour. 501., 41, 249-50. {0.1. 10, 987) The determination of chromium and vanaditm in steel by electrometric titration. u. L. Kelley & Joe. E. Conant. ind. Eng. Chem. 8, 719-23. ‘ (0.3. 10, 2179) - Electronrtric titration of vanadium. G. n. Kelley & .09. L. Conant. 3.3.0.3., 38, 341-51. (C.A. 10, 729) The volumetric determinaticn of alkaloids ty physio- chemical methods. P. Dutoit & leyer-Uev*. Jour. Chem. ehvs., 14, 553-60. (0.1. 11. 1eoo) o) 1 17 KO new form of conductivity cell for electro-titration. F. E. Robbins. 3.3.0.3., 59, 646-8. 'C.A. ll, 1062) Electrometric methcd of titration and its application to the examination of gastric juices. Leonor Lichaelio. tiochem. z., 79, 1-54. (0.1. 11, so 3 (‘3 ‘4 ['21 '7 CC] C) O 07. l. 96 1917L7cont. Convenient a paratuo for electrometric titration depend- ins on cha nse of oxidation potential. Determination of fl - chronium in steel. ~. u. Lelley, J. R. (i small amounts oi Adams a C. A. Wiley. 1nd. Ens. ihen., 9, 730-2. 10.1. 11, £567) Conductivity measurements upon oxidation-reduction re- actions. ”rahen Edgar. 3.1.0.3., 59, 914-28.(C.L.11,15J0. 11 1'" '.1:e elee.ro1etric titration of zinc. 1. us sell V. Bich- OWO1::’7. ind. Eng. Uhefll., 9, 668-71. (00“. 1.1, 2:: f3) :. “fad-9h. .‘lxcad. r:Cj.. , 7, 141.3. (8.1L. 1]., lEOC’) ‘ Tne determination of iron in glass ('3 and. {ohn B. Ferguson. '1 '3' '7' T; (‘1 J. , (_1 L-" . C ()1 r1 A '1 . J- 8' p Ind. Eng. 0hem., 9, 941- The meas Ireu1ent of oxidation potentials at mercuzy cloc- trodes. G. S. Forber & H. 7. Richter. 5.1.0.3., SJ, 1140. (C.A. 11, 2365) 1J18 The determination of manganese in steel in the preser cc of chromium and vanadium by electrometric titration. G. t. Kelley. I-I. G312 ncer, C. 3. 11111151101111, and '3. Gay. F-‘I nd. Eng. Chen., 10,19J-2.. (0.A. 12, 4581 a method for making electronotric titrations of solutions conta inino proteins. iohn C. Baler & Lucius 1. Van Dyke. (our. Eiol. 0hen., 35 157-45. (0.4. 12, 1383) New reduction methods in volvnetric a11alys's. inc 1t & Hibhert. p. 65. Zonsmans, Green a Company. 35. 56. 58. 59. 40. 41. 42. 43. 97 1919 Electrometric titrations. I. D. Treadwell & L. Weiss. Helv. Chim. Acta., 2, 680-97. (C.A. 15, 1262) The theory of electrometric titrations. 7. D. Treadwell. Helv. Chim. Acta., 2, 672-80. (C.A. 15, 1265) End point in oxidation titrations determined by means of the potentiometer. I. M. Kotthoff. Chem. Weekblad, 16, 408-16. (C.A. 15, 1263) Electrometric method for the determination of ferrocyan- ides depending on a change in oxidation potential. 'G. L. Kelley & R. T. Bohn. J.A.C.S., 41, 1776-83.(C.A. 14, 30) Electrometric titration of mixtures of acids. P. A. Meer- burg. Chem. Weekblad, 16, 1358-47. (C.A. 14, 257) The application of electrometric titrations. J. Pinkhoff. Chem. Weekblad, 16, 1165-7. (C.A. 14, 257) The estimation of ferrous iron by electrometric titration. I. M. Kolthoff. Chem. Weekblad, 16, 450-61.(C.A. 14, 3204) Electrometric analysis with potassium ferrocyanide. E. Mflller. angemo. Chem., 32, I, 351-2. (C.A. 14, 5205) The electrometric titration of plant juices. A.R.C. Uass. Soil Sci., 7, 487-91. (C.A. 14, 420) Titration by means of changes in potential. J. Pinkhoff, Pharm. Weekblad, 56, 794. (C.A. 13, 1793) The determination of vanadium in steels by electrometric titration. The selective oxidation of vanadium salts by nitric acid in the presence of chromic salts. 0. L. Kelley, 98 1919, cont. J.A. Wiley, R.T. Bohn, & W. C. Wright. Ind. Eng. Chem. 11, 632-34. (0.4. 13, 1985) 44. Electrometric titration of iodides. i. M. Kolthoff. Chem. Weekblad, 16, 926-9. ’C.A. 13, 2167) 45. Electrometric titrations, with Special reference to the determination of ferrous and ferric iron. J. C. Hastetter and H. L. Roberts. J.A.C.S., 41, 1337-57. (C.A. 13, 2319) 46. The electrometer as an indicator for titrations. J. Pink- hoft. Pharm. Weekblad, 56, 1218-34. (C.A. 13, 3102) 47. Electrical apparatus for use in electrometric titrations. R. S. Roberts. J.A.C.9., 41, 1358-62. (C.A. 13, 2302) 48. The effect of dilution in electro-titrimetric analyses. G. A. Freak. Jour. Chem. 800., 115, 55-61.(C.A. 13, 2645) 49. The rapid electrometric determination of iron in sone Optical glasses. J. B. Ferguson and J. C. Hostetter. Jour. Am. Ceram. Soc., 2, 608-21. (C.A. 13, 2580) 49a. Rapid determination of chromium in steel by electrometric titration. G. L. Kelley and W. C. Wright. iron Age, 103, 1507. (C.A. 13. 1802) 50. A simple method for the analysis of bearing metal and similar alloys. 0. Oesterheld and P. Houegger. helv. Chim. Acta. 2, 398-416. (0.3. 13, 3106) 51. G. Redrick. Diss. Dresden. 52. J. Pinkhoff. Diss. p. 44. Amsterdam. 99 1920 53. The oxidopotentiometric titration of iodides in the presence of chlorides and bromides. I. M. Kolthoff. Rec. trav. Chim., 39, 208-4. (C.A. 14, 3204) 54. The use of electrometric titration methods. 0. 0. Bann- ister. Electrician, 85, 535-7. (C.A. 15, 352) 55. Review of the application of potentiometer titrations. I. M. holthoff. Chem. Weekblad, 17, 659-64. (C.A. 15, 996) 56. The electrometric titration of phenols. i. M. Kolthoff. z. anorg. allegem. Chem., 112, 187-95. (0.3. 15, 1669) 57. The electrometric titration of alkaloids and their salts. I. M. Kolthoff. Z. anorg. allegem. Chem., 112, 196-208. (0.4. 15, 1670) 57a. The determination of hydrogen ions. W. M. Clark. Chapt. XIV. The relation of hydrogen electrode potentials to reduction potentials. 58. The acidimetric estimation of heavy metals in their salts. 1. M. holthoff. z. anorg. allegem. Chem., 112, 172-86. (0.2. 15, 1670) 1921 59. The electrotitration of hydriodic acid and its use as a standard in oxidimetry. W. 9. Hendrixson. J.A.C.S., 43, 14-23. (C.A. 15, 639) 60. The theory of electrometric titrations. W. D. Treadwell. Relv. Chim. Acta., 2, 672-80. (0.1. 15, 1263) 61. 62. 63. 64. 67. 68. 100 1921, cont. Electrometric determination of bromate, dichromate, nitrite, and chloride ions. 7. S. Fendrixson. J.A.C.S., 43, 1509—17. (C.A. 15, 3793) The electrometric titration of iodides by means of per- manganate. 1. M. Kolthoff. Rec. trav. Chim., 40, 532-8. (0.4. 15, 3799) The determination of vanadium and chromium in ferrovan- adium by electrometric titration. C. L. Kelley, J. A. Wiley, R. T. thn, and 7. C. Wright. Ind. Eng. Chem., 13, 939-41. (C.A. 15, 3955) The determination of chromiun in ferrochromium by elec- trometric titration. G. L. Kelley and J. A. Wiley. 1nd. Eng. Chem., 13, 1053-4. (0.4. 16, 37) Simple and rapid electrometric method for the deter- mination of cobalt in an ammonical electrolyte and its recovery from cobalt nitro-B-naphthal. K. Wagonmann. Metall u. Erz, 18, 447-9. (C.A. 16, 695) The acidimetric titration of dichromate. I. m. Kolthoff and E. H. Vogelenzanz. Rec. trav. Chim., 40, 681-5. (C.A.—l6, 1056) The determination of iodic acid and silver by electro- metric titration. W. S. uendrixson. J.A.C.%., 43, 858-66. (0.4. 15, 1668) Oxidimetric determination of manganese in hydrofluoric acid solution. I. Josef. Halluta and Josef. Christ. nonateh., 41, 555.71. (0.2. 15, 2800) 69. 70. 71. 72. 73. 74. 75. 76. 77. 101 1921LAcont. The electrometric titration of hypochlorous acid. W. D. Treadwell. Helv. Chim. Acta, 4, 396-405. (0.4. 15, 3052) Electrometric control in chemical industry. Erik. K. Rideal. Chem. Age, 5, 232-3. (0.4. 15, 3797) Modified laboratory apparatus. 0. 0. Kiplinger. Ind. Eng. Chem., 15, 715. , (0.4. 15, 3569) Reductions with zinc and cadmium in volumetric analysis. 7. D. Treaduell, n. Luthy, and A. R. Rheiner. Helv. Chim. Acta, 4, 551-65. (0.4. 15, 5041) 1922 The application of amalgams in volumetric analysis. III. Estimation of iodic, bromic, and chloric acids. Suetaro Kikuchi. J. Chem. Soc. Japan, 45, 175. (0.4. 16, 1716) The use of the iodine (I2) electrode in potentiometric titrations. l. M. Kolthoff. Rec. trav. Chim., 41, 172-91. (0.4. 16, 2277) Electrometric titration of uranium with potassium per- manganate and potassium dichromate. D. T. Ewing and E. F. Eldridge. 3.4.0.3., 44, 1484-9. (0.4. 16, 2459) The electrometric determination of cyanogen in the pres- ence of halogens. Erich. muller and Hans Lauterbach. Z. anorg. allpun. Chem., 121, 178-92. (C.A. 16, 2818) The use of potassium ferrocyanide in potentiometric titrations. I. The titration of potassium ferrocyanide 78. 79. £1 80. 81. 82. 83. 84. 102 1922, cont. by means of potassium permanganate. I. M. Kolthoff. Rec. trav. Chim., 41, 343-52. (0.4. 16, 3281) II. The potentiometric titration of zinc. Ibid. 41, 425-37. (0.4. 16, 3281) Electrometric titration of ferrocyanic acid. Erich Muller and Pans Lauterbach. Z. anal. Chem., 61, 398-403. (0.4. 16, 3601) The electrometric titration of dichromate with ferrous sulfate. Jarion Eppley and 7. 0. Vasburgh. J.4.0.S., 44, 2148-56. (0.4..16, 3931) lectrometric titrations. 4. Lassieur. Bull. soc. Chim., 31, 817-31. (CJA. 17, 37) Bimetallic electrode systems in electrometric analysis. I. Systems comprising two dissimilar metals. H. R. Willard and F. Fenwick. J.A.C.S., 44, 2504-15; 2516-19. (0.4. 17, 37;38) The electrometric determinations of end points. E. Muller. 3. ans. Chem., 35, 563-6. (0.4. 17, 38) The electrometric standardization of titanous solutions. W. S. Rendrixscn and L. M. Verbeck. J.4.C.S., 44, 2382-7. (0.4. 17, 38) Electrometric titration of sulfurous acid with perman- ganate. W. S. Hendrixson and L. M. Verbeck. Ind. Eng. Chem., 14, 1152-5. (0.4. 17, 59) 85. 86. 87. 88. 89. 90. 92. 94. 105 1922, cont. Electrometric determination of nickel with silver nitrate. Erich. muller a Bans Lauterbach. Z. anal. Chem., 61, 457-64. (0.4. 17, 249) Some applications of the oxygen electrode, air electrode, and oxidation potential measurements to acidimetry and alkalimetry. N. H. Furman. J.4.0.S., 44, 2685-97. (0.4. 17, 505) The successive electrometric titration of iron, vanadium, and uranium. R. T. Gustavson and 0. M. knudson. J.4.0.S., 44, 2756-61. (0.4. 17, 507) Potentiometric titration of copper. E. Lintl and E. Wattenberg. Ber. 558, 3366-70. (0.4. 17, 702) The electrometric determination of iron and vanadium when present together. Erich Muller and H. Just. Z. anorg. allegem. Chem., 125, 155-66. (0.4. 17, 1401) Acidimetric titration of magnesium in its salts. I. M. Kolthoff. Rec. trav. Chim., 41, 787-94. (0.4. 17, 2092) 4 simple method of electrcmetric titration in acidimetry and alkalimetry. P.F.Sharp and E.B. McDougall. J.4.C.S., 44, 1193-6. (0.4. 16, 2277) 4 continuous reading electrotitration apparatus. K. R. ‘GCOde. JOAQCOS.’ 44, 26-9. (GOA. 16, 665) Electrometric titration of azo dyes. D.0. Jones and H.R. 189. Ind. Eng. Chemo, l4, 46*8. (00A. 16. 1155) 95. 96. 97. 98. 99. 100. 101. 104 1922, cont. Electrometric titration as a means of determining the free sodium sulfide in a sulphur black dye bath. W. W. Russell and T.T. Arnold. 4m. Dyestuff Rep., 10, 346; 375-6; 451-2. (0.4. 16, 3208) Construction of platinum coated glass electrodes and methods of measuring with them. 4. Eilert. Z. angew. Chem., 35, 445-6; 452-5. (0.4. 16, 4095) Titrations in ethyl alcohol as solvent. Edna R. Bishop, Esther B. Kittredge, and Joel E. hildebrand. J.4.0.S., 44, 155-40. (0.4. 16, 885) The effect of alkali on the titration of certain metals with ferrocyanide. W. D. Treadwell and D. Cheruet. nelv. chim. 40ta, 5, 633-9. (0.4. 17, 38) Reductions with cadmium in volumetric analysis. W. D. Treadwell. nelv. Chim. Acta, 5, 732-43. (0.4. 17, 39) 4 simple apparatus for electrometric titration. 7. E. Garner and C. 4. Waters. Jour. Soc. Chem., 41, 337-8. (0.4. 17, 229) 4 new vessel for electrometric titration. W. T. Eovie. J.4.C.3., 44, 2892-5. (C.A. 17, 654) 1925 Electrometric acidimetry and alkalimetry without the use of hydrogen. P.A. Van der meulen and F. Wilcoxson. Ind. Eng. Chem., 15, 62-3. (0.4. 17, 505) 105. 104. 105. 106. 107. 108. 109. 110. 105 1923L cont. 4 new method for the electrometric titration of van- adium in the presence of iron and chromium. H. H. Willard and F. Fenwick. 3.4.0.3., 45, 84-92. (0.4. 17, 507) The bimetallic electrode applied to neutralization reactions. H. R. Willard and F. Fenwick. J.4.0.S., 45, 715-16. (0.4. 17, 1396) The electrometric titration of the halides in the pres- ence of one another. R. H. Willard and F. Fenwick. J.4. 0.8., 45, 623-33. (0.4. 17, 1397) Electrometric determination of sulfur in soluble sulfides. 8. R. w'illard and F. Fenwick. J.4.C.S., 45, 645-9. (0.4. 17, 1398) Potentiometric titration of arsenic and antimony. E. Lintil and H. Wattenberg, Ber. 56, 472-80. (0.4. 17, 1604) Electrometric titration of molybdenum with a titanous salt. H. R. Willard and F. Fenuick. J.4.C.S., 45, 928-55. (0.4. 17, 1766) The electrometric titration of selenium in the presence of tellurium, iron, and 00pper. H. H. Willard and F. Fenwick. J.4.0.5., 45, 933-9. (0.4. 17, 1766) An electrometric study of the neutralization of phos- phoric acid by calcium hydroxide. G. R. Tendt and 4. R. Clarke. 3.4.0.8., 45, 881-7. (C.4. 17, 1767) 111. 112. 113. 114. 115. 116. 117. 118. 119. 106 1923, cont. Electrotitration with the aid of the air electrode. N. H. Furman. Trans. Amer. Electrochem. Soc., 43, 1923. (0.4. 17, 1930) Electrometric determination of zinc with silver nitrate. Erich. Muller and 4. Adam. Z. Electrochem., 29, 49-53. (0.4. 17, 2093) Electrometric titration of reducing sugars. Wanda E. Daygett and 4. W. Campbell with J. L. Whitman. 3.4.0.8., 45, 1043-5. - (0.4. 17, 2545) The electrometric titration of zinc and cadmium. T. Muller. z. anorg. allgem. Chem., 128, 125-30. (0.4. 17, 2689) Electrometric titration of acids and bases with an anti- mony indicator electrode. Alfred Uhl and Wilhelm Kes- tranck. Monatsh. 44, 29-34. (0.4. 17, 3303) Electrometric titration of iodate, bromate, chlorate, and ferrocyanide with titanous sulfate. 7. S. Fendrixson. 3.4.0.8., 45, 2013-7. (0.4. 17, 3306) The electrometric determination of manganese. Eric. muller and 0. Wahle. Z. anorg. allgem. Chem. 129, 33-40. (0.4. 17, 3306) Recent applications of electrotitrimetry to chemical analysis. Jean Barbandy. Technique Moderne, 15, 545-53. (0.4. 17, 3846) Simultaneous electrometric determination of iron and manganese, Erick. Muller and 0. Wahle. Z. anorg. allgem. Chem., 130, 63-8. (0.4. 18, 363) 122 O 125. 124. 125. 126. 107 1923, cont. Simultaneous electrometric determination of copper and silver with potassium thiocyanate. Erick. Muller and 4. Rudolph. 3. Anal. Chem., 63, 102-11. (C.4. 18, 640) 4 titrometric micro-method for the determination of sodium. E. muller. Helv. Chim. Acta 6, 1152-61. ’ «0.1. 18, 641) Electrometric determination of vanadium and uranium alone, together, and in the presence of iron. Eric. Muller and 4. Flath. 3. Electrochem. 29, 500-8. (00:10 18, 643) Electrometric method of measuring acidity and alkalin- ity. H. T. Bovie. J. Optical Soc. 4mer., 8, 149-68. (0.4. 18, 797) The titration of ferric chloride with sodium hydroxide, usins the oxygen electrode, a proof of the non-existence of iron oxychloride. R. B. Smith and P. M. Giesy. J. 4m. Pharm. Assoc., 12, 855-6. (0.4. 18, 1099) Simultaneous electrometric determination of iron and manganese. Eric. Muller and O. Wahle. Z. anorg. allgem. Chem., 132, 260-4. (0.4. 18, 1628) The use of the mercury electrode in potentiometric titrations. Determination of halides, cyanides, sulfides, and thiosulfates. I. M. Lolthoff and E. J. A. H. Verzyl. Rec. tran. chim., 42, 1055-64. (0.4. 18, 1799) 127. 128. 129. 130. 132. 133. 134. 108 1923, cont. Electrometric determination of cobalt with silver nitrate. Eric. Muller and Kust Gabler.:3. anal. Chem.. 62, 23-8. (0.4. 17, 942) The electrometric titration of zinc and lead in the presence of one another with potassium ferrocyanide. E. Muller and Kust Gablerx Z. anal. Chem., 62, 29-34. (0.4. 17, 943) The titration of hypochlorous acid. 4. Schleichter. z. anal. Chem., 62, 329-35. (0.4. 17, 2543) Standardization of solutions used in iodimetry. 3. Pop- off and F. L. Chamhers. 3.4.0.5., 45, 1358-60. 1 (0.4. 17, 2247) ‘The titration of solutions of permanganate and sodium arsenite. 7. T. Hall and C. E. Carlson. 3.4.0.9., 45, 1615-20. (0.4. 17, 2687) The titration of silver ions and chloride ions in the presence of protective colloids. W. D. Treadwell, S. Janett, and M. Blumenthal. Helv. Chim. 4cta, 6, 13-8. {0.4. 17, 3003) The influence of alkali on the titration of certain metals with ferrocyanide. W. D. Treadwell and D. Chervet. Helv. Chim. Acta, 6, 550-9. (0.4. 17, 3005) An electrometric method of following certain inorganic hydrolytic reactions. G. S. Tilley and O. C. Ralston. Trans. Am. Electrochen. Soc. 44 (preprint)(0.4.17, 2836) 109 1923LAcont. 134b. An application of the vacuum tube to chemistry. D. F. Calhane and R. E. Cashing. 1nd. Eng. Chem., 15, 1118-20. $0.4. 17, 3846) 1924. 1340. The accuracy of the potentiometric titration of zinc with ferrocyanide. I. M. Zolthoff and E. 3. 4. H. Verzyl. Z. anorg. allgem. Chem., 132, 318-20. (0.4. 18, 1627) 135. The electrometric determination of soluble sulfates. E. muller and R. Wertheim. z. anorg. allgem. Chem., 133, 411-6. (0.4. 18, 1626) 135b. Electrometric titration of mercury with ammonium thic- cyanate. R. Muller and O. Eeuda. z. anorg. allgem. Chem., 134, 102-4. (0.4. 18, 1959) 136. The potentiometric determination of chlorides in the presence of colloids. P. Siebert. Chem. Weekblad. 21, 167-9. (0.4. 18, 1960) 137. The estimation of nitrates by electrometric titration. 3. B. Robertson and 4. 3. Belling. 3. S. African Chem. Inst., 7, 9-13. (0.4. 18, 1960) 138. The practical utility of the potentiometric titration of zinc with ferrocyanide. E. 3. 4. H. Verzil and I. M. Kolthoff. Rec. tran. chim., 43, 380-8. (0.4. 18, 2482) 139. The electrometric titration of boric acid in the pres- ence of polyphenols and organic acids. M. G. Mellon and V. N. Xorris. P. Indiana 4cad. Sci., 35, 85-91. (0.4. 18, 2484) 140. 141. 142. 143. 144. 145. 146. 110 1924, cont. The electrometric titration of nickel and cobalt with potassium cyanide. E. nuller and W. Schluttip. Z. anorg. allgem. Chem., 134, 327-43. (0.4. 18, 2662) Electrometric titration - investigation of its methods and application to certain metallurgical analyses. G. A. to Shires. 3. Chem. net. Mining 800. S. Africa. 24. 9-45. (0.4. 18, 2851) The electrometric determination of barium alone, and in the presence of calcium. E. Muller and R. Wertheian z. anorg. allgem. Chem., 135, 269-72. (0.4. 18, 3017) Electrometric titration of ferrocyanic acid with potass- ium iodide. E. Muller. Z. anorg. allgem. Chem., 135, 265-8. (0.4. 18, 3020) The potentiometric determination of vanadium, chromium, and iron in the presence of each other and the use of the method in steel analysis. I. M. Kolthoff and 0. Tomicek. Rec. trav. chim., 43, 447-56. (0.4. 18, 3571) The theory and practice of electrometric titration. Fr. Auerbach and E. Smolczyk. Z. physik. Chem., 110, 65-141. ,(0.4. 19, 222) The application of titanous chloride to potentiometric titrations. I. General considerations - the reducing action of titanous solutions. I. n. Kolthoff. Rec. tran. chim., 43, 768-74. II. Purity, preparation, and standard- ization of the titration liquid. I. m. Iolthoff and 0. 111 1924, cont. Tomicek. Ibid. 775-83. III. Estimation of oxidizing anions. O. Tomicek. ibid. 784-97. IV. Estimation of oxidizing cations. ibid. 798-807. (0.4. 19, 449) 147. Electrometric titration of antimony and tin by potass- ium dichromate. n. H. Fleysher. 3.4.0.3., 46, 2725-7. (0.4. 19, 451)' 148. Electrometric determination of formaldehyde. E. muller and W. Low. 3. anal. Chem., 64, 297-302.(0.4. 19, 452) 149. The electrometric titration of hydrazine and its salts. E. 0. Gilbert. 3.4.0.9., 46, 2648-55. ‘ (0.4. 19, 452) 150. Electrometric titrations. E. Muller. Metall 1L Erz, 21, 265-9. (0.4. 19, 620) 151. The electrometric determination of tin from hydrochloric- oxalic acid solution. E. Eckert. Metall 11 Erz, 21, 202-4. (0.4. 19, 621) 152. The behavior of electrodes of platinum and platinum alloys in electrometric analysis. R. G. Van Naue and F. Fenwick. 3.4.0.3., 47, 9-29 (1925) (0.4. 19, 795) 153. Potentiometric determination of bismuth alone and in the presence of lead. E. Lintl and 4. Rauch. £1.anorg. allgem. Chem., 139, 397-410. (0.4. 19, 798) 154. Theory of certain electrometric and conductometric tit- rations. E. D. Eastman. 3.4.0.8., 47, 332-7. 155. 156. 157. 158. 159. 160. 161. 112 1924, cont. Oxidation potentials of ferrous and ferric salts in concentrated hydrochloric and phosphoric acids. S. B. Carter and F. B. Class. J. Chem. Soc. 125, 1880-8. (C.A. 19, 208) A convenient power-line circuit for the potentiometer. A. Eeighton. Ind. Eng. Chem. 16, 1189-90.(0.A. 19, 422) The titration of ferric and cupric salts separately and in the presence of one another, also in the presence of antimony, by means of titanous chloride. 1. M. Kolthoff. Rec. trav. Chim. 43, 816-22. (0.A. 19, 450) A new dial potentiometer. A. berthelot. Bull. soc. chim. biol. 6, 683-6. (0.A. 19, 1211) Quantitative electro-analyses. J. H. Frydelender. Rev. prod. chim. 27, 757-62. (C.A. 19, 1233) Electrometric titration of chlorides. E. Muller. Z. Electrochem. 30, 420-3. (0.2. 19, 1236) Potentiometric determinations with mercuric salts. E. Muller and H. Aarflat. Rec. trav. chim. 44, 874-8. (0.1. 19, 1387) 1925 Electrometric titrations with special reference to the use of titanous chloride for one analysis. A. Mcmillan and W. C. Ferguson. J. Soc. Chem. Ind. 44, 141-2 T. (C.A. 19, 1828) 164. 165. 166. 167. 168. 169. 170. 171. 1925,_cont. The electrometric titration of hypochlorous acid. A. Schleicher and L. Toussant. Z.ana1. Chem. 65, 399-405. (0.4. 19, 1829) The electrometric titration of chlorous acid and its determination in the presence of hypochlorous acid. A. ’Schleicher and W. Wesly. Z. anal. Chem. 65, 406-11. (C.A. 19, 1829) Electrometric titration in the estimation of ferrous and ferric iron in magnetites. H. 8. Adam. J. S. African chem. Inst. 8, mo. 1, 7-10. (C.A. 19, 1832) An improved calomel electrode. 0. J. Schollenberger. Ind. Eng. Chem. 17, 649. (0.A. 19, 1969) Electrometric titration. J. C. brumich. ind. Eng. Chem. 17, 631-2. (0.A. 19, 1999) The use of radio receiver tubes for electrometric tit- rations. W. D. Treadwell. Helv. Chim. Acta. 8, 89-96. (C.A. 19, 1999) New calomel half cells for industrial hydrogen-ion measurements. H. 0. Parker and C. A. Darmerth. Ind. Eng. chem. 17, 637-9. (C.A. 19, 2147) The potentiometric standardization of potassium perman- ganate solutions with sodium oxalate. 0. del Fresno. Z. Elektrochem. 31, 199-200. (C.A. 19, 2314) Electrometric titrations using quinhydrone. H. niklas and A. Hock. z.angswu. chem. 38, 407-9. (0.A. 19, 2314) 114 1925, cont. 172. Differential electro-titration. D. C. Cox. J.A.U.S. 47, 2138-43. . (0.A. 19, 2610) 173. Electrode vessel for liquids heavier and lighter than the liquid junction potential eliminator. L. E. Dawson. J.A.C.S. 47, 2172-3. (0.A. 19, 2761) 174. Standardization of solution used in iodometry. II. S. Popoff and J. L. Whitman. J.A.U.S. 47, 2259-75. (0.1. 19, 2921) 175. The potentiometer determination of cerium. O. Tomicek. Rec. trav. Chim. 44, 410-5. (C.A. 19, 2922) 176. continuous measurement of the e. m. f. of titration cells. Arthur W. Gardner, Thesis for degree of B. 3., M. 3. 0., 1925. 177. A Text-Book of Electra-Chemistry. Max Le Blane. Trans. by Whitney and Brown. The Macmillan 00., N.Y., 1910. w ......lvilkfiuhuwuulfiE .. hi I ht»... b..E[EEl-o§.i{. 9|- ]. I? a )))sblv) «In; " '.'-, "." "_ .- - ‘ ‘f a ‘ t‘b;_h,; .4!) 3 : “.4; V ‘f:.'~’.'l.n.:A‘i‘ . ‘u . - (.A _J . . . . . . M ‘ 3'25]? ' '~.-.- . t.- 1'- 4 'L‘L .‘I' d 3'19, .. .- ... 3772 193870 ..a ..‘ 1,! r- . .‘ ,'._ in . A": Spurway I, ‘3‘?“ wk: , Z'fi-"J'V- ,- Ir r- n r w. fifi'fo' “E: .c’ffxgfit}fi $2.1?- ' ' [29" *- “if -' *-"€““’~ + *1: c,‘ 05%." 3“; ._ :5; '._fi. 1. ,-‘ 31293 02446 6942