STORAGE BATTERIES THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO STORAGE BATTERIES THE CHEMISTRY AND PHYSICS OF THE LEAD ACCUMULATOR BY HARRY W. MORSE, PH.D. ASSISTANT PROFESSOR OF PHYSICS IN HARVARD UNIVERSITY gorfe THE MACMILLAN COMPANY 1912 All rights reserved Ml, Engineering Library COPTBIGHT, 1912, BY THE MACMILLAN COMPANY. Set up and electrotyped. Published February, 1912. J. 8. Cashing Co. Berwick & Smith Co. Norwood, Mass., U.S.A. CONTENTS CHAPTER PAGE I. INTRODUCTORY AND HISTORICAL ... 1 II. SOME ELECTROCHEMICAL FUNDAMENTALS . 10 III. ABOUT IONS 30 IV. THE FUNDAMENTAL CELL-REACTION . . 39 V. THE ACTIVE IONS 47 VI. SOME PERTINENT PHYSICAL QUERIES . . 56 VII. ENERGY RELATIONS 64 VIII. REACTIONS AT THE ELECTRODES ... 80 IX. CHARGE AND DISCHARGE 94 X. CAPACITY 116 XI. EFFICIENCY 141 XII. INTERNAL RESISTANCE ... . . 148 XIII. PHYSICAL CHARACTERISTICS .... 172 XIV. FORMATION OF PLANTE PLATES . . . 179 XV. PASTE PLATES . ... . . .194 XVI. DISEASES AND TROUBLES ... . . 205 XVII. SOME COMMERCIAL TYPES ,, . . 225 XVIII. ACCUMULATORS IN GENERAL .... 246 APPENDIX . . . . . . . . . . 255 238199 STORAGE BATTERIES CHAPTER I INTRODUCTORY AND HISTORICAL 1. Into our present age of power, where we reckon by thousands and tens of thousands of kilowatts, there has come down from a previous era one single form of the galvanic cell which retains sufficient commercial importance to be worth consideration in connection with modern power plants and modern power operation. This is the lead-sulphuric acid accumulator. It was invented and perfected in the heyday of galvanic cells at a time before the dy- namo and the electric motor had any technical im- portance. In our own laboratory, hidden away in the attic where cast-off things are stored, lie the remains of the big Bunsen cells which were once the source of our heaviest currents and with which the remarkable phenomena of current electricity were shown to classes and in public lectures in those days. These same cells were used to charge small storage cells of the original Plante type mere strips STORAGE. BATTERIES of lead, separated by soft rubber insulators arid rolled into spiral form ; then formed with the aid of the primary cells, by a series of reversals, until the plates attained a certain capacity. One of these cells is shown in Figure 1. With these storage cells, which have low resistance and high current-giving capacity even in comparison with the large Bunsen cells, the most wonderful experiments could be performed experiments which are to us now so commonplace and so much a part of our everyday life that their de- scription brings a smile from the high- school boy who has studied physics and chemistry. These cells would run an arc light for several minutes; heat small platinum wires to the melting point ; provide current for electro- magnets of power enormous for that FIG. i. Original time. It was the duty of the labora- type of Plants ^ orv ass i s tants to set up the battery accumulator. . (About i full * Bunsen cells. Huge zincs in dilute size.) sulphuric acid and great blocks of car- bon were arranged in glass jars with porous cups, and from this fuming source the storage cells were charged all day, to be used the day following in demonstrations of the power of the electric current. After the charge was finished the big Bunsens were taken apart and cleaned up, then stored away until INTRODUCTORY AND HISTORICAL 3 the time for the next lecture on electric currents approached. These early Plante batteries were so arranged that they could be easily thrown into parallel connection, and in this way they could be charged from the Bunsen battery of a few large cells. We still use one of these batteries of 20 cells, dating from the early eighties or earlier. After charge was com- plete the simple mechanism permitted all the cells of the set to be connected in series by simply turn- ing the handle through 90, and clips were provided to show the melting of wires of various metals by the current. The current which could be drawn from these small sets of storage cells reached its maximum at forty or fifty amperes an enormous value then, a mere bagatelle now, for we have electrolytic cells and electric furnaces which require tens of thou- sands of amperes for their operation. Since then lead cells have grown in size along with everything else electrical, and I have seen large batteries which can furnish thirty or forty thousand amperes for a short time and ten thousand for several minutes of discharge. 2. No one of the very numerous primary cells which have been devised and patented has ever reached commercial importance for the heavier work of the present period, though a few have survived to 4 STORAGE BATTERIES do the lighter tasks. The Leclanche and numerous similar types are used in large numbers for bell- ringing installations and similar open-circuit appli- cations. And the dry cell has a very large and distinct place of its own in sparking batteries for motor cars and boats and everywhere that internal combustion engines are used. Certainly well over ten million of these little primary cells are made and used each year in the United States. From the beginning of the nineteenth century until the early eighties was the era of the primary cell. Then came the dynamo and the motor, ac- companied by improvements in our main prime source of power, the steam engine, and the stor- age cell has grown along with all of these in a somewhat subordinate place. It is a mere assistant, to be called on for temporary aid in time of need, either to help over an ugly peak in the load on the prime source, or as insurance to be called in when the main source is disabled for a short time, and its aid is often quite invaluable under these conditions. As a real factor in the problem of prime power sources it has of course no place at all. There is not much value in prophecies about scien- tific or technical things and no particular credit is due the prophet who utters them. Nevertheless, I feel impelled to say that I believe the day of the primary cell will come again. From every funda- INTRODUCTORY AND HISTORICAL 5 mental and theoretic point of view we must admit that it should be possible to make a primary galvanic cell which should be more efficient than a steam engine can possibly be ; more flexible as a primary source of power ; a better appliance in every way. 3. At first glance a lead-sulphuric acid storage cell seems a very simple and uninteresting sort of machine. It is only a plate of lead and a plate cov- ered with lead peroxide, dipping into rather concen- trated sulphuric acid. But for those who make them and those who care for them in service they become much more complex and puzzling, and worth careful consideration. As an integral and essential part of many power arrangements they are of inter- est to the engineer and as a complex of puzzles and problems they demand attention from the electro- chemist and the physicist. Many books have been written about them, some purely scientific and others nearly purely technical. As far as the fundamental chemical reaction is concerned we seem to be on pretty firm ground, and there is every reason to be- lieve that we know how the cell works. But there is still plenty of room for speculation and research on the more minute physical changes and a good many questions on such important matters as forma- tion, cementing of pastes, sulphation, and life under various conditions cannot even now be answered very clearly. 6 STORAGE BATTERIES A very large number of combinations have been suggested for storage battery purposes since Plante began to study his cell in the late fifties, but until within the last few years no one of them has seemed able to meet the rather difficult and peculiar require- ments. Now comes the Iron-Nickel Oxide-Alkali combination as applied by Edison in this country and Jungner on the continent of Europe, and this type seems destined to find a place of its own in light traction work. But by far the greater part of all storage battery plates now made are descendants of the original Plante type hardly recognizable with their highly developed, ribbed, or corrugated surfaces, and formed in the factory by rapid methods, but still " Plante " plates. We have in active use in our own laboratory a unique battery which harks back to the earliest form. It has twenty thousand cells, made of test tubes, and the plates are merely corrugated strips of lead. It is used to give the small currents necessary for vacuum tube and spark work, and it was formed by the old method of re- versals (see page 179) until it reached the needed capacity. 4. Faure was the inventor of the " paste " plate, and this seemed at first so great an improvement that prophets were not wanting to predict that the older type, with its greater weight, comparatively small capacity, and higher cost, would be completely INTRODUCTORY AND HISTORICAL 1 ousted by the new invention. These prophecies have not been fulfilled. The. paste plate has been gradually relegated to traction work and to duty where weight is the important factor, and the plates which are direct descendants of the Plante originals do the really hard work. It took much experience and expense to reach the decision that the Faure plates could not compete in the more strenuous posi- tions, but now we seem to appreciate fairly well the limitations of both types. 5. As the storage battery developed to a point where it could handle real power loads, there came a time when its powers were somewhat overestimated. It was suggested for many positions where it would have been quite unfit for the work for farm pur- poses, for motor cycles, and even for airships. For long-continued discharge, where it must take the place of the prime source of power over considerable periods of time, the storage battery is often a cum- brous and expensive substitute for the source itself. But for many kinds of work, and especially where a very large amount of power is needed suddenly or for short periods, the battery is the ideal machine. In many modern plants the load fluctuations are very great a thousand per cent or more, and this within a fraction of a minute. No mechanical arrangement can absorb this and regulate the load on the power source in a satisfactory way. But a storage battery 8 STORAGE BATTERIES can, for there is hardly a limit to the rate at which large-surface Plante plates can be discharged or charged without injury. In certain classes of work in submarines, as a source of under- water power, for example the bat- tery is an absolute necessity. In the regulation of irregular loads it is of the utmost importance, and in emergency or " stand-by " work as well. Car and train lighting systems demand its use. It has proven itself economical and efficient in traction work, espe- cially for electric road vehicles. Study of the storage battery calls for attention to two rather distinct viewpoints one chemical, the other physical ; and these will be found of "nearly equal importance. The questions about the funda- mental reactions, and many others as well, are purely chemical. Questions about the life of the cell, and its behavior in service, are nearly purely physical. In manufacture or operation the chemical side must be kept in mind, but the anatomy and physiology (and sometimes the pathology, too) of the individual plate are matters of prime importance. Underlying all, we will need as a foundation for study the funda- mental ideas and laws of general electrochemistry. The following chapters are based on lectures which have been given for the last few years at Harvard University. In the course the work on storage cells is preceded by study of the general theory of gal- INTRODUCTORY AND HISTORICAL 9 vanic cells, and the simplest of this theory has been included in this book. No attempt has been made to give any of the detail of storage battery engineer- ing, but only to introduce the reader to the peculi- arities of the cell itself. CHAPTER II SOME ELECTROCHEMICAL FUNDAMENTALS 6. Theoretically any chemical reaction whatever which takes place of its own accord can be so coupled and arranged that it will work as the source of energy for a galvanic cell. Practically there are difficulties which exclude a large percentage of the known reactions of chemistry from such service. It is also true that a great many of the combinations which have practical value as primary cells can be considered theoretically reversible enough to be used as storage cells. As a matter of fact, only a very few of the cells which have been used or thought of are chemically and mechanically reversible enough to fit them for actual use as storage cells. In some cases the fault is in the reaction itself, and the cell is not chemically reversible. In others, the reaction reverses smoothly enough, but the materials of the cell do not go into and out of solution well. Here the fault is a mechanical one. As far as the general theory is concerned, we must choose fundamentals which fit all the cases, even those which cannot be realized practically. 10 SOME ELECTROCHEMICAL FUNDAMENTALS 11 7. Faraday's Law. We have one general funda- mental electrochemical law, which apparently fits every case, and which brings order of the simplest kind out of what at first appeared to be a most cha- otic mass of unrelated material. This is Faraday's law, and it states the relation between the quantity of material used up in a galvanic cell and the quan- tity of electricity which can be obtained from it. This law says : The amount of each substance which takes part in an electrochemical reaction is proportional to the quantity of electricity which passes through the circuit. And when various substances enter an electrochemical reaction, their amounts are proportional to their chemical equivalent weights. Numerically, and in terms of a unit later to be de- fined : 96,540 coulombs pass through the cell and the external circuit with each gram-equivalent of each substance involved in the reaction. 8. Faraday's Definitions. This law applies to elec- trolytes. Faraday himself felt the necessity of a careful set of definitions for the new ideas involved in this law and its application, and no one has since given better ones, so we shall use them wherever it is possible to do so. To quote Faraday (" Experimental Researches," Series VII, 1834): 12 STORAGE BATTERIES "... In place of the term pole, I propose using that of Electrode, and I mean thereby that substance, or rather surface, whether of air, water, metal, or any other body, which bounds the extent of the decom- posing matter in the direction of the electric current. . . . The anode is therefore that surface at which the electric current, according to our present ex- pression, enters. It ... is where oxygen, chlorine, acids, etc., are evolved; and is against or opposite the positive electrode. The cathode is that surface at which the current leaves the decomposing body, and is its positive extremity ; the combustible bodies, metals, alkalies, and bases, are evolved there, and it is in contact with the negative electrode. "... Many bodies are decomposed directly by the electric current, their elements being set free ; these I propose to call electrolytes. . . . " Finally, I require a term to express those bodies which can pass to the electrodes. ... I propose to distinguish such bodies by calling those anions which go to the anode of the decomposing body, and those passing to the cathode, cations, and when I have occasion to speak of them together, I shall call them ions. Thus, the chloride of lead is an electrolyte, and when electrolyzed evolves the two ions, chlorine and lead, the former an anion, and the latter a cation. ..." Figure 2 shows the different parts of a cell as Faraday denned them. SOME ELECTROCHEMICAL FUNDAMENTALS 13 These definitions of Faraday's were made with the greatest care, but since they were formulated, rather careless use has sometimes been made of them. Note the term anode. It is the surface where the current enters the cell, and Faraday meant just exactly this whenever he used the word. The plates of a cell are not anode or cathode in this sense, but the surface between plate and DIRECTION cell solution is. OFCURRENT ^ There will often be occasion to retain this strict meaning of the word. Again, an electro- lyte is the body which carries the current and which EL TRODE ELECTR INODE) (CATHOD f E n I ANIOM ELECTROLYTE CATHION FIG. 2. The parts of an electrolytic cell. is at the same time decomposed by it. In this sense a dry salt is not an electrolyte, but a solution of a metallic salt, or a molten salt, belongs in this class. 9. Electrical Units. Before we can apply this law of Faraday's we should review a few more electrical definitions. In what is called the practical system, we use as unit of quantity of electricity one coulomb. This is derived from the unit of current, the ampere, and one coulomb is the quantity of electricity which passes through a circuit altogether, when a current of one ampere has been flowing constantly for one 14 STORAGE BATTERIES second. These units have been fixed with reference to the magnetic effect of a current and not specially, with reference to Faraday's law. It is, however, an easy calculation to state them in terms of units which bear directly on electrochemical effects. Suppose we have in the circuit an amperemeter which measures the current in amperes. We keep the current con- stant and note the entire time during which it flows through an electrolytic cell in which silver is being deposited from silver nitrate solution. We will find that one ampere flowing for one second deposits 0.00111775 gm. of silver. The equivalent weight of silver is in this case the same number of grams as its atomic weight, and has the value 107.88 gm. The number of coulombs required to deposit this weight of silver is then 107.88 0.0011175 96,540 coulombs. This same number of coulombs will deposit the equivalent weight of any other metal which can be electroplated in the same way, and it is the electro- chemist's unit of quantity of electricity. If the silver were to be used in a galvanic cell as a source of power, exactly the same relation holds be- tween the weight of silver and the quantity of electricity 107.88 gm. of silver always travels SOME ELECTROCHEMICAL FUNDAMENTALS 15 through an electrolyte and dissolves or precipitates at the electrode in company with 96,540 coulombs. Silver ion is univalent, and the equivalent weight is the same as the atomic weight. In most of its reactions, chemical and electrochemical, copper forms a bivalent ion. This means, that in company 'A B FIG. 3. Diagram of apparatus to show Faraday's law. with the atomic weight of copper (63.6 gm.) twice 96,540 coulombs pass through the circuit; so the equivalent weight of copper is 31.8 gm., and this is the electrochemist's unit weight of copper. 10. Experimental Arrangement for Faraday's Law. Figure 3 gives diagrammatic representation of an experiment to illustrate Faraday's law. Current is supplied by the battery A and passes first through the tangent galvanometer B, which measures it, and then on through the various cells in which electro- 16 STORAGE BATTERIES chemical reactions take place. In (7, a molten salt, silver chloride, for example, is decomposed. D might represent a copper coulometer, in which copper is dissolved at one electrode and precipitated at the other. The same arrangement might be used for many other metals. HI is one form of silver coulometer, and here the current enters at a silver anode, which goes into solution, and leaves the cell at the surface of a platinum crucible (cathode) on which silver is deposited. The electrolyte is a strong solution of silver nitrate. Last in the row is a gas coulometer jP, containing dilute acid or alkali as electrolyte and having platinum electrodes. Oxygen gas is formed at the anode, the electrode where the current enters the apparatus, and hydro- gen gas is evolved at the other electrode. Suppose we have sent a constant current of one ampere through the circuit for 96,540 sec. We have weighed the electrodes before and after the passage of this current, and we have measured the volumes of the two gases produced. We should find : 1. At (7, 107.88 gm. of silver dissolved from the wire at which the current enters the cell and the same weight of silver deposited on the other wire. The electrolyte remains unchanged. 2. At Z>, 31.8 gm. of copper dissolved at one plate and precipitated at the other. No change in the electrolyte. SOME ELECTROCHEMICAL FUNDAMENTALS 17 3. At E, the same amounts of silver dissolved and precipitated as in C. 4. At F, 8 gm. of oxygen formed, or 5.6 1. if measured at C. and 760 mm. pressure, and at the other electrode, 1 gm. of hydrogen, having a volume of 11.2 1. 5. Inside the cells at A, there will have been exactly equivalent effects, and they will be the same in each cell. Whatever the materials of the anode and cathode, equivalent weights of each will have entered into reaction, for as far as the application of Faraday's law is concerned, it makes no difference whether work is performed as the result of a reac- tion, or must be performed from without in order to make the reaction take place. The law describes every electrochemical reaction, and has been shown to be as exact as any law we have. 11. Practical Application. Let us examine some applications of this law. A great deal of copper is purified in this country by an electrolytic process. It is interesting to calculate the quantity of electric- ity needed to deposit a pound of copper in this way. 1 Ib. = 453 gm. 96,540 coulombs deposit 31.8 gm. We therefore need 453 31.8 X 96,540 = 1,376,000 coulombs per pound. 18 STORAGE BATTERIES Since an ampere is 1 coulomb per second, it will require 1,376,000 ouo = 382 ampere-hours ooOO to deposit a pound of copper in a single cell. 382 amperes deposit 1 Ib. of copper per hour in a single cell, and if we wish to obtain a ton of copper per hour in such a cell, it would take a current of nearly 760,000 amperes to give the desired result. As a matter of fact cells of this size are never used. It is better to arrange a number of cells in series, so that the current flows through one after the other and produces the same effect in each. The yield of copper is then to be found by multiplying the yield per cell by the number of cells. The atomic weight of lead is about 207, and it is formed from a bivalent ion, so the equiva- lent weight of lead is 103.5. Rather more than three times as much lead as copper is deposited by the same quantity of electricity. The calculation is x 96,540 = 422,000 coulombs per pound of lead. 12. Electrolysis in the Daniell Cell. In the Daniell type of primary cell the chemical reaction is a very simple one : Copper is deposited as metal from cop- per sulphate solution ; zinc (metal) passes into solu- tion as zinc sulphate. Zn + CuSO 4 = ZnSO 4 + Cu. SOME ELECTEOCHEMICAL FUNDAMENTALS 19 The reaction is indicated in the diagram of Fig- ure 4. How many ampere-hours can we get from a Daniell cell per pound of zinc? The atomic weight of zinc is 65.4, and it acts as a bivalent ion, so we will get 96,540 coulombs from ZINC 1 PART ITION c ra op PER ZINC su LPHATE COPPER s ULPHATE SO LU riON SOI in P ION 65.4 FIG. 4. Diagram of the reaction in a Daniell cell. = 32.7 gm. of the metal. A pound is 453 gin. Per pound of zinc we can therefore obtain 453 32.7 x 96,540 = 1,337,000 coulombs, and since an ampere-hour is 3600 coulombs, one pound of zinc will give 372 ampere-hours. We can get this same number of ampere-hours per pound of zinc in any galvanic arrangement whatever, and it requires the same number to deposit a pound of zinc electrolytically from its solution. 20 STORAGE BATTERIES How much copper sulphate must we supply dur- ing this time to keep the copper side of the Daniell cell active ? Its formula is CuSO 4 + 5 H 2 O, and the total weight equivalent to 65.4 gm. of zinc is therefore 249 gm. Copper ion passes through a bivalent step in its deposition as metallic copper, so it requires -|^ = 124.5 gm. of "blue vitriol" to give 96,540 coulombs. To furnish 1,337,000 coulombs we must use x 124.5 = 1725 gm., or 3.8 Ib. Since all our electrochemical reactions are really only chemical ones arranged in such a way that they furnish or require a current of electricity, we could calculate the amount of copper sulphate needed for our run with the Daniell cell directly from the pre- ceding figure for the deposition of metallic copper in the purification process. />o (* A pound of blue vitriol contains = 0.255 Ib. of copper, and we found that it required 382 ampere- hours to deposit a pound of copper. The same quantity of electricity will pass through the Daniell cell with a pound of copper, and to get 1,337,000 coulombs from the cell we must deposit 1*887.000 = Q.972 Ib. of copper. 382 x 3600 SOME ELECTROCHEMICAL FUNDAMENTALS 21 This amount of copper is contained in 3.8 Ib. of blue vitriol. 13. Electrochemical Units. It is evident that the 96,540 coulomb unit which the electrochemist is obliged to use is a rather cumbrous one and leads to large numbers. If we had the choosing of our own unit we would of course make 96,540 coulombs = 1 electrochemical unit of quantity of electricity, and then the calculation for copper would look like this : 63. 6 g. Cu~2 units, 1 Ib. copper ~ 14. 24 units, and for zinc it would be equally simple. But elec- trochemistry is not a big anough branch of science to be able to dictate units to the dynamos which fur- nish the current, and we must be content to accept the electrical engineer's unit. In every case it is necessary to know the complete and exact chemical reaction with which we are deal- ing before we can apply our law, for it very often happens that metals carry different multiples of the unit quantity of electricity with them in different chemical reactions, and they sometimes complicate things still further by changing the number of units carried as the concentration of the solution from which they are deposited is changed. But if we arrange to have the conditions in the cell constant 22 STORAGE BATTERIES and have once found the correct chemical reaction, the law can always be applied without fear of error. 14, Electromotive Force. Faraday's law gives a complete statement of the quantity of electricity which accompanies the reaction of gram-equivalent weights of various substances in any galvanic com- bination or electrolytic cell. But it can tell us no more than this. It says nothing about the amount of work we can do with this amount of electricity, nor about the amount of work we must do to cause the separation of a gram-equivalent of a metal from solution. The driving force of the chemical reaction and the corresponding electromotive force of the cell are specific for each reaction and cannot be calcu- lated by any inclusive general law. The driving force is called the chemical potential of the reaction, and it can be very conveniently and accurately measured by coupling the reaction into the form of a galvanic cell and measuring the electromotive force. Very early in the development of galvanic elec- tricity Volta found that the various metals could be arranged in a series, such that the most favorable combinations for producing current were to be made by choosing metals as far apart as possible in the series. Better results were obtained from cells using zinc and copper than from those using iron and copper, or zinc and tin. We know now that not only the metal, but the whole reaction must be taken into ac- SOME ELECTROCHEMICAL FUNDAMENTALS 23 count, but the " Voltaic series of the metals," as it is called, gives an approximate view of the matter. It was found very early that more work could be obtained from a pound of zinc in a cell where copper is deposited at the cathode, than from a cell where iron is used in the same way. The same quantity of zinc is used up in each case, and since we get different results in the various combinations, there must be some other factor of importance and some other law besides Faraday's to be considered. Suppose we have a very large Daniell cell, where the reaction Zn + CuSO 4 = Cu + ZnSO 4 is taking place. We choose a big cell in order that we may send 96,540 coulombs through it without any danger of changing the concentrations in the differ- ent parts of the cell. When this quantity of elec- tricity has passed through the cell, 32.7 gm. of zinc have gone into solution at the anode and have become zinc ion. During this same time 31.8 gin. of cop- per ion have changed into metallic copper. The SO 4 part of the reaction has not been affected at all. Electrochemically we could write the reaction 15. Ions. The small sign + indicates that the sub- stance carrying them is an ion and that it moves toward the cathode it is a cation. Two of them 24 STORAGE BATTERIES indicate that this particular ion carries with it per gram-atom twice the unit quantity of electricity (2 x 96,540 coulombs). The SO 4 ion (SO 4 ), which remains unchanged in this particular case, carries two times the unit quantity also, but toward the anode. It is an anion. And in chemical parlance both of these are divalent ions. Now suppose we connect the cell with an external source of current and send 96,540 coulombs through it in the opposite direction. 32.7 gm. of zinc will deposit on the zinc plate, now the cathode, and 31.8 gm. of copper will go into solution at the copper plate, now the anode. By the time we have sent our unit quantity through the cell it has been com- pletely restored to its original condition. The case of the Daniell cell is theoretical rather than practical, for zinc does not behave very well when it is forced out of solution. It grows in sponge and trees and often reaches across to the other plate and short- circuits the cell. But we have chosen our cell so large that this does not bother us, and the Daniell cell can be considered completely reversible in its re- actions. It might therefore be used as an accumu- lator. 16. Other Electrical Units. Besides the coulomb, we have been supplied with two other units, and these fortunately fit electrochemical needs pretty well with- out requiring so many figures. One of these is the SOME ELECTROCHEMICAL FUNDAMENTALS 25 volt, the unit of difference of potential, and the other is the ohm, the unit of resistance. The following terms and relations are important: Coulomb ( PbSO 4 . Pb0 2 + H 2 + H 2 S0 4 -> PbS0 4 + 2 H 2 O. In sum Pb + Pb0 2 + 2 H 2 S0 4 -> 2 PbS0 4 + 2 H 2 O. 34. At the Peroxide Plate. It does not require a very vivid scientific imagination to discover a simple 50 STORAGE BATTERIES and reversible reaction which takes in the ionic change at the lead plate. Pb _> Pb ++ . Metal Solid For the peroxide plate we need a more complicated set of changes, and Liebenow has suggested an ion which fits the facts very well indeed. Suppose the peroxide plate to be reversible with respect to the PbO 2 ion. We then have at this plate during discharge PbO 2 - PbO 2 -~, Solid PbO + 4 H + -> Pb + ^ + 2 HO, Solid and if we add the reactions at the lead and lead peroxide plates, we get Pb + Pb0 2 + 2 S0 4 ~ + 4 H+ * 2 PbS0 4 + 2 H 2 O, Metal Solid Solid ' which is our fundamental reaction Pb + Pb0 2 + 2 H 2 SO 4 2 PbS0 4 + 2 H 2 O. This is completely reversible, and it will also be found that our separate ionic reactions represent completely reversible changes. 35. Diagrams of Charge and Discharge. The accom- panying diagrams may make all this still clearer. The cell is discharging it is furnishing current THE ACTIVE IONS 51 for use in the external circuit. The current is flow- ing into the cell at the lead plate, which is therefore the anode. Here metallic lead passes through the electrode (Fig. 13) and changes into lead ion, Pb ++ , carrying 96,540 coulombs with it for each 2-^1 gm. of lead that go into solution. The lead ion has hardly passed the electrode before it meets with SO 4 in the electrolyte (Fig. 14). Lead sulphate being so slightly soluble, it requires only a very small concen- tration of lead ion and sulphate ion in solution to reach the limit of solubility of lead sulphate. This substance is therefore formed from the two ions as a solid, and removed from the electrolyte as fast as it is produced. 36. Discharge. On discharge (see Figure 14) the lead peroxide plate is the cathode. It is certainly reversible with respect to some ion, and PbO 2 seems to fit the necessary conditions. This PbO 2 is con- stantly formed from the solid PbO 2 of the plate, just as Pb ++ is formed from the solid lead of the anode. It starts toward the anode, being an anion, as its two signs indicate. Before it has more than passed the electrode it meets with H + , of which there is always plenty about in a concentrated sul- phuric solution, even if it were not moving toward the cathode carrying the current. It reacts with this H + , forming Pb ++ and water (Fig. 15), and the Pb ++ , finding SO 4 in plenty, soon saturates the FIG. 13. The begin- ning of discharge. 8 < 5 UJ O Ld FIG. 15. The third stage in the dis- charge reaction. n FIG. 14. The second stage in the discharge reaction. n FIG. 16. Discharge com- plete. THE ACTIVE IONS 53 solution with lead sulphate, which is precipitated very nearly in the spot from which the peroxide started (Fig. 16). It will do no harm to go over the changes in the reverse direction, just to fix the whole reaction more firmly in our minds. Charge. The cell is charging (see Figure 17) . The peroxide plate is now the anode, and contains a con- siderable proportion of finely divided lead sulphate from the previous discharge. Pb ++ and SO 4 are formed as fast as they are needed from this reser- voir in the plate, and the Pb ++ reacts with the water of the electrolyte, forming H + and PbO 2 (Fig. 18). The PbO 2 ~ passes through the electrode (Fig. 19) and is deposited as solid PbO 2 very close to the point where lead sulphate went into solution. H + and SO 4 are left in the electrolyte in proportion to the amount of current which has passed (Fig. 20). The lead plate is cathode during charge. Here also there is a reservoir of fine lead sulphate from the previous discharge. This furnishes a constant supply of Pb ++ and SO 4 ~~, and the electrode is re- versible- with respect to Pb ++ . So Pb ++ passes out and changes to metallic lead, sending a correspond- ing quantity of electricity along through the ex- ternal circuit, while the SO 4 ~~ finds itself moving toward the anode. It will find its equivalent of H+ in the solution, and our equations show that E II ge ~*H5 3i 5n o ^S nr}| ^hH Fio. 19. Third stage in charge reaction. FIG. 20. Charge complete. THE ACTIVE IONS 55 acid is produced during charge in proportion to the amount of material reacting, and that it is used up in the same proportion during discharge. It also expresses everything else that is contained in our fundamental reaction, and gives us at least a pos- sible picture of what takes place at the electrodes as well. We have shown that it is quite possible to have all the current carried through the cell from plate to plate by the ions of the acid, provided these two ions react near the electrodes to produce ions like the ones we have assumed. Our electrode reactions are perfectly reasonable ones, and are, as matter of fact, supported by a great deal more evi- dence than we can yet call to their support. We shall return to them in a later chapter. CHAPTER VI SOME PERTINENT PHYSICAL QUERIES 37. A host of questions arises even at this early point in the discussion of the lead storage cell. Even if we suppose that we have satisfactorily dis- posed of the chemical changes, and found a pair of ions that might do the work at the electrodes, how can we explain a good many things about the pe- culiar nature of the materials of the cell ? Premises. These questions can best be discussed if the reader will keep in mind : (I) The ions which pass back and forth at the electrodes have only molecular distances to travel. (II) The particles of active material are very small indeed. (Ill) The active materials: lead, lead peroxide, and lead sulphate are all very slightly soluble in con- centrated sulphuric acid. 38. Queries and their Answers. QUERY 1. How can storage plates keep their shape? How does it happen that a battery can be sent through thousands of charges and discharges without much growth of trees or sponge ? 66 SOME PERTINENT PHYSICAL QUERIES 57 Just because all the solid substances concerned are so very slightly soluble in the electrolyte. The ion which passes back and forth at the electrode has no chance to wander far enough to deposit at even k a measurable distance from its point of origin. SO 4 is everywhere waiting for the Pb ++ , and in- soluble PbSO 4 is precipitated almost instantly. This is one of the prime secrets of the success of the lead cell, and the main reason why its plates preserve their mechanical structure as well as they do. In another sense it is a disadvantage, for it means that the particles of active material will be exceeding fine and small, and that there will not be much inter- growth and interlocking between neighboring par- ticles. In the ideal cell both extreme insolubility and intergrowth of particles might occur simul- taneously, but not in practice. QUERY 2. The lead peroxide of the positive plate is in contact with a lead support. Why does not the plate discharge of its own accord? Does it not contain all the necessary substances for the reaction Pb + Pb0 2 + 2 H 2 S0 4 -> 2 PbS0 4 + 2 H 2 ? It does ; and self-discharge always takes place when a peroxide plate is standing fully charged. But before it has gone far all the finely divided rough lead on the surface of the lead support has reacted and then the plate is protected by its dense 58 STORAGE BATTERIES layer of lead sulphate, just as a lead plate protects itself in sulphuric acid. If the surface of the lead support is roughened or increased, the action will be stronger, and Plante plates were originally formed for service by means of this very action. Our modern plates have a very much greater proportion of active material to surface of lead support, and therefore the loss of energy due to this "local action" is a comparatively small one. (See page 182.) QUERY 3. How does it happen that a lead accu- mulator with a difference of potential of two volts between its plates can stand on open circuit without immediately discharging itself? Under proper con- ditions water (made acid with sulphuric acid) can be completely decomposed into hydrogen and oxy- gen at 1.5 or 1.6 volts. Why does not our cell begin to decompose its electrolyte and keep on form- ing gas until the plates are quite discharged? Because the plates of our cell are made of lead and lead peroxide. There is a great difference in the amount of work required to form bubbles of hydro- gen rapidly on surfaces of various metals. It takes 2.5 or 2.6 volts to cause gas to form rapidly in a lead accumulator, and at 1.6 volts the electromo- tive force at which gas forms on platinum electrodes hydrogen forms bubbles so slowly on a lead sur- face that losses due to this cause are quite negligible. SOME PERTINENT PHYSICAL QUERIES 59 Even at 2 volts the evolution of hydrogen is so slow as to be immeasurable. (See page 217 for the effect of impurities.) QUERY 4. How can it be that lead sulphate is formed during the discharge of our cell, and how can this substance change back so readily to lead and lead peroxide ? Is not " sulphation " the most dangerous disease that can come upon a battery ? The explanation is a matter of surface, like so many others in this subject. The lead sulphate which forms in the plate during a healthy discharge differs greatly in size of grain from the same sub- stance taken from the bottle on the laboratory shelf, and just as much from the material which causes what is called in battery parlance "sulphation." If ordi- nary commercial lead sulphate be made into a paste and filled into a lead support, it does not change to lead at the cathode and lead peroxide at the anode easily. It can be subjected to the action of the cur- rent for a very long time without being completely transformed, arid it never does make a good coherent plate. When a cell is allowed to stand discharged for many weeks the fine grains of sulphate which are formed during normal discharge suffer an inter- esting change. True crystallization begins on the larger particles, and the substance goes into solution at the small ones. It moves through the solution and continues to deposit on the large grains until 60 STORAGE BATTERIES the small grains have completely dissolved and the large ones, fewer in number, have grown to consider- able size. The plate is now sulphated, and if it is charged for the ordinary time, it by no means returns to its original condition of healthy charge. The large crystals of sulphate do not go into solution com- pletely. In fact, they hardly dissolve at all, arid long before the cell has been brought back to its charged state reaction has ceased and the current is merely producing gas. It is possible to restore a sulphated cell, but the charge must be continued so long that gassing breaks up the active material, and even when the remaining sulphate has all been forced to react, a large part of the original capacity of the cell has been lost. (See page 216.) QUERY 5. Metallic lead in the form of a bar or plate is not dissolved by sulphuric acid under ordi- nary circumstances, and this is especially true of acid of the concentration used in storage batteries. The grids of paste plates and the main body of Plante plates resist the attack cf the acid during the whole life of the plates. Lead is one of the metals which "protects itself" from solution in reagents by the formation of a dense layer of slightly soluble material on the surface. It is a familiar fact that lead pipes cannot be used for pure distilled water without danger of contamination, for in this case the sub- stance formed is not dense and does not protect the SOME PERTINENT PHYSICAL QUERIES 61 metal. The hydroxide which forms under these cir- cumstances is fluffy and breaks away from the sur- face, and the plate rapidly dissolves. But if the water passing through the pipe is not pure, if it contains carbonates, chlorides, and sulphates even in small amounts, dense protecting coatings of carbon- ate, chloride, or sulphate are formed and the metal is no longer dissolved. It is safe enough to use lead pipes for ordinary water even if it is to be used for drinking purposes. How is it, then, that the lead of the negative plate can pass easily and rapidly into the form of lead ion? Why do not the particles of lead so protect themselves and refuse to react? And if because of their very fineness the protecting layer which might be formed makes up a considerable part of the whole bulk of the grains, why does not the self-discharge necessary to produce this protecting layer greatly reduce the activity of the lead plate? While it is quite true that the particles of lead on the negative plate are very small, they are still quite large in comparison with the protecting layer of sul- phate which is sufficient to prevent farther action. At the end of charge a part of the energy is lost by formation of sulphate at the lead plate, but in prac- tice it is a very small fraction of the whole. But when current is passing through the cell in the dis- charge direction a very different state of things pre- 62 STORAGE BATTERIES vails. Suppose our cell to be first on open circuit and that we are looking at what happens at the lead plate and able to see everything that occurs. Lead changes to lead ion, Pb ++ , and this goes into solution, leaving the plate negatively charged. The Pb ++ finds SO 4 waiting and precipitates as in- soluble PbSO 4 , but it leaves 2 H + behind it, and the condition of strain set up by the positively charged ion in the electrolyte and the negatively charged plate is not relieved (Figure 21). It only takes the presence of a very small concen- Fia. 21. Electrostatic equilibrium tratlon of ion in solu- about a lead plate. , tion to set up an at- traction so strong that no more ion leaves the plate. The electrode is in equilibrium with respect to Pb ++ . It has protected itself sufficiently by sacrificing a very minute fraction of its whole mass. But as soon as the external circuit is closed and LU SOME PERTINENT PHYSICAL QUERIES 63 current begins to pass, the H + is no longer bound by an electrostatic attraction. The lead plate can dis- charge itself through the wires and the H + can pro- ceed on its way toward the cathode, carrying its equivalent of electricity with it. The electrode is no longer in equilibrium, and more lead goes into solution, becomes Pb ++ , reacts with SO 4 , and frees more H + . This continues as long as current is being taken from the cell. CHAPTER VII ENERGY RELATIONS 39. Any arrangement whatever which runs of its own accord and which can furnish energy for doing outside work as well must draw upon some store for the energy expended. A charged storage cell con- tains potential chemical energy. It differs in no way from any other galvanic cell in this, and if we knew of practical ways of manufacturing lead sponge and lead peroxide of exactly the same physical character- istics as those possessed by the active materials of our charged accumulator, we could build a cell just like it in every way without any charging process whatever. It merely happens that the very best way of manufacturing lead sponge and lead peroxide of exactly the right quality is to pass a current of electricity through a discharged storage cell. The materials themselves are no more electrical than the same substances in bottles on the laboratory shelf. 40. Transformations of Energy. There is hardly a branch of science where we can be so sure of our footing as in calculations which involve the trans- formation of quantities of energy from one form to 64 ENERGY RELATIONS 65 another, especially in the calculation of reversible changes, and it is difficult to imagine any arrange- ment which could be more perfectly reversible than a storage cell. Small losses occur even in a big storage cell. Some gas escapes and cannot be taken into our calculation, and there is some local action at the plates with corresponding evolution of a little heat. But the same is true in any arrangement known to man, and in most cases the losses are very much greater than in our cell. Electrochemical Reaction. We can apply the law of the Conservation of Energy. Applied to our own particular case this law says : If we have at our disposal a system, represented by Pb + Pb0 2 + 2 H 2 S0 4 and consisting of 207 gm. of lead, 239 gm. of lead peroxide, and 196 gm. of sulphuric acid, and this system changes of its own accord into another 2 PbS0 4 + 2 H 2 consisting of 606 gm. of lead sulphate and 36 gm. of water, a definite and determined amount of energy will be set free, which can be utilized for doing work. If the reaction is perfectly reversible and no energy has managed to get away from us, we can restore the original condition of the system by ex- pending the same quantity of energy on it. 66 STORAGE BATTERIES Our own special interest lies in a chemical reaction, but the same law applies for any change whatever. The original condition might be represented by a certain mass of water at the top of a dam and the final condition by the same mass at the bottom. Here we would have no difficulty in calculating the quantity of work obtainable by the fall of the water, and the same amount of work would carry it back to the top, provided all our machines were friction- less and worked with 100 % efficiency. 41. Thermochemical Reaction. Now for the next step. If we should take the amounts of the various materials on the left side of our fundamental equa- tion, and should mix them all up into a pasty mass, we would not get any electrical current from it, but we would get a definite amount of heat set free. We will get the same total amount of energy from the reaction in either case, provided our cell does not itself heat up or cool down during the reaction of these amounts of its materials. In the one case we should measure the amount of available energy in heat units, or calories, and a calorie is the amount of heat required to raise the temperature of 1 gm. of water 1 C. In the other case we should measure the amount of available energy in electrical units, joules (volt-coulombs). 42. Heat Changes in the Cell. If our cell does heat up while it is sending out its 96,540 coulombs, we ENERGY RELATIONS 67 must remember the amount of heat which appears in this way, and we must expect to get less energy from the cell for use in the external circuit if a part of the total energy of the reaction has been used to heat the air of the room. If the cell cools while it is working, we might expect to get more than the calculated amount of energy, and to this point we will come back later. But if the cell neither heats nor cools during the passage of 96,540 coulombs, the law of the Conser- vation of Energy gives us our First Fundamental Equation chemical energy expanded = electrical energy produced. Before we can go any farther we must know the numerical factor for transforming joules to calories (or vice versa), and this has been often determined. It takes 4.18 joules to raise the temperature of 1 gm. of water 1 C. The determination of the heat of the reaction Pb + PbO 2 + 2 H 2 SO 4 ;2 PbSO 4 + 2 H 2 O cannot be carried out directly with accuracy because of the slowness of the reaction when the substances are mixed up together. It can only be determined by indirect measurement, and the best results have been obtained by using very dilute sulphuric acid. Applying a correction to be explained immediately, the heat of this reaction for acid of density 1.044 68 STORAGE BATTERIES (0.70 gm.-mol. H 2 SO 4 per liter of electrolyte) is 87,000 calories. A cell containing acid of this den- sity neither heats nor cools while it is working. Now see how simple our calculation becomes : 87,000 calories x 4.18 = 364,000 joules, and this is the amount of electrical energy which be- comes available when 207 gm. of lead and 239 gm. of lead peroxide have reacted with 196 gm. of sul- phuric acid (in rather dilute solution) to produce 606 gm. of lead sulphate and 36 gm. of water. If we arrange things so that the reaction can take place in a galvanic cell, 2 x 96,540 coulombs will pass through the cell by the time these amounts have reacted. These 193,080 coulombs will have given us 364,000 joules of work, and the voltage of the cell must therefore be 364,000 volt-coulombs _ i QQ u 2 x 96,540 coulombs This agrees closely with the measured voltage of a cell containing this rather dilute acid as electrolyte. While there is no doubt whatever about the cor- rectness of this principle, there is often a great deal of difficulty in obtaining accurate data on the heats of reaction. In this case a number of reactions had to be used, and the final result calculated in a round- about way by eliminating the heats of the various ENERGY RELATIONS 69 intermediate steps. Even in this case there is no doubt as to the correctness of the method, but the final result is always afflicted with a large experi- mental error. 43. Heating and Cooling of the Cell. The ordinary practical storage cell contains acid of density about 1.210. It cools during discharge and heats during charge, and can therefore not be brought under the simple law we have just used. We can make some qualitative statements about it, however. Since it cools during discharge, it must take into its system a certain amount of heat from the room during the passage of 96,540 coulombs. At least a part of this^ heat will be transformed into electrical energy. Since we always calculate on the basis of 96,540 coulombs, the voltage of this cell must be higher than it would be if it did not cool down while it was working. During charge, the cell gets hotter than the room. A part of the energy supplied to charge it is used in heating the surrounding objects, and it therefore takes more energy to completely reverse the reaction than it would if the cell did not change its tempera- ture during charge. Since we use the same 96,540 coulombs for the reversal, the charging voltage must be higher than it would be if the cell did not heat up. 44. The General Equation. We can handle this case quantitatively just as easily as the simple previ- 70 STORAGE BATTERIES ous one, for we have what is called the Second Law of Thermodynamics, which states For our case W ' available electrical energy. Q = heat of the chemical reaction. T= the absolute temperature. = the temperature coefficient of available elec- trical energy. Since all our calculations are based on gram-equiv- alents, 96,540 coulombs are always supposed to pass through the cell, and the electromotive force of the cell is therefore a measure of the available electrical energy. If e = the electromotive force of the cell, we can put this formula into a form adapted specially for the case of galvanic cells. $ . m St+ r &> F^ dT" F being our 96,540 coulombs. For an acid concentration corresponding to a den- sity of 1.210 we have for Q (per gram-equivalent) about 43,000 calories. ^ is positive and has a value of about 0.0003 at 20 C. ENERGY RELATIONS 71 Numerically e = 43,000x4^ + [290x0.0008], e = 1.86 + 0.087 = 1.95, which is a little lower than the usual measurement of 2.04 to 2.06 volts. The complete derivation of the formula will be found in the Appendix, page 255. This is the general form of the expression for the electromotive fprce of a galvanic cell in terms of the chemical heat of reaction and the temperature coeffi- cient of the electromotive force. It is perfectly general and suggests many interesting things. There are cells which warm up a good deal while they work. These are the ones whose electromotive force de- creases rapidly when their temperature is raised. Others cool down, and the reverse effect is produced on these by warming them from without. In the first class, part of the energy of the chemical reaction is used to heat the room. In the second class some energy is taken from the room in the form of heat and converted in the cell into electrical energy. There are cells in which the heat of the chemical reaction is zero and in which all the electrical energy is produced at the expense of heat absorbed from the surrounding air. These are the "concentration cells," and they are very interesting and important 72 STORAGE BATTERIES theoretically, even though none of them are used as practical sources of current. 45. Temperature Coefficient. The usual commercial storage cell has a fairly large positive temperature coefficient about 0.0003 per Centigrade degree. But it gains no energy from this fact because we eo 90 iao TIME OF DISCHARGE (IN MINUTES) (80 FIG. 63. Resistance curves of Plant6 cell during discharge at va- rious temperatures. 94. Resistance Curves. It is quite true that the internal resistance of a storage cell is usually negli- gible as far as loss of energy is concerned. There are, however, many things of great theoretical (and therefore practical) interest about this factor. Hardly anything about a lead cell gives so clear an insight into its internal workings as its internal resistance. Even its voltage curve cannot tell more 154 STORAGE BATTERIES about the minute phenomena of charge and dis- charge than can be seen from its resistance curve. Figure 63 gives a set of curves of resistance taken during the discharge of a Plante cell at various tem- peratures, and Figure 64 gives both voltage and RESISl ANCE TIME-MINUTES FIG. 64. Curves of resistance and voltage during complete discharge and partial reversal of a Plant6 cell. resistance for the same cell at one temperature. It will be noticed that the change in resistance is con- siderable, if the cell is discharged down below its usual end voltage say down nearly to zero. Fig- ure 65 gives voltage and recovery curves during par- tial discharge and recovery curves after open circuit immediately following the discharge. INTERNAL RESISTANCE 155 95. Factors of Resistance. The total cell resistance is evidently made up of at least three distinct parts as indicated in the diagram of Figure 66 : A. Support plate. L7 g- 06 I 05 20 100 120 VO 60 SO TIME-HINUTES. FIG. 65. Curves of resistance and voltage during discharge and re- covery. Plante cell. B. Active material, including electrolyte in the pores. (7. Main body of electrolyte. A and we can consider practically constant, and if O changes, we can calculate the amount of the change from the data of Figure 61, which gives the relation between resistance and acid concentration. B is the variable part of the system. 156 STORAGE BATTERIES During charge the active material first to react is near the surface of the plate, and the electrolyte does not have to diffuse far through the narrow channels of the mass. As the diffusion path increases and the cell becomes more fully charged, concentrated acid is produced in the pores. But all through the FIG. 66. Diagram of the parts of a Plante cell. charge it is the solid plate itself which does most of the conducting, and the change of resistance to be expected during charge is therefore not great. During discharge a very different state of affairs exists. In this case also the action begins at the surface, where there is plenty of both electrolyte and active material. But as discharge proceeds the area of activity moves back deeper into the mass, acid is used up within the plate and must be replaced by diffusion. The acid concentration becomes much INTERNAL RESISTANCE 157 lower at the point of activity, and there is added to this the loss of conductivity by the solid plate itself. The particles of lead and lead peroxide in the outer layers have now become* covered with a layer of lead sulphate and have been more or less insulated from each other. The result is as if the distance between the plates had been increased, for the plate surface which is actually carrying the current has moved from the surface back into the interior of the plate. The surface of the plate in contact with electrolyte has also been greatly decreased by this displacement of the active plate surface. Such changes as these are quite sufficient to account for the change found in the resistance of cells under the usual conditions of charge and dis- charge. We should not expect, and we do not find, any very large or very rapid changes in cell resistance. 96. Sulphation. On long standing, a storage cell may acquire a very high resistance indeed as the re- sult of complete "sulphation." This means that the active lead sulphate formed during normal discharge has gradually changed into the inactive crystalline form, and that crystals of this inactive modification have completely covered the particles of lead and lead peroxide with an insulating coating. Authentic cases are known of large cells with internal resist- ance as high as 10 ohms. As usual, it is hard to make things act properly 158 STORAGE BATTERIES when you want them to. I have left a completely discharged cell for six weeks or more, carefully fol- lowing its internal resistance every day, and found no change of more than a few per cent in its resistance. It seems very likely that the ordinary cases of sul- phation, which are rather common and most annoy- ing in their results, do not lead so much to a very high internal resistance as to poor contact between particles of active material. The electrolyte can get into the plate or the grid well enough, and the in- ternal resistance of the cell can therefore not be very high. But the capacity of the plate has suf- fered because a good deal of what ought to be avail- able active material has been incapsulated by sulphate and removed from the reach of plate activities. In ordinary practice, the cell is discharged only until its electromotive force sinks to about 1.7 volts. This means that only perhaps a quarter of the active material of the plates has entered into reaction, and that the increased resistance in the active mass is due rather to separation of particles by sulphate coatings than to complete transformation of the active mate- rial at any place into insulating material. During the charge, sulphate coatings and bridges are rapidly broken down, and the decrease in resistance during charge is therefore more rapid than could be explained by a change in concentration of electrolyte within the pores of the plate. INTERNAL RESISTANCE 159 After a period of discharge, with corresponding increase in resistance, the cell recovers its original electromotive force along a carve nearly like a diffusion curve when the circuit is opened. It also recovers its original resistance along a very similar curve. (See Figure 65.) This fact indicates the dynamic nature of the equilibrium which causes the cell to have any particular electromotive force or re- sistance at a particular place in its discharge, charge, or recovery curve. The particles of active material cannot have been completely covered by insulating sulphate, for on standing, the plate returns to its original condition as far as we can measure it by an examination of either electromotive force or resistance. We must evidently think of the lead sulphate as swelling up and almost plugging canals which lead to unchanged lead and lead peroxide. The density of the sulphate is much less than that of the materials from which it is formed, and while the particles of lead or peroxide may have had plenty of space be- tween- them at the end of charge, the sulphate must shut off much of this from activity at anything like a practical rate of discharge. As long as no current is flowing, acid does make contact with the remanent active material and the active plane in the plate draws out toward the exterior. In Figure 62 the full-line curve gives the open circuit resistance of a small Plante cell at various 160 STORAGE BATTERIES temperatures. The dotted curve shows only the shape of the curve for the electrolyte, and not its true value, which would be only about half that of the cell at any point. The acid curve was plotted in this way to show how the cell resistance departs from the acid resistance at higher temperatures. Probably the solid resistances of grid and active material be- gin to make themselves felt, and as these have posi- tive temperature coefficients, the increased resistance makes the cell take a sharper turn than the elec- trolyte. That the resistance of the plate material becomes a factor is shown by the fact that pasted plates of slightly greater area, placed as nearly as possible the same distance apart, show a decidedly greater resistance on open circuit than the Plante plates. The cells with paste plates have about 25% higher resistance. 97. Effect of Distribution of Material on Resistance Curves. The curves of Figure 49 speak for them- selves. The only queer thing about them is the flat place which appears after 60 to 80 minutes of discharge. This is characteristic of Plante plates with ribs, and does not appear in the curves for paste plates. The ribs of these plates are formed into active material, which lies close to the ribs at their tops, but which forms a solid mass down at the bottoms of the ribs. (See Figure 67.) During the first part of the dis- charge the electrolyte finds active material on the INTERNAL RESISTANCE 161 ribs, and diffusion takes place largely through the open space between them, and only for a small dis- tance through active material. As this easily avail- able material is used up, the action moves farther down into the plate and presently reaches the mass of material at the bottom of the grooves. Here for a time there is material enough at a nearly constant distance from the surface of the plate, and after this has been passed the resistance rises very rapidly and the plate poten- tial shows that the cell is com- pletely discharged. If there is anything in our fun- damental theory of the dependence of electromotive force on acid con- centration, the curves of electro- motive force of these Cells OUght FIG. 67. Diagram of . distribution of active to sllOW a Corresponding flat place material on ribbed somewhere near the same point in Plant6 P late - the discharge curve. The curves of Figure 52 show it clearly except in the one for 8 C. We missed it here by not taking points near enough together, for it shows clearly in the curve of Figure 64, which was made on the same cell at another time. This curve gives the course of electromotive force and resistance during a complete discharge followed by partial re- 162 STORAGE BATTERIES versal. If our explanation is correct, the resistance ought to decrease very rapidly after passing through a maximum at about the end of complete discharge. The curve is in agreement with this idea. 7 X)9 .08 J07 15' 25 J05 60 80 160 TIME- MINUTES FIG. 68. Change of internal resistance during discharge at various temperatures. Paste plates. 98. Paste plates show smooth curves of resistance, as shown in Figure 68. Our resistance curves should also be characteristic when taken for different rates, and Figure 69 shows this for the same Plante plate cell at constant tem- perature. 99. A most interesting idea of the lively dynamic INTERNAL RESISTANCE 163 nature of the momentary equilibrium existing in the cell at any time during the cycle is obtained by plotting curves of constant composition at various times and temperatures. The curves of Figure 63 / ^ 4c y J &~ Z- r- ~ ^ 7Q* 08 "AMPEF r*" 20 40 60 80 100 120 (40 TlldE-MINUTES FIG. 69. Change of internal resistance at various discharge rates. Plante cell. are isothermal curves. Each one shows the course of the change of resistance during discharge at con- stant rate and constant temperature. Since Fara- day's law is true, the cell contains exactly the same amount of lead, lead peroxide, lead sulphate, sul- phuric acid, and water at the end of the same time of discharge. Curves of constant composition will 164 STORAGE BATTERIES therefore result if we cut these isothermal curves at times 30 min., 1 hr., 2 hr., etc., and plot the values so found resistance against temperature. Figure 70 shows a set of curves so found. The curve T = is for open circuit, and it gives the temperature g z. s \ \ x \ \ ^ ^J0. -^. ^^ x ^ s^ ^ -^c ^ ~^ x ^ \ ^ x \ X \ 5 ' x \ \ \ FIG. 101. Discharge curves of Edison cell at various temperatures. Weight of complete cell, 19.25 Ibs. [ampere-hours, 225. Capacity y [watt-hours, 248. Ampere-hours per pound of cell, 11.3. Watt-hours per pound of cell, 12.4. Ampere-hour ef- ficiency, 82%. Watt-hour effici- ency, 60%. An examination of the temperature effect shows the im- portant part which FIG. 102. Summary showing change in diffusion plays in ampere-hour capacity with temperature. . . [Exide and Edison.] the Cell activity. F256 a.