June, 19661 QUAVLE AND COOPER 355 A Precise Coulometer BY J. C. QUAYLE AND F. A. COOPER (Inzperial Chemical Industries L t d . , Heavy Organic Chemacals Division, P.O. B o x No. 2, Billingham, Co. Durham) This paper is a contribution to the application of coulometry to accurate analysis, and describes an apparatus which can be used for the accurate assay of “pure” sodium carbonate. An instrument has been built which measures coulombs with a probable error of f 2 5 p.p.ni. as the product of a constant current and its time of flow. The current is maintained constant by an electric servo-system, and it is adjusted so that the voltage drop across a precise resistor is equal to the e.m.f. of a standard cell. Time is measured by a quartz-crystal clock. The resistor and cell are checked against local standards, which in turn have been calibrated against international standards by the National Physical Laboratory.The clock is checked against a broad- cast frequency and the General Post Office Speaking Clock. Thus the quantity of electricity for a titration is referred ultimately to the fundamental standards of mass, length and time; the titre is independent of knowledge of the purity of any chemical substance. COULOMETRIC titration as an analytical technique may be said to have originated with the work of Szebelledy and Somogyil in 1938. Since then the subject has developed rapidly, and many papers and reviews have appeared; Swift, Furman, Lingane and Tutundzic have been responsible for most of the early work. The accuracy reported has been adequate for routine analyses, but has seldom been better than kl000 p.p.m.* Despite this, Tutundzic2 suggested in 1958 that the coulomb should replace silver as the ultimate standard3 for acidimetry.Tutundzic’s proposal received considerable discussion, including some opposition. The following year Taylor and Smith4 reported the coulometric standardisation of acids and bases, including sodium carbonate, with the same order of precision as the best volumetric titrations. Their standard deviations ranged from 30 p.p.m. for potassium hydrogen phthalate to 100 p.p.m. for hydrochloric acid. They assayed sodium carbonate with a standard deviation of 70 p.p.m., but they controlled the current manually; the assay was not confirmed independently. The present work seeks to overcome these two objections recognising that, if accuracy as good as, or better than, that by volumetric titration can be attained, it may lead to the recognition of the coulomb as a universal standard in volumetric analysis.Such a standard is independent of absolute knowledge of the purity of the chemical substances used as standards (knowledge that is difficult to obtain), and takes advantage of the high degree of precision that can be reached by electrical measurements. The instrument must therefore be able to determine the number of coulombs taking part in a reaction with a coefficient of variation no greater than 100 p.p.m., this representing about the best that can be obtained in ordinary volumetric analysis. The efficiency of the electrode reaction must approach the theoretical very closely.Experimental work on the coulometric titration of sodium carbonate, to be described later, provides evidence that the neutralisation of bases by electrically generated hydrogen ions can be carried out quantitatively. The entire process, the generation of hydrogen ions and measurement of current and time, is simpler and no less precise than reference of the sodium carbonate to silver, which is probably the best chemical method of assaying sodium carbonate. APPAKATUS This paper describes the apparatus we have designed for the purpose. All the known types of coulometer, including the current - time integrating motor,5 were considered. Others, such as the silver perchlorate method, might give similar precision but none was so directly related to the fundamental physical standards.The instrument comprises (i) a precisely regulated constant-current source, whose output is monitored against a voltage standard, coupled with (ii) a means of measuring the time of flow of the current and (iii) a suitable cell wherein the reaction takes place. The cell is described elsewhere.6 The remaining two main items will now be described. quantities such as voltage and current, as well as chemical quantities. * All errors and deviations are expressed in p.p.rn. throughout the report. This applies to physical356 QUAYLE AND COOPER: A PRECISE COULOMETER [Analyst, Vol. 91 R I I A +YD b /-l f--W 1-7------- +w + D.C.source, R 4 + b constant voltage I I 9 1 Fii manually i I i I ------ ---I Power supply and control unit A, = Fast-acting current stabiliser D = Working reference cell A, = Slow-acting trim amplifier E = Ammeter A, = Amplifier G = Galvanometer B = Controlling reference cell R,, R,, R,, R, = Resistances C = Coulometer cell VR = Manual current adjuster Fig.1. Coulometer block diagram CURRENT SUPPLY (Fig. 1)- This is a rectified a.c. supply, the voltage of which can be adjusted manually to be approximately correct, and is thereafter not disturbed. The current flowing in the cell circuit is controlled at the desired value by comparing the voltage drop across a precise 4-terminal resistor with the reference voltage, so that in maintaining constant voltage drop it also main- tains constant current. This is achieved by varying the impedance of a group of control transistors influenced by two separate correcting amplifiers : (a) a fast-acting circuit which corrects for transient variations in the mains supply but does not have high long-term accuracy, ( b ) a slow-acting circuit which compensates circuit (a) for thermal and other drifts during the titration.Interaction between the two control amplifiers is avoided by the considerable difference between their time constants. Variations in the resistance of intermediate connecting leads and circuits are unimportant. In addition to these automatic corrections a manual adjustment is provided in the form of an adjustable shunt across R,. This enables the current to be brought to the exact value required. It is necessary not only to hold the current steady but also to measure it accurately.This is achieved by the use of a precise resistor connected in series with the titration cell. The value of the resistor is chosen so that, at the desired current, the voltage drop across it shall be equal to the e.m.f. of a Weston unsaturated cadmium - mercury cell. A galvano- meter is used to detect any errors, and manual correction to circuit ( b ) above can then be made. In practice these adjustments are small and are only occasionally required during a titration. A 1-mm deflection of the galvanometer represents a current change of about 7 p.p.m. The current variations can thus be held by automatic means, aided by occasional manual adjustment, to 10 to 20 p.p.m. during a titration, and its value is known to within +ZO p.p.m. For currents of the order of 1 amp a resistor of 1 ohm is used for measurement purposes.Provision is made for the use of lower currents by replacing the 1-ohm standards by 10 or 100-ohm standards. This means that R, and R, must also be replaced with appropriate values at the same time.June, 19661 QUAYLE AND COOPER: A PRECISE COULOMETER CIRCUIT DESCRIPTION 357 The principles of circuit operation are as follows. The current from the main d.c. source (Fig. 1) passes through the five regulator transistors connected in parallel, amplifier A,, resistors R,, R,, and R, and the coulometer cell. R, is a very precise and stable resistor which is accurate within +12 p.p.m. of its stated value (1 ohm), and is used for current measurement as described above. R, and R, are good quality wire-wound resistors, but have neither the stability nor the accuracy of R,.They are used to provide the voltage-drop signals for the two stabiliser circuits (a) and (b). FAST-ACTING STABILISER (a)- The voltage developed across R, is compared with the voltage from potentiometer R,. This is in turn supplied from a stabilised power unit. Any difference between the two voltages will appear as an error signal fed into amplifier A, and thence into the regulator transistors A,. The transistors change their impedance and cause the current to return to its correct value. The control action, which takes place in a fraction of a millisecond, can thus hold the current steady in the face of most cell-impedance changes, mains-voltage variations and so on. The stabilised power unit supplying R, is unlikely to produce transient variations in voltage but will certainly drift.This is corrected along with other slow drifts by the following circuit. SLOW-ACTING STABILISER (b)- The voltage developed across R, is compared with a Mallory RM42R cell, and any error signal is fed into amplifier A, which terminates in a servo motor geared to the potentiometer R,, and this re-sets the operating point of the fast-acting stabiliser. In practice two resistors, R, and R,, are connected in series across the 50-volt stabilised supply. The slow-acting servo motor corrects the value of R,, and R, is manually adjusted before the equipment is used so that R, starts from about the middle of its range. R, and its fine adjustment resistor, R,, are wound with precious-metal wire and use a precious-metal sliding contact, thus eliminating for all practical purposes the electrical noise from these components.The amplifier is a typical chopper type using vacuum tubes with an input sensitivity of about 12 pV. The response time for full-scale travel is determined by the servo-motor gearing and is about 10 seconds. The choice of the reference cell is governed by the requirements of low drift during a titration and the ability to deliver appreciable currents into the amplifier input. The control transistors perform their function by absorbing the difference between the voltage that the titration cell requires, and the output voltage of the power supply. The difference, which must be kept positive, is set manually to a value that is always within the maker’s rating.By means of a switch the titration cell can be replaced by a resistor of approximately equal resistance. This enables the current to be set to the desired value before a titration is started. After 15 minutes the rate of drift is low enough for the equipment to be used. The cell is then switched back into circuit and the current is controlled almost immediately at the correct value. PROTECTION- Protection of the power supply unit against accidental short-circuits is particularly necessary with transistor circuits, and is provided internally by a high-speed electronic trip circuit. Both this and the working of the fast-acting stabiliser are described more fully in Appendix I. TIME MEASUREMENT In the early stages of development a 100-kilocycle per second quartz-crystal oscillator was used, followed by several frequency divider stages using vacuum tubes.For a variety of reasons this proved unreliable and was replaced by the present equipment which uses a 10-kilocycle per second quartz-oscillator, followed by a number of solid-state binary frequency dividers to a final frequency of 10 cycles per second. This registers time in units358 QC'AYLE AND COOPER: A PRECISE COULOMETER [Analyst, Vol. 91 of 0.1 second on a pair of electro-magnetic counters. The counters are run simultaneously as a check on each other. One counter can be pre-set to switch off at a selected number of counts. The crystal is not temperature controlled as such effects are not significant over a range of 15" to 25" C.Checks on the time-keeping of this equipment against standard broadcast frequencies and the General Post Office Speaking Clock show the most significant error to be possibly one unit of 0.1 second at the end of the titration. In a normal period of 6000 seconds, this could be 15 p.p.m. STANDARDS- Current and time require to be measured accurately. Current is measured by observing the voltage developed across a resistor. Thus standards of voltage, resistance and time are required. KO standards of time are kept by the Agricultural Division as there is ready access to certain broadcast frequencies and the General Post Office Speaking Clock. RESISTANCE STANDARD- The lowest resistance (1 ohm) comprises a network of ten 10-ohm resistors, connected in parallel to make a 1-ohm, 4-terminal resistor.The wire is double fibre-glass covered which, besides acting as an insulator, provides a soft bedding layer against differential expansion stresses. The wire material is a grade of manganin with a resistance with temperature curve as Fig. 2. This curve was compensated by the addition of a single-series element of copper to give an improved form with a variation over the range 17" to 32" C of 15 p.p.m. The initial stresses are removed by prolonged annealing. -IZ0 t I I 30 Temperature, "C 10 - 20 0 Fig. 2. Comparison of compensated and uncompensated resistors The resistor, which is enclosed and oil filled, rises to an equilibrium temperature of 3" C above the oil temperature. This enables the final wire temperature to be compared with the resistance - temperature curve (Fig.3) to ensure that no significant resistance change has occurred. During the period of the tests (about 15 months) the resistance value changed from 1.00032 to 1.00035 ohms. VOLTAGE STANDARD- An unsaturated l!eston cadmium - mercury type cell is used (Muirhead D-942-C), which reduces the variations of e.m.f. due to temperature - electrolyte concentration changes found in the saturated type. The cell is enclosed and lagged to reduce temperature differentials between the limbs. The over-all variation of e.m.f. is about 2 pV per "C. Because of the supposed inferior long-term stability of the unsaturated type of cell, the working cell has been compared frequently with the I.C.I. Agricultural Division standards (see below).The results show that the working cell varied by *lo p.p.m. over a period of 3 months.June, 19661 QUAYLE AND COOPER: A PRECISE COULOMETER 359 REFERENCE STANDARDS- Both voltage and resistance standards are maintained by I.C.I. Agricultural Division Standards Laboratory along with a 5-decade standard potentiometer. All these items carry National Physical Laboratory certificates, so the possible errors can be assessed as follows- voltage: 5 p.p,m. * errors in the value of the absolute volt, resistance: within 1 or 2 p.p.m. errors in the value of the absolute ohm. The possible errors of measurement of coulombs are as follows: VOLTAGE ERRORS PARTS PER MILLION . . .. .. f 10 Uncertainty in the absolute volt . . . . National Physical Laboratory certification of standard .. .. f 5 Lagged unthermostatted . . .. .. .. .. .. f 10 Later lagged and thermostatted . . .. .. .. .. r t 4 Uncertainty in the absolute ohm . . .. .. .. .. f 10 Maker’s certification . . . . .. .. .. .. .. $ 1 .. .. * . .. f 5 15 Divisional standard cell temperature- RESISTANCE ERRORS Potentiometer discrimination . . .. TIMING ERRORS (including errors due to the timing of intervals) The probable over-all values for the initial and final arrangements are 25 and 24 p.p.m., respectively. Standard deviations of 50 p.p.m. have been obtained by using the coulometer in work that will be reported later. These results include the errors due to manipulation, weighing and any deviations from stoicheiometric reactions at the electrodes. .. DISCUSSION ACCURACY AND STABILITY- Within the limits of discrimination of the experimental measurements, no change in the working standards has been detected over a period of 3 months.Checking against the Divisional standards has become a precaution against random damage and unforeseen variations. Now that steady values are established, checking can be much less frequent. RELIABILITY- control. on the one occasion when the current drain from it exceeded the maker’s maximum. so that it gives no cause for anxiety. duration of the driving impulses. The working reference cell is protected by a variable high resistance as a sensitivity Its robust construction was shown by its return to its original e.m.f. within 24 hours, The working standard resistor is liberally rated, and its stability has been established, The timer counters gave some trouble at first but this was cured by an increase in the The remainder of the apparatus has functioned continuously without trouble.The original purpose of the work was to produce a coulometer of improved accuracy in comparison with the current - time, and motor coulometers previously r e p ~ r t e d . ~ , ~ A bench instrument was made to demonstrate the working principles, and the results of titration (see following paper6) confirm that our estimated probable errors of the order of 25 p.p.m. are realistic. Improved temperature control of the standards of resistance and voltage, and repeated calibrations at the National Physical Laboratory to establish their rates of drift, will reduce total possible electrical error to about 20 p.p.m.The error in time standardisation should always be negligible. With errors at this level, no further development is profitable until present work in various national laboratories to establish more accurately the values of the Faraday, the volt and the ohm has reduced their probable errors to below the present values. CONCLUSIONS The accuracy of the instrument, and its capability of being checked against internal and external standards, renders it suitable for the most precise work. It is reliable and versatile enough for general purpose work. We thank our colleagues, PuIessrs. J. J. E. Kess and J. Lindsley, who constructed and maintained the apparatus.360 QUAYLE AND COOPER: A PRECISE COC‘LOMETER [Analyst, Vol. 91 Appendix I DESCRIPTION OF REGULATED POWER SUPPLY^,^ (Fig.3) The main 52-volt transformer secondary winding, connected to a “Variac,” enables any voltage between 4 and 52 volts to be set manually. The a x . is rectified and fed to the regulating transistors, TR, to TR,,, which are connected in parallel. Voltage rise on open circuit is minimised by resistors R, and R,. The bases of TR, to TR13 are fed by the differential amplifier TR, and TR,, followed by TR,, TR, and TR,, giving an over-all control factor of 2000. The input signal to this amplifier is the difference between the e.m.f. developed across R, and the nominally equal e.m.f. from the stabilised supply. This supply is stabilised in two stages by gas-discharge tubes and is thus largely free from short-term variations. The current flowing through the cell is by this means held constant against short-term fluctuations arising from mains-voltage variations or changes in cell impedance.Protection against accidental overcurrent is provided by a trip circuit comprising TR,, which monitors the e.m.f. across resistor R,, and, if this is excessive, triggers the bi-stable TR,, and TR15 into its other state. This causes TR, to cut off, and with it TR, and TR,,, thus stopping the current flow before it can cause any damage. The change over of the bi-stable also releases relay RL, and opens the a.c. feed to the rectifier. Thesystemis re-set by applying a temporary earth potential to the base of TR,,, which causes the bi-stable to revert to the normal condition of TR,, conducting and TK15 cut off.The internal power supplies for the amplifiers and protection current are obtained, as shown, from additional secondary windings on the main transformer. These are conven- tional and do not merit comment. The output of the unit is up to 2 amps, 50 volts. Appendix I1 LIST OF COMPONENTS Rl, R2, R, = Precise 4-terminal resistors (see text) = 500-ohm potentiometer, palladium - silver, with J & M alloy 625 wiper = 0-076-ohm. 5-watt. wire-wound resistor = 1000-ohm, &watt, wire-wound resistors = 50,000-ohm potentiometer, molybdenum - palladium - gold, with J & M alloy = 33-ohm, +watt resistor = 15,000-ohm, &-watt resistor = 3900-ohm, &-watt resistor = 8200-ohm, &watt resistor = 12,000-ohm, +-watt resistor = 18,000-ohm, &-watt resistor = 1000-ohm, &watt resistor = 6800-ohm, +watt resistor = 3900-ohm, +-watt resistor = 12,000-ohm, +-watt resistor = 1000-ohm, Q-watt resistor = 10,000-ohm, &watt resistors = lfiOO-ohm, $-watt resistors = 100-ohm, &-watt resistor = 3000-ohm, 3-watt wire-wound Potentiometer = 100-ohm, $-watt resistor = 33,000-ohm, 78-watt resistor = 8200-ohm, 1-watt resistor = 5000-ohm, 3-watt wire-wound rheostat = 22,000-ohm, Q-watt resistor = 10,000-ohm, +watt resistor = 47.000-ohm, ,?-watt resistor 625 wiper 2-ohm, &watt resistors 250-puF capacitor, 50-volt working 8-pF capacitors, 450-volt working 47-pF capacitors, 150-volt working 2-pF capacitor, 12-volt working 250-pF capacitor, 50-volt working 5000-pF capacitor, 100-volt working Over-load trip relay GET 874 transistorsR3 22 Lv “t: TR - Control I ing reference cell R27 z‘oLJ R26 52 V 4 a v a.c. 7”””9 -Emitter --+ fol I o we r amplifier current amplifiers -Difference - Voltage Overload amplifier amplifier signal Fig.3. Power supply and control unit al Manual voltage setting[A7z,aZyst, Vol. 91 362 QUAYLE AND COOPER TR,, TR,, TR,,, TR,, = GET 102 transistors TR,,, TR,,, TRlS = OC 36 transistors TR,, TRs, TRg, TRIO, Vl v, = 150B2 valve = 85A2 valve = Main supply transformer, with earthed screen between primary and secondary V H = 1000-ohm, 3-watt rheostat Ti windings Illput, 10-0-200-220-240 Volts, 50 C/S. Output, 200 volts, 30 mA; 20 volts, 0.5 amp; 20 volts, 100 mA; 0-48-52 volts, 2 amps. = Rectifier, 5D23 = Rectifiers, OAZ 204 z, 2,s 2 3 2 4 = Rectifier, GJ4M z63 ' 8 = Rectifiers, 80 AS z,, 2 8 , 2 9 , 21, = Rectifiers, DDOOO Zll = Rectifier, lBlBlN538 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. Szebelledy, L., and Somogyi, Z., 2. annlyt. Chem., 1938, 112, 313, 323, 332, 385, 391, 396, 400. Tutundzic, P. L., Analytica Chim. Acta, 1958, 18, 60. The Analytical Chemists' Committee of Imperial Chemical Industries Ltd., Analyst, 1950, 75, 577. Taylor, J . K., and Smith, S. W., J . Res. Natn. Bur. Stand., 1959, 63A, 153. Rett, N., Nock, W., and Morris, G., Ibid., 1954, 79, 607. Cooper, F. A., and Quayle, J. C., Amlyst, 1966, 91, 363. Brown, T. H., and Stephenson, W. L., Electron. Engng, 1957, 29, 425. Kemhadjian, H., and Newall, A. F., Mullard Tech. Commun., 1959, 4, 40. Received April 19th, 1963