June, 19661 COOPER AND QUAYLE 363 Precise Coulometry: The Titration of Pure Sodium Carbonate BY F. A. COOPER AND J. C. QUAYLE (Imperial Chemical Industries Ltd., Agricultural Division, P.O. Box N o . 6, Billingham, Co. Durham) A method is given for the precise and accurate titration of sodium carbonate with hydrogen ions generated by the coulometer described in the preceding paper. This coulometer maintains automatically a constant current for a measured length of time. The results are in good agreement with those obtained by titration with standard acid referred to pure silver as the ultimate standard, and support proposals to establish the coulomb as a standard in volumetric analysis. Factors are discussed that affect the accuracy and precision of analysis by controlled current coulometry.TAYLOR and Smith1 have shown that acids and alkalis can be analysed coulometrically with high precision by using a manually controlled low current, but apparently there was no independent assay of the compounds titrated. No earlier work is known to the authors in which high currents, macro amounts and automatically controlled currents were used. The ifistrument used in our investigations2 measures time, and controls and accurately measures currents high enough to be used in macro-scale titrations. The construction of the coulometer and its mode of operation were described in the previous paper,2 but it was realised that other factors such as cell design, weighing and transfer of the sample, and even the value of the Faraday would affect the over-all accuracy and precision obtainable in coulometric titrations.In this paper these factors are discussed for the titration of sodium carbonate, a precise and accurate method for which is given. The sodium carbonate used was laboratory working standard material that had been analysed in recent inter-laboratory trials by the Society for Analytical Chemi~try,~ and was of the purity (100 0-2 per cent.) required by the Analytical Standards Sub-committee of the Analytical Methods Committee for primary standards. COULOMETER- The coulometer2 used in this work controls the current by maintaining a constant voltage across a precise standard resistor. The voltage drop across this resistor is compared with the e.m.f. of a standard cell, and the difference between them is shown on a sensitive galvanometer where a 1-mm deflection corresponds to a 7 p.p.m.error in current ; little manual correction is necessary. Three current levels of 1 amp, 100 mA and 10 mA are provided. Each level can be adjusted on a dummy load approximately equal to the cell resistance before the current is switched on to the cell. Time is measured by a quartz-crystal clock that is checked against standard radio transmission. The probable error2 in the quantity of electricity, i.e., the product of current and its time of flow, is t-25 p.p.m. Time is registered in units of 0.1 second by an electro-magnetic counter with cyclometer presentation of 5 digits. One counter can be pre-set to switch off at a given number of counts. Two independently driven counters are run in parallel; by comparing them, miscounts can be detected and erroneous experiments discarded .SUMMARY OF THE METHOD- The working electrode at which hydrogen ions or hydroxyl ions are generated is of platinum. Sodium sulphate is used as the supporting electrolyte, and is boiled in the cell before the titration to remove carbon dioxide. Copper and cupric sulphate are used as auxiliary electrode and electrolyte. The sodium sulphate solution is pre-titrated by generating, at 10 mA, hydrogen ions and hydroxyl ions to traverse the inflection, finishing at a pH just lower than that of the point of inflection. The sample is added and titrated a t 1 amp for a pre-set time that is approximately 0.2 per cent. longer than would be required if the sample were 100 per cent.pure. After boiling the solution again to expel carbon dioxide, it is cooled and back-titrated at 100 mA by generating hydroxyl ions until it is just alkaline. Hydrogen ions are then generated at 10 mA to give a known excess beyond the pH of inflection as in the pre-titration. The net anodic generation is used to calculate the purity of the sample. EXPERIMENTAL364 COOPER AND QUAYLE [Analyst, Vol. 91 In both the pre-titration and back-titration precautions are taken to ensure that no adsorption of hydrogen ions or hydroxyl ions has occurred, as shown by the reproducibility of repeated traverses of the point of inflection. TITRATION CELL- The cell used follows the design of Taylor and Smith,l and is modified to permit increased current, easier manipulation and easier replacement of the agar gel.Several designs in glass and Perspex were tried; the design eventually used, made of both borosilicate glass and Perspex, is illustrated in Fig. 1. Figures for weight loss, etc., are published in the Pyrex Bulletin No. 7, February, 1962. The rate of extraction of sodium was experimentally deter- mined as 0.5 mg on boiling 300 ml of de-mineralised water in the cell for 30 minutes, and then allowing it to stand for 20 hours. A = Titration compartment, B, C, D = Demountable sections, E =Auxiliary electrode compartment, Parts marked in black are made from PTFE. Fig. 1 . Cell for acid - alkali titration The glass titration compartment, A, containing M sodium sulphate is cylindrical with a diameter of 8.5 cm, and has a Fluon cap, the underside of which has a smooth domed shape to facilitate washing down.The lower edge of the rim is “feathered” (made thin and tapering) so that it produces a liquid-tight seal against the rim of the titration compartment. When the solution is boiled in the cell considerable differential expansion occurs, but the flexibility of the “feathered” edge accommodates this without overstressing the glass. To prevent the solid part of the cap from wedging itself into the taper aperture of the cell, because the feathered edge is flexible under load, the top edge of the cap is extended by a stainless-steel ring which rests on the rim of the glass (Fig. 2). The cap contains apertures to hold- (a) the generator electrode at which the titrant is produced. This is a piece of bright platinum foil, 7 cm by 4 cm, bent in an arc, approximately 4 cm in radius, outside the heater ( d ) ; (b) a combined pH-reference electrode (Ingold type 401-S) for end-point indication. Being coaxial in form it is less affected by potential gradients in the electrolyte than a separate glass electrode and reference half-cell ; a glass tube to inject nitrogen for removing carbon dioxide; (c) ( d ) a silica-sheathed heater ; (e) a resistance thermometer ; (f) a mercury-in-glass thermometer ; (g) a water condenser (when required), or a glass stopper (B34).Fig.2. Titration cell showing details of cell cap [To face page 364June, 19661 365 The heater is a multi-stranded helix of thin Nichrome wire, wound on a stout core wire insulated with Fibreglass braids.The core and heater are welded together at the inner end, and connected at the outer end to a metal-shrouded 2-pin plug with a bayonet safety catch. All the heating spiral is below liquid level; the rising portion of the sheath remains cool as it carries only connecting wires. Maximum heat dissipation is 13 watts per inch length, 150 watts total. A glass compartment, E, similar to A, contains the auxiliary generator electrode (copper sheet measuring 9 cm by 6 cm) and M cupric sulphate. The two compartments are connected by a tube 3-6cm in diameter, consisting of three de-mountable components B, C and D, held in position by screwed stainless-steel couplings. B and C are made of glass and are filled, by suction, with sodium sulphate from A. They contain medium-grade (No.3 porosity) sintered-glass discs to decrease the diffusion of sodium carbonate from the titration com- partmeqt A, and inlets, connected to a nitrogen supply, to blow back the solution into A. D is made of Perspex and contains a fine (No. 4 porosity) sinter cemented in with Tensol Cement No. 7 , and a gel of 3 per cent. of agar in 0-5 M sodium sulphate, to prevent liquid diffusion. PRECISE COULOMETRY: THE TITRATION OF PUKE SODIUM CARBONATE A No. 4 sinter is also held in a gasket between D and E. WEIGHING AND TRANSFER OF SAMPLE- The normal method of transfer from a glass weighing-bottle was attempted, but the capacity of the titration vessel did not allow a sufficient volume of wash water to be used. The finely powdered carbonate readily dispersed into the air when handled, probably aided by static electrification in the dry weighing-bottle.To overcome these difficulties a weighing capsule was designed in polythene, and was gold-coated all over to eliminate static effects (Fig. 3). The lid is a fairly tight fit so that it is possible to lift the capsule and contents by , 30 mm diameter Fig. 3. 12‘eighing capsule the knob on the lid. Samples are inserted by grasping the knob with ratchet forceps, lowering the capsule until it is completely immersed in the electrolyte, and pushing the bottom away from the lid by pressing on the platinum stud Lvith a spatula. The forceps and spatula are then rinsed with the minimum amount of water and removed. The capsule $Em sample is sufficiently heavy to settle to the bottom of the cell until most of the sample has dispersed; the capsule then rises clear of the electrodes and stirrer, but remains submerged, tilted on its side by the weight of the platinum stud so that the last traces of sample can dissolve, The capsule and top remain in the solution throughout the titration.pH MEASUREMC 4 NT- A Pye “Dynacap” pH meter is used to indicate the variation of pH with millicoulombs generated in the pre-titration and back-titration; the output of the pH meter is recorded on a Honeywell-Brown strip-chart recorder with a chart speed of 40 inches per hour. In order to check that the titration efficiency was 100 per cent. a t the beginning and end of366 COOPER AND QUAYLE [AnaZyyst, VOl. 91 the titration, the point of inflection was traversed three times, switching off the current at a chosen (but not critical) pH.The reproducibility of the number of coulombs required to titrate the solution from this pH to the point of inflection shows that one can ignore the possibility of the diffusion of impurities. To allow for the response time of the pH electrode only times of generation in the same direction are compared. REAGENTS- reagent grade) in de-mineralised water. grade). Sodium szd+hate--Prepare an approximately M solution of sodium sulphate (analytical- Cupric suZ$hate-Prepare an approximately M solution of cupric sulphate (general-purpose DETAILED PROCEDURE SAMPLE PREPARATION- dish, frequently stirring with a platinum rod. add a catch-weight of approximately 3 g to the capsule. AGAR GEL- Mix sufficient agar powder with de-mineralised water to give a 6 per cent.w/v solution, and boil. Add an equal volume of boiling neutral M sodium sulphate and mix thoroughly to give a final 3 per cent. w/v gel. Pour into a warm, dry gel compartment, and when the surface of the gel is firm (after approximately 20 minutes) cover with distilled water by using a tangential jet. Store in boiled-out 0.5 M sodium sulphate solution adjusted to pH 7 and protected from carbon dioxide. PREPARATION AND ASSEMBLY OF CELL- Remove any grease from the platinum electrode with chromic - sulphuric acid, rinse and finally immerse the electrode in aqua regia for a few seconds. Then rinse thoroughly. Clean the copper electrode with emery cloth. The deposition of copper is of no interest, but simply ensures that neither hydroxyl ions nor hydrogen ions are produced at this electrode.Clean the components of the glass cell thoroughly and finally boil in de-mineralised water. Grease the ground-glass faces with a silicone grease free from alkali-metal esters, and assemble the cell as indicated in Fig. 1, with A on a magnetic stirrer. Insert a plastic coated stirring rod. Partly fill A with M sodium sulphate solution, and fill compartments B and C completely with M sodium sulphate solution by suction from A. This expels air, containing carbon dioxide, from B and C, keeps the gel moist, and allows the solution level in ,4 to be adjusted so that the cell contains the minimum volume necessary for titration, thus reducing the risk of loss by splashing.E must also be filled above the level of the side-arm with sodium sulphate solution of at least 0.5 M concentration so that the gel is kept moist and its conductivity is not reduced by loss of ions due to diffusion. If cupric sulphate is in contact with the gel, some transfer of cupric ions may occur, so the sodium sulphate solution in E is not replaced by cupric sulphate solution until immediately before the titration. Insert a water-cooled condenser in the main aperture in the cap, switch the heater on full to boil the solution in A, and remove carbon dioxide. Blow back the solution from B and C, taking care to use a sufficiently low nitrogen pressure (corresponding to a flow of 2 litres per hour) to avoid rupturing the gel. Roil for 10 minutes, switch off the heater and cool the solution by bubbling through it a fast flow of "white spot" nitrogen, which is passed through a soda - asbestos column to remove carbon dioxide.The cooling rate can be increased by blowing air on to the side of A. PRE-TITRATION- In order to pre-titrate the solution, remove the condenser when the solution temperature has dropped below 75" C and insert the combined pH-reference electrode which can tolerate this temperature. Switch the pH meter to the 6 to 8 pH range, reduce the nitrogen flow, and fill B and C by suction to a depth of a few millimetres, which is sufficient to carry 100 mA but constitutes a negligible volume (3 per cent.) of untitrated solution. Titration of this volume at a pH between 6.5 and 7.5 to the equivalence point would require less than 1 second Dry the sodium carbonate sample to constant weight at 270" C, 2 10" C in a platinum Cool the sample in a desiccator and quickly Insert the lid firmly and re-weigh.June, 19661 367 at 10 mA, i.e., 2 p.p.m.of the total titre. Siphon the 0.5 M sodium sulphate solution from E, replace with M cupric sulphate solution and insert the copper electrode. Connect the electrodes to the output sockets of the coulometer. Adjust the current to 10mA on dummy load. Switch off, re-set the counter to zero, switch on the recorder chart drive and the current to the cell generating hydroxyl ions. Two hands are required. The recorder pen is not jolted on switching, but the slight effect of the generator field on the reading of the pH electrode gives a small marker (0.05 pH unit).Mark the start of the pre-titration on the recorder chart. Titrate at 10 mA to pH 7-4, or until sufficient of the curve is recorded to allow determination of the point of inflection (Fig. 4). Yote on the chart the point at which the current was switched off and the number of seconds counted. Ten p.p.m. of the total titre is equivalent to +5 seconds. Re-set the counters to zero, reverse the current and repeat the pre-titration until the number of milli- coulombs between the cut-off pH and the point of inflection in the direction of generation of acid is reproducible. PRECISE COULOMETRY: THE TITRATION OF PURE SODIUM CARBONATE Location to this precision permits an error of FO.1 pH units. Finish the pre-titration on the acid side.ADDITION OF SAMPLE- Fill B and C by suction from A before adding the sample, so that the sinters and intervening electrolyte minimise the risk of diffusion of carbonate into the gel. Switch off the stirrer to make manipu- lation of the sample capsule in the solution easier. Turn off the nitrogen supply and lower the capsule, held in ratchet forceps by the knob on the lid, under the liquid surface to prevent dispersion of the sample into the air when the capsule is opened. Push the capsule away from the lid by pressure on the platinum stud, using a glass rod or spatula. Release the lid, rinse the forceps and rod or spatula with de-mineralised water before removal so as to wash into the cell any traces of sample which may adhere to them. Insert the stopper in the cell cap and re-start the stirrer.Remove the combined pH electrode, rinse and store in distilled water. TITRATION- The resistance of the cell is approximately 30 ohms. The temperature reaches 40" to 50" C, but the gel will not suffer unless 70" C is exceeded. Re-set the counters to zero and pre-set the main counter for a time 10 seconds in excess of that required if the sample were 100 per cent. pure. Switch to hydrogen ion generation in the cell. Adjust the current if necessary every 2 minutes for the first 15 minutes, and then every 15 minutes until the end of the titration when the current will be switched off automatically. Adjust the current to 1 amp on the dummy load. Switch off the current. BACK-TITRATION- Switch the heater full on to boil the solution and expel carbon dioxide.Blow back the solution from B and C so that any carbonate which has diffused into these compartments will be neutralised and the carbon dioxide expelled. Wash down the underside of the cell top and stopper with de-mineralised water and replace the stopper with a water condenser. Boil for 10 minutes, switch off the heater, and cool by bubbling purified nitrogen through the solution. Fill B and C to a depth of a few millimetres. Adjust the current to 100mA on the dummy load. Switch off the current and re-set the counters to zero. Switch on the current to generate hydroxyl ions in the cell to a pH of approximately 7.4. Switch off and note the time. Fill and empty B and C until less than 0-03 pH change occurs (usually not more than three flushes are required) to ensure that no hydrogen ions or hydroxyl ions can be held in the sinters.Re-fill to a depth of a few millimetres. Adjust the current to 10 mA on the dummy load and repeat the procedure for pre-titration. CALCULATION- Calculate, from the chart speed and chart distance, the number of seconds of excess hydrogen ion generation after the last point of inflection in the pre-titration. In the same way, calculate the total number of seconds of hydrogen ion and hydroxyl ion generation at 10mA before the last point of inflection in the back-titration (Fig. 4). Multiply each current, in amps, by the time passed, in seconds, to give coulombs. Subtract the total number of coulombs of hydroxyl ions generated from the total number of coulombs of hydrogen368 COOPER AND QUAYLE [Aqcalyst, Vol.91 I I i I Point of inflection I , r . 1 - iL1 , pH 6.4 PH- Generation time (in seconds) at lOmA Traverse number H+ OH- I 76.0 (from starting pH) 2 - 103.0 3 102.0 - 4 - 102.0 5 52.0 (to point of inflection) - Total 230.0 205-0 Net time of H+ generation 25-0 seconds (Note: A 3 second error in back-titration is approximately 10 p.p.m. for a 3-g sample) Fig. 4. A typical record of back-titration. Chart speed 40 inches per hour ions generated; any lags in electrode response to changing pH in the pre-titration and back- titration will cancel out. Divide by the Faraday and the weight of sample, and multiply by the equivalent weight and by 100 to give the percentage purity, e.g., Standard cell voltage . . .. .. .. . . 1.01943 volts Resistor (nominal 1 ohm for 1 amp) .. .. . . 1.01806 ohms Current (nominal 1 amp) . . I . .. .. . . 1.00135 amps Weight of sodium carbonate in vacuo . . .. .. 2.99688 g Equivalent weight of sodium carbonate . . .. .. 52-9945 Gram equivalent of sodium carbonate in sample. . .. 0-0565508 Value of the Faraday . . .. . . .. . . 96,489 absolute coulombs per g cquivalent Number of coulombs required for 100 per cent. purity . . Switch off main current at . . .. .. .. . .-: + 10 = 5459 seconds 5456.52 Hydrogen ion generation- Current, in amps Time, in seconds Coulonibs 1-00135 5459-0 5466037 0.01 33.0 0.33 0.1 102.0 10.2 0.01 25-0 0.25 Total coulombs used = 5466.70 - 10.45 = 5456.25 couIombs Hydroxyl ion generation- 5456.25 Percentage purity = 5456.52 x 100 = 99.995 per cent.Atomic weights are based on lac = 12 scale. KESULTS An estimate of the diffusion of sodium carbonate into the agar gel was obtained by performing the pre-titration to pH 7 , then adding 3 g of sodium carbonate to the solution in A and leaving it there for 1.5 hours instead of titrating it. The pH of the solutions from compartments B and C was then measured, and the solutions titrated with 0.01 N sulphuric acid to pH 7 (see Table I). Diffusion into compartment C was negligible, and as C was separated from the gel by a KO. 4 porosity sinter, loss of carbonate into the gel was assumed to be nil. TABLE 1 DIFFUSION OF SODIUM CARBON-4TE INTO COMPARTMENTS B AND C Compartment PH required to bring p1-I to 7 Volume (in ml) of 0 . 0 1 ~ reagent B 10.0 6-0 C 6-5 0.1June, 19661 369 In order to assess the diffusion of cupric ions, compartments A, B and C were filled with sodium sulphate solution, compartment E was filled with cupric sulphate solution and they were left for 16 hours.No visible contamination was detected; the cupric-ion content of the solution from B and C was determined colorimetrically and polarographically and found to be 0.036 mg, thus showing that a transfer of cupric ion would give an error of only 20 p.p.m. if a titration had been performed. As the gel is never left in contact with the cupric sulphate during actual titrations for more than 7 hours, the error due to copper diffusion would be much less than 20 p.p.m. Diffusion of hydrogen ions from the cupric sulphate solution into compartment C was found to be nil.To test the reproducibility of the instrument, 25-ml aliquots of an approximately 120 g per litre solution of analytical reagent grade sodium carbonate were titrated. These were weighed into the titration cell from a glass weight b ~ r e t t e . ~ The balance was calibrated by using it to weigh Sational Physical Laboratory certified weights. The results are given in Table 11. The atomic weights used were those agreed by the International Union of Pure and Applied Chemistry5 in 1962, based on 12C = 12, giving 52.9945 for the equivalent weight of sodium carbonate. TABLE I1 DETERMINATIO?; OF REPRODUCIBILITY WITH A STANDARD SOLUTION OF SODIUM CARBONATE (SAMPLE 1) PRECISE COULOMETRY: THE TITRATION OF PURE SODIUM CARBONATE Weight of Weight of in grams in grams in grams sodium carbonate sodium carbonate Coulombs Sodium carbonate Percentage solution added, in vaczco, required found, purity 26-6718 3.142 15 5717.88 3.14042 25.9257 3.05425 5558-26 3.05275 25.47 13 3.00072 5460.1 9 2.99889 26.8610 3.16444 5758.59 3,16278 27.4556 3.23449 5885.55 3.23251 30.5787 3.60242 6555.32 3.60037 26.5084 3-12290 5683.09 3.1 21 31 Mean .. .. 99.945 99.951 99.939 99.948 99.939 99.943 99.949 99.945 Catch-weights of approximately 3 g of carefully dried sodium carbonate of a different make (sample 2) were weighed in gold-coated polythene capsules which were subsequently transferred to the titration cell. Results of the determination of purity are given in Table 111. TABLE I11 PURITY OF SODIUM CARBONATE (SAMPLE 2) sod Weight of in vacuo, in grams 3.0232 3.0067 3-0052 3.0077 3.0034 3.0099 3.0073 .ium carbonate Coulombs required 5504.16 5474.27 547 1.44 54 7 5.3 2 5468.16 5480-02 5475-15 Weight of sodium carbonate found, in grams 3-02304 3.00662 3.00502 3.00720 3-00327 3.00978 3.0071 1 Mean .. .. Percentage purity 99.995 99.997 99.994 99.983 99.996 99.996 99.994 99.994 Combined standard deviation (Tables I and 11) 0.005. Sample 2 is kept as a laboratory working standard and has been assayed independently by weight titration with hydrochloric acid standardised against silver. The mean value and the standard deviation of eighteen results obtained over 2 years were, respectively, 99.993 per cent. purity and 0-003, with extreme figures for purity of 100.000 and 99.990. The mean values obtained by the weight titration and coulometric assay differ by only 10 p.p.m.Eight samples of sodium carbonate from the second source were weighed into polythene capsules and titrated. The operator knew the weight only to k2 mg (660 p.p.m. in 3 g), and the excess acid was calculated from the upper limit of the weights. Table IV compares the sodium carbonate found with the sodium carbonate added, i.e., the weight in vacua corrected for the percentage purity found by the weight titration method. Sodium sulphate370 COOPER AND QUAYLE [Analyst, Val. 91 from a different manufacturer was used for the last four determinations. The solution was initially much more alkaline (pH >8 instead of between 6 and 7), but it was not realised until the titration was in progress that this solution had been used to make the gel.Diffusion of alkali from the gel made with this solution probably accounts for the high result of 190 p.p.m. ; the solution was neutralised before being used for gels for the subsequent titrations. TABLE IV TEST OF REPRODUCIBILITY ON UNKNOWN WEIGHTS Sodium carbonate added, in grams 3.00533 2.99783 3.00302 3.00131 3.00552 3.00508 3.00789 3.00167 Sodium carbonate found, in grams 3.00560 2.99773 3.00379 300143 3-00609 3.00488 3.00764 3-00137 Difference, in p.p.m. + 90 - 30 4- 60 + 40 + 190 - 70 - 80 - 100 In titrating sodium carbonate from the same source (sample 2), different quantities of excess hydrogen ions were generated in order to test the effect of varying the excess. The results are given in Table V, and also indicate the efficiency of generating hydrogen ions when no sodium carbonate is present to react with them, and of generating hydroxyl ions at one-tenth the current density used during the main part of the titration of sodium carbonate.TABLE V EFFECT OF VARYING THE EXCESS HYDROGEN IONS GENERATED Excess Percentage of I \ Percentage Weight (in grams) of sodium carbonate- h coulombs main titration added found purity 10 0.2 3.00051 3.00039 99.996 23 0.4 3.00704 3.00695 99.998 50 1.0 3,00172 3.00 145 99.991 As the mean of the results given in Table 111 is 99.994 and the standard deviation is 0.005 it can be seen that, unless errors compensate, within this range- (;) the quantity of excess hydrogen ions generated is not critical, (ii) the efficiency does not decrease when no titratable substance is present, (iii) the titration efficiency is at least 99 per cent.with hydroxyl ions generated at one-tenth the current density of that used in the main part of the titration of sodium carbonate, shown by the generation of 10,000 p.p.m. of hydroxyl ions which resulted in less than 100 p.p.m. error. SUMMARY OF POSSIBLE ERRORS- Errors in the weight of samples handled in capsules were initially kO.1 mg, but this value was later reduced to f- 0.05 mg by the use of a more sensitive balance. These correspond to 30 and 15 p.p.m., respectively, in 3 g. The equivalence point can be determined to + l o p.p.m. The errors associated with the determinations of atomic weight are those assigned by I.U.P.A.C. in 1962.5 A summary of the estimated possible errors is given below- Atomic weight of sodium.. .. . . .. . . &- 2-5 p.p.m. Atomic weight of carbon .. .. .. . . & 4 p.p.m. Atomic weight of oxygen.. . . .. . . . . + 6 p.p.m. Weight of samples in capsules . . .. . . . . 1 3 0 p.p.m. (initially) Weight of samples in capsules . . . . . . . . +15 p p m . (finally, see Tables IV and V) Determination of the equivalence point . . . . &lo p.p.m. Value of the Faraday . . . . .. .. . . 5 3 3 p.p.m. Timer . . . . . . .. .. .. . . & 3 p.p.m. Time (to nearest 0.1 second) a t 1 amp . . .. . . &lo p.p.m. Uncertainty in the absolute volt . . probably 5 1 0 p.p.ni. National Physical Laboratory certification . . . . & 5 p.p.m. Temperature . . ,. . . .. .. . . f 1 0 p.p.m. (initially) Temperature .. ,. .. .. .. . . f 4 p.p.m. (finally, see Tables IV and V) Standard cell voltage-June, 19661 PRECISE COULOMETRY: THE TITRATION OF PURE SODIUM CARBONATE Precise resistor- Uncertainty in the absolute ohm . . probably A10 p.p.m. Makers’ certification . . .. . . probably f 1 p.p.m. Instrument discrimination . . .. .. . . f 6 p.p.m. DISCUSSION 371 The determinations in Tables 111, IV and V were consecutive, though obtained over several weeks. The results in Tables I1 and I11 show that it is possible to achieve a standard deviation of 50 p.p.m. in the coulometric titration of sodium carbonate that is slightly less precise than that obtained by reference to silver. If there is any bias, values for the purity given by this method are likely to be high, due to contamination of the hydrochloric acid by other chlorides before analysis.Errors in the coulometric method are likely to be caused by low generation efficiency and will, therefore, also give high apparent purities. Xever- theless, the agreement to 10 p.p.m. of the means by the two methods suggests that the errors are comparable. The coulometric analogue of the normal volumetric practice of adding excess acid, boiling out carbon dioxide and back-titrating with dilute alkali was followed, because it was found tedious to remove the carbon dioxide by passing nitrogen through the solution.1 Because this method gave satisfactory results, no check was made of the effect of changing parameters other than the excess of hydrogen ions generated. It is thought unlikely that highly critical conditions were selected by chance.Nevertheless, further investigation to define more closely the optimum conditions might succeed in reducing the errors still further and simplifying the actual titration. CELL DESIGN- After the determinations in Table I11 were completed, considerable difficulty was experienced with leakage, particularly from the joint between A and B. The screwed stainless- steel coupling was finally replaced by “Tufnol” flanges (Fig. 5), so providing an exposed - 4 B A I 10.16 cm (b) Fig. 5. Tufnol flanges. Fig. 5 (a) : the flanges are held in position by silver steel rods with 2BA and 4RA threads. They are fitted by sliding into the holes and screwing the nuts tight. Fig. 5 ( b ) : method of fixing the flanges (centre section) glass-to-glass joint so that any leakage could be detected.Cell design is still a major problem involving a compromise between ease of cleaning and replacement, low electrical resistance and precautions to avoid loss of sample. The cell and electrode design were chosen purely for the practical reasons already mentioned, and since satisfactory results were obtained these conditions were not vaned, CHOICE OF AUXILIARY ELECTRODE SYSTEM- It is important to suppress the generation at the auxiliary electrode of ions which can migrate and take part in either the chemical or electrode reaction in the titration compart- ment. Taylor and Smith1 accomplished this in titrating acids by using the oxidation of silver372 COOPER AND QUAYLE [Amlyst, Yol. 91 to silver chloride as an auxiliary system.Insufficient details of their sodium carbonate analysis are given, but a silver cathode was apparently used, possibly after deposition of silver chloride so that the reduction involved only the liberation of chloride ions. A silver - silver chloride electrode with potassium chloride was therefore tried, but it was found difficult and tedious to deposit sufficient quantities of silver chloride in an even coating. During electrolysis hydroxyl ions were produced, and chloride ions migrated to the anode where they were oxidised, so giving incorrect results. No significant improvement resulted on replacing the potassium chloride solution with sodium sulphate. In deciding on an alternative auxiliary system the following points were considered- (a) electrode potential, (b) pH of the solution, (c) preference for a salt of sulphuric acid, (d) a simple method of detecting diffusion through the gel.Copper and cupric sulphate were chosen as fulfilling most of these conditions. The Cu2+/Cu potential is low under the given conditions, and the deposition of copper, preferen- tially to the reduction of water, is well-known. It gives an acid solution, and although the pH is as low as 3.2 for M cupric sulphate, hydrogen ions and cupric ions are attracted to the copper cathode during most of the titration. The strong blue colour of the hydrated cupric ion also gives immediate indication of penetration into the agar gel. SUPPORTING ELECTROLYTE- It is essential that the electrolysis of impurities in the sodium sulphate does not cause errors, particularly as the concentration of sodium sulphate is ten times that of sodium carbonate at the beginning of the titration.The maximum impurity which may react during electrolysis, according to the makers’ specification, is 0-002 per cent. as reducing substances; chloride, heavy metals and ammonium ions may be present up to 0.001 per cent., and iron up to 0.0005 per cent. In 300 ml of M sodium sulphate solution, in comparison with 3 g of sodium carbonate, these become 280 p.p.m., 140 p.p.m. and 70 p.p.m., respectively. In the authors’ experience chloride can be oxidised irreversibly, even in alkaline media. However, any irreversible reaction would take place during the pre-titration, Errors due to reversible oxidation or reduction should not appear, as the pre-titration and back-titration finish in oxidising conditions.Therefore, impurities in the sodium sulphate should not affect the accuracy of the titration, whether they are reversibly or irreversibly oxidised. For the last four determinations in Table IV, sodium sulphate from a different manu- facturer had to be used. Although this latter sodium sulphate was within specification, the initial pH was 8.1 instead of between 6.0 and 7.4, and the equivalence pH was 7.3 instead of approximately 7. Some precautions were taken, such as neutralising the solution before making up the gel. Care must obviously be taken to avoid absorption into the gel of any alkali (or acid), which may diffuse out and cause errors. THE VALUE OF THE FARADAY- For accurate coulometric titrations the value of the Faraday must be known accurately.Remy6 has summarised the determinations to date, re-calculated these on the basis of the isotope lZC = 12, and considered critically the reliability of the results. The mean of these, excluding the one which he considers seriously in error, is 96,489 absolute coulombs per g equivalent. A statistical examination of the errors which each observer gives for his deter- mination indicates that the 95 per cent. confidence limits for the mean are &3 absolute coulombs per g equivalent. THE COULOMB AS A STANDARD IN VOLUMETRIC AXALYSIS- This has already been suggested7 and would be useful because many of the present standard substances used in volumetric analysis continue to be the subject of much critical examination.The Society for Analytical Chemistry has, so far, recommended to the Inter- national Union of Pure and Applied Chemistry only sodium carbonate as being of sufficient purity (100 +_ 0-02 per cent.) for use as a primary standard, and this has not yet been accepted. The definition of the coulomb, on the other hand, is already agreed internationally and, as is well known, it can be measured without great difficulty against the fundamental standards of mass, length and time. Most inorganic reactions involve electrons, and if aJune, 19661 PRECISE COULOMETRY: THE TITRATION OF PURE SODIUM CARBOXATE 373 reaction can be made to proceed with 100 per cent. over-all efficiency by generation of ions at an electrode, and the completion of the reaction and the number of coulombs used can be accurately determined, then the coulomb may be used as a standard for volumetric analysis. These conditions have been satisfied for the titration of sodium carbonate with the technique described and electrical apparatus which is easily operated and stable. It is planned to investigate the titration of other primary standard compounds, including those that may be recommended for oxidation - reduction and precipitation reactions. CONCLUSION The results show that the coulometric titration of sodium carbonate can be almost as precise as titration with hydrochloric acid standardised against silver. The mean values of the coulometric and volumetric results for the purity of samples agree to within 10 p.p.m. Compared with the established method, which starts from silver and takes at least 5 days, the coulometric method is rapid, taking less than 1 day. It is therefore an attractive alternative to the present procedure. If investigation of coulometric titrations of other acids and alkalis, and of reactions involving oxidation and reduction shows the same accuracy and precision, this should establish the coulomb as the ultimate titrimetric standard. We thank Mr. R. M. Pearson for the initial suggestion on which this work was based, and for his continued help and advice. Mr. J. Lindsley and Mr. A. W. Remmer carried out most of the experimental work, and Mr. H. N. Redman prepared and weighed the samples. REFERENCES 1. 2 . 3. 4. Redman, H. N., I b i d . , 1963, 88, 654. 5. 6. 7. Taylor, J. I<., and Smith, S. W., J . Res. Natn. Bur. Stand., 1959, 63A, 153. Quayle, J. C., and Cooper, F. A., Analyst, 1966, 91, 355. Analytical Methods Committee, I b i d . , 1965, 90, 261. Commission on Atomic Weights, Pure and Applied Chemistry 1962, 1-2, 255. Remy, H., Chernikerzeitung, 1962, 86, 167. Tutundzic, P. S., Analytica Chim. Acta, 1958, 18, 60. Received April 19th, 1963