138 SEYLER AND LLOYD: XV.-Studies of the Carbonates. Part 11. Hydro-lysis o f Sodium Carbonate and Bicarbonate and the Ionisation Constants of Carbonic Acid. By CLARENCE ARTHUR SEYLER and PERCY VIVIAN LLOYD. THE ionisation constant of carbonic acid in the equilibrium equa-tion [HI x [HCO,] =k2[H2C03] is well established by the experi-ments of Walker and Cormack and has the value 3 * 0 4 ~ 1 0 - ~ a t 18O. The value of the second ionisation constant in the equation [HI x [CO,] =k,[HCT03] is however lstill uncertain even after correction of the value deduced by Bodlander (Zeitsch. physilcal. Chem. 1900 35 32) from the experiments of Shields (ibid. 1893, 12 167) which was first made by McCoy (Amer. Chem. J. 1903, 29 437). This is due t o the fact that the value of k found experimentally varies with the concentration of the carbonate.Two methods have been used namely: (1) That of McCoy (Zoc. cit.) who determined the ratio (2) That used by Shields (Zoc. cit.) who determined the ratio 5 = - IHW1 [OH] by experiments on the hydrolysis of ethyl k [C%l acetate and by Auerbach and Pick (Arb. Kais. Gesundheitsamt, 1911 38 II) who determined the hydrogen concentration colori-metrically. increase decidedly with dilution but not in the same ratio as would be k In both cases the values of -t and 5 A3 7% expected if k were really subject t o variation. This can scarcely be thO case so that the cause of the apparent variation must b STUDIES OF THE CARBONATES. PART TI. 139 sought i n the degree of ionisation of the carbonate and bicarbonate.c N f ~ H C 0 3 and Let k be the apparent value of the ratio -CNa&Os [H,co3] k,l of the ratio 'h'aHC03. [OH]. Cln.a2c0:< The values of [H2C0,] and [OH] do not involve any ionisation correction the latter having been directly determined either by the hydrolysis of ethyl acetate or by a colorimetric method; but the values of C N ~ ~ I C O and C(NaaCO:2 require to be multiplied by tho degree of ionisation of From this it is evident a t eIy. Attempts have b,een the values of a and the respective salts a and fl. Hence k f and (2) '3 = ktE i. k , that k and /cci will not increase proportion-made by all workers to form estimates of p. S t i egli t z (Car iz eg i e Ins t . Pu b 1 i CQ t .i o i l , No. 107) assumes the dissociation of sodium bicarbonate to be the same as t h a t of sodium acetate.This is probably a fair approxim-ation. The ionisation of the carbonate has be'en assumed to be the same as t h a t of sodium sulphate. This is more doubtful. Stieglitz assumes f o r a concentration of 100 x 10-3 fl=O*687 and for 300 x 10-3 p=0*584. These are no doubt too high since Harkins and Bray show ( J . Amer. Chein. Soc. 1911 33 1864) that ions such as NaSO exist in concentrated solutions. Bray estimates for c = 100 x 10-3 p = 0.598 and for c = 1000 x 10-3 p=0*420. Auerbach and Pick simply assume a value p=0*60 for c=95 x 10-3. It appeared to us t h a t the problem could be attacked in another way. If we have good determinations of k, and kdat corresponding concentrations it is evident that we can calculate a by eliminating k from equations (1) and (a) namely, k k kt" * k, a = - 2, Were k is well established.Most workers have taken too high For 2 5 O McCoy used 1~,,=1*2 x 10-14 Auerbach The later determinations of Kanolt (Cctrjzegie Inst. f'ublicatioiz, Auerbach and Pick have recalculated Shields's values for k d as a value f o r k,. and Pick k,= 1-05 x 10-14. No. 63) give decidedly lower figures namely 0.82 x 10-14 a t 25O. follows : c (equivalents). kd. 380.0 x 8.16 x lo-' 188.0 9-50 95.4 11-30 47.6 12.60 H 140 SEYLER AND LLOYD: The figures plotted on logarithmic paper lie very nearly on a straight line. McCoy gives values for k which are subject to correction for the diminished solubility of carbonic acid in saline solutions as shown by Stieglitz (Zoc.cit.): C. k uncorrected. Ic corrected. 100 x 10-3 5290 6397 3 00 4460 4691 1000 3120 3726 When k is plotted against logc (where c=coiicentration in milligram-equivalents per litre) the results lie nearly on a straight line k = 8739 - 1671 log c. We thus get values for I; correspond-ing with the concentrations in Shields's experiments : C. kd. k,. a calculated. 95.4 x 10-3 11-30 x 10-5 5400 0.775 188.0 9.50 4970 0.708 380.0 8.16 4450 0.680 The values for sodium acetate according t o Kohlrausch are: C. (36.4 x 10-8 188.0 380.0 a 0.785 0.739 0-660 The results are close enough t o show that no great error will be made by taking the dissociation of the sodium bicarbonate as equal to that of the acetate.The dissociation of sodium chloride is decidedly greater. The empirical formula for k,=S739 - 1671 log c serves t o express the results between c=lOOO and 100 but does not allow us t o calculate the value at infinite dilution. I f however by experi-ments a t t,he highest possible dilutions we can obtain an approxim-k a t b n to 2 = k a! a t such dilutions that a"= we should have k P data for calculating /3 a t least' approximately since I n the experiments to be described we determined k at dilu-tions c = 12.5 x 10-3 G = 10 x 10-3 and even c-5 x 10-3 and found that it approached a maximum value of 7124 which we take as '2. k3 This gives us the value of li,=4*27 x 10-11 and kcl = !?! = 19.2 x 10-5. k3 k p = -C a2. 7124 It also enables us to calculate fl from the formul STUDIES OF THE CARBONATES.PART 11. 141 Thus we get: C. kc. a. a2 B . 1*104-0*32010g C. ~ O O X ~ O - ~ 5397 0.783 0.613 0.464 0.464 300 4691 0.700 0.490 0.323 0.311 1000 3726 0,525 0.275 0.144 0.144 It will be found that' if fi is plotted against logc the result is a straight line P = 1.104 - 0.320 log c. This formula will enable us to evaluate fl approximately between c=100 x It probably holds good even a t far smaller concentrations since the formula 8739 - 1671 log c gives for c = 1 0 x 10-3 a value 7068 against 7124 found. Since a2=7124 Pit follows t h a t a is very well represented by and c = l O O O x 10-3. k, (1.104 - 0.32 logc) 8739 - 1671 logc ' t,he formula a2= 7124 The following values for a and P are calculated f o r round con-The concentrations are milligram-equivalents per litre : centrations.C X 103 50 100 200 300 400 500 700 800 1000 P 0-560 0.464 0.368 0.311 0.271 0.240 0.194 0.175 0.144 a 0.822 0.782 0.731 0.694 0.663 0.636 0.588 0.566 0.525 a2 -1 - ac. 190.4 x 10-3 281.6 398-6 472.4 523.0 556.8 588.9 592.4 579.4 NoTE.-These figures are carried out to three decimal places for purposes of calculation but it is not of course supposed that they are significant to anything like this degree. These values represent the activity of sodium carbonate t h a t is to say the active mass (as regards the CO ion) and of sodium bicarbonate (as regards the HCO ion) in equilibriuni with each other and with carbonic acid.Those for a are founded on the ionisation of sodium acetate calculated from the conductivity. The values for P are much smaller than would be expected from analogy to sodium sulphste even after allowing for the presence of ail intermediate ion NaSO (Harkins and Bray Zoc. cit.). There is however evidence shortly to be presented t h a t P really corresponds with the concentration of the CO ion and t h a t the dissociation is n o t represented by Na,CO = 2Na + CO, b u t by Na,CO = Na + NaCO and NaCO,= Na + CO,. I n the former case the sodium ion concentration would be 2[C03]=2fic where c is the molecular (not equivalent) concen-tration whilst the non-ionised sodium carbonate would be (1 - P ) c 142 SEYLER AND LLOYD: I n the latter case the sodium ion concentration will be greater, “a’] = 2[C03J + [NaCO,] whilst.the non-ionised carbonate will be smaller Cxa2coJ = c - [CO,] - [NaCO,]. If a be the degree of ionisation of sodium carbonate in the first stage we shall have CNa2Co3 = c(1- a) [CO,] = c p ; also since we have [NaCO,] = c - [CO,] - C N ~ ~ C O ~ = c - c/3 - C( 1 - a ) = c(a - /3). c = [CO,] +[ NaCO,] + Cha2c03, Further “a’] = 2pc + c(a - /3] = c(a + p). I n the mixtures such as we have been dealing with in which the bicarbonate largely preponderates we have assumed a to be the same as that of sodium acetate a t the same total sodium con-centration. I n this case the assumption will not be far from the truth. I n seeking t o apply the results to solutions of pure carbonate, Some other assumption with regard to the first-stage ionisation will have to be made since the sodium ion concentration of a solution of pure carbonate is undoubtedly less than that of a solu-tion of bicarbonate of the same equivalent concentration.It may be said that for the same reason the value of p will be different in a decinormal solution of pure carbonate from what it would be in a mixture consisting chiefly of bicarbonate. How-ever in McCoy’s experiments the carbonate varies from a trace to 32 per cent. whilst in those of Shields it varies from 100 per cent. to 50 and 20 per cent. without showing any noticeable drift in the constant. As a first assumption we shall assume that /3 is the same in all mixtures of carbonate and bicarbonate of the same total sodium concentration.Experiments on the value of L d = for piire carbonates would k a enable us to test the question. As regards a several assumptions niay be made. (1) That ~ r ~ ~ = k n is the same a3 for solutions of “a,C%I sodium acetate a t the same sodium ion concentration (Harkins and Bray loc. cit.). (2) That the degree of ionisation according to the first stage, Na,CO,=Na+NaCO, is the same as that of sodium acetate at the same total sodium concentration. (3) That i t is the same as that of sodium acetlate a t the same rnoIecular concentration. (4) That i t is the same as that of sodium acetate a t the same sodium ion concentration. Of these (1) and (4) require us to know approximately the total sodium ion concentration. This could be obtained roughly o STUDIES OF THE CARBONATES.PART 11. 143 assumption (2) or (3) and then corrected by a series of approxim-ations. Assumption (1) we think is very doubtful since I, varies with concentration and we do not know that its variation is dependent on the sodium ion concentration when [NaCO,] and [Na] are not present in equal quantity. I n the dissociation NaA = Na + A the negative and positive ions are equal in number but in the dissociation Na,C03=Na+ NaCO they are not since [NaCO,] is reduced and [Na] increased by the further reaction NaCO,=Na+ NaCO,. Assumption (3) has been used in the case of sodium bisulphate with success by Noyes (Cnrnegie Inst. Publication No. 63). We may use it as an approximation and calculate the value under assumption (4) therefrom (c = milligram-molecules per litre).- -Under assumption (3) we have the following results, 2c. 100 400 1000 2c. 100 400 1000 C. a. (l-a) B. 50 0.822 0.178 0.464 200 0.731 0.269 0.271 500 0.636 0.364 0.144 c. [Na,CO,]. [NaCO,]. [CO,]. [Na]. 50 8-88 17.9 23.2 64.3 200 53.70 92.0 54.3 200.6 500 181.80 246.1 72.0 390.1 (a-8). 0.358 0.460 0,492 E x 103. 129.7 343.6 528.1 (a+B). 1.286 1.002 0.780 ka x lo3. 83.3 118.3 114.1 If we use these figures for the sodium concentration to obtain t,he degree of dissociation a’ on assumption (4) and recalculate the sodium concentration therefrom we shall obtain the following values : 2c. 100 400 1000 2c. 100 400 1000 C. a’. (1 -a’). B. 50 0.80 0.20 0.464 200 0.69 0.31 0.271 500 0.58 0.42 0.144 c.[Na,CO,]. [NaCO,]. [CO,]. “a]. 50 10.0 16-8 23.2 63.2 200 62.0 83.8 54-3 192.2 500 210-0 218.0 72.0 362.0 (a’ - B ). 0.336 0.419 0.436 E x 103. 106.0 259.0 376.0 k is the value of the factor CNaI X [ NaCo21 bnd L Na,CO,I kb = “a1 x I C0,l . [ NaCO,] (a‘+B). 1.264 0.961 0.724 kb x lo3. 87.0 124.0 119.0 It is to be observed that kb (which is concerned only with ions) is not greatly affected by the assumption as regards a and is more nearly constant than k, which involves the concentration of the non-ionised salt. The value of k increases with the concentration but on eithe 144 SEYLER AND LLOYD: assumption is less than t h a t for sodium bicarbonate (or acetate) a t the same molecular concentration or sodium ion concentration.Th,e Vulzre of %.-This we calculated to be 19.2 x 10-5 at$ con-JG centrations of a b o i t 10 x 10-3 and under. I n order to check this we made some determinations of the value by Shields's method namely the velocity of hydrolysis of ethyl acetate. For c = 100 x 10-3 we obt'ained k d =12.69 x 10-5 11-72 12.15 mean 12.18 x 10-5. This result is rather higher than that calculat'ed from Shields's For c = 12.5 x 10-3 we obtained Ic,~ =21.5 x experiments namely 11.6 x 10-5. 22.2 21-8 A second series gave: 16.8 10-5 16.8 10-5 For some reason two experiments gave decidedly lower results The mean of all the experiments is 19.8 x The average would give lc,=4.15 x 10-l1. The Effect of Sodium Ghloride.-For the purposes of another investigation it was desired to know what effect would be pro-duced on the equilibrium of carbonat,es and carbonic acid by a salt with a common sodium ion such as sodium chloride.It was expected t h a t if in a decinormal solution of sodium carbonate the sodium concentration was raised to normal strength by sodium chloride the value of k would be diminished until it had about the same value as in a normal solution of pure carbonate and bicarbonate. It was found that k was indeed reduced but the value was about 23 per cent. higher than t h a t in the absence of sodium chloride. than the others b u t we could see no reason for rejecting them. Concentration of carbonate (equivalents). 100.0 x 10-3 100.0 1000*0 12.5 12-5 100.0 Concentration of sodium chloride.Total Na. k,. 0.0 100.0 x 10-3 5300 900.0 1000*0 3836 0.0 1000~0 3120 0.0 12.5 7124 87.5 100.0 6258 0.0 100.0 530 STUDIES OF THE CARBONATES. PART 11. 145 Hence starting with a pure N/lO-solution of carbonate for which kc=5300 the value of JsC decreases to 3120 when the sodium concentration is increased to N by carbonates of sodium but only to 3836 when the sodium concentration is due t o the chloride. That is to say the value of kc will depend not only on the sodium concentration but on the ratio of the chloride to the carbonate. k’ k C Let this ratio be called r then with r = 9 the value of - C = 1-23, k‘ For the dilute solutions of carbonate we have for 1-=7 L= 1.18. kc It thus appears that the effect of sodium chloride on k is of the same order for dilute or concentrated solutions and depends upon r the ratio of chloride t o base as carbonates.The effect of the salt must’ be due to the alteration of tho ionisation of the carbonate and bicarbonate since as before, It is to be expected that the ionisation of sodium bicarbonate will not be greatly affected by the presence of sodium chloride, but will have much the same value when the total sodium con-centration is the same whatever be the value of r. If this is the case the effect must be due t o the alteration of the ionisation of k’ p‘ kc P * the carbonate. Putting uf =a we have 2 = I n order to express the effect of salt we shall assume that fi’ has a similar form t o P that is can be expressed by the formula f i f = d - b f logc where c is the total sodium concentration in k’ a‘ - b’ log c k CL- blogc milligram-molecules.Then 2 = ~~~ . We have already found k,= 8739 - 1671 log c. For k’ we have a t c=100 kf,=5397. At c=lOOO we obtained 3836. This requires correction for the diminished solubility of carbonic acid which makes i t 4581. We then find kfc=7029-816 log c. k’ - 7029 - 816logc k, _ -8739 - 1671 logc ’ When c=100 we have no salt present and kfc=k,. If salt be added it is evident that c=100 ( r + l ) therefore log c =log (r + 1) + 2 whence k’ - 5397 - 816 log (r+ 1) 1 - 0.1512 log (Y+ 1) = _-- 5397 - 1671 log (r + 1) I - 0.3096 log (r +T) ‘ H 146 SEYLER AND LLOYD: Hence generally we have for P (assuming that the effect of ealt is the same a t other dilutions) 1 - 0.1512 log (r + 1) 1 - 0.3096 log (r + 1) ’ p = (1.104 - 0.320 1.g~) _ _ _ ~ - - - - - - -When no salt is present, r=O; this reduces to The effect of the salt was deduced from the experiments on N/lO-sodium carbonate but it must apply approximately to more dilute solutdons.For instance with N/80-solut~ions T = 7 T + 1 = 8, B= (1.104 - 0.320 log c). k’ we should get $ =1*22 against 1-18 found. E X P E R I M E N T A L . The object was t o determine the ratio of carbonate and bicarbonate in a very dilute solution in equilibrium with air containing a known amount of carbonic acid. Preliminary trials showed that a N/80-solution of sodium carbonate reached equil-ibrium with pure air when about 80 per cent.of the base existed as bicarbonate and 20 per cent. aa carbonate. Ordinary air there-fore contained a suitable percentage of carbonic acid. The actual amount of carbonic acid in the air used (drawn from outside the laboratory and washed) was determined by drawing the air in series through N / 10- and N/80-solutions of carbonate. I n order to be sure that equilibriunl was reached the check solutions of N/lO-strength were placed in some cases both before and after the dilute solution. The temperature was kept a t 2 5 O by a Hearson’s regulator and the solutions were agitated by being shaken in flasks (steamed Jens glass) on a small .truck running on rails at the same time that air from outside the laboratory was drawn through them. Special arrangements were made to prevent the liquids passing from one flask to the other.The amount of carbonic acid in the air was calculated ‘from the analysis of the decinormal solutions by McCoy’s formula, 2c xs 5300 1 -x * [H,CO,] = ___ -where c is the concentrat-ion of the base in equivalents 100x the percentage of bicarbonate in the liquid and [H2C03] the concen-tration of the carbonic acid. For the analysis of the liquid the method of double titration with phenolphthalein and methyl-orange was adopted with certain precautions. Kuster Lunge and Lohoffer and others have thrown grave doubts on the accuracy of this method alleging that it give STUDIES OF THE CARBONATES. PART 11. 147 results for the carbonate which may be 3 or 4 per cent. too high. Kuster attributes this to the supposed considerable alkalinity of bicarbonates t o phenolphthalein.McCoy has already shown that the alkalinity of bicarbonates is very small and Seyler (AnaZyst, 1897 22 314) showed that if loss of carbonic acid is avoided the results are correct to within less than 1 per cent. although usually on the high side. This question is the subject of an investigation by Xeyler and Tripp shortly t o be published. It was found that the point of neutrality to this indicator is very close to that required for the bicarbonate. It may be slightly on one side or the other. The end-point depends on the conditions of visibility of the colour the amount of indicator used and not only the total sodium concentration but the ratio of sodium chloride to bicarbonate a t the end of the titration.To avoid errors from this source the following precautions were adopted. Loss of carbonic acid was avoided by titrating in a tall Nessler glass adding the acid slowly from a burette with a long delivery tube reaching to the bottom of the vessel and stirring continually with a circular stirrer which was never lifted above the surface. Under these conditions it was proved that no appreciable loss of carbonic acid occurred even in fairly concentrated solutions. The amount of indicator was carefully measured and the colour a t the end-point compared with a check experiment. Other influences were allowed for as follows. A check experiment was conducted with each determination in which the conditions were the same as regards concentration of bicarbonate and sodium chloride.A standard solution (usually NjlO or N / 2 0 ) of sodium carbonate in boiled neutral distilled water was prepared and kept out of contact with carbonic acid. The standard hydrochloric acid was made with boiled water and acid and protected. An equivalent solution of neutral sodium chloride was prepared and protected. A preliminary titration was made with phenolphthalein and methyl-orange on the liquid t o be analysed. Let z be the number of C.C. of acid required with phenol-phthalein. Let m be the number of C.C. of acid required with methyl-orange. A comparison tube with the same amount of irdicator and an equal volume of water saturated with carbonic acid was used to judge the end-point. The standard employed was 2(m-z) C.C.of carbonate diluted to a given volume and very carefully titrated with phenol-phthalein. This was used as a comparison cylinder in the titra-H* 148 SEYLER AND LLOYD: tion of the liquid to be analysed. standard is: The final condition in the Sodium bicarbonate m - x C.C. Sodium chloride (m - x) C.C. (produced in the titration). If the titration differs from this by say y c.c. then y is the correction t o be applied to the titration. To the liquid to be analysed is added m - Zx C.C. of the salt solu-tion. A t the end of the titration the conditions will therefore be : The point of theoretical neutrality is m - x . m - 2 x C.C. bicarbonate pre-existing. x C.C. formed from carbonate in titration. Final bi-carbonate m - x. Sodium chloride ?rz - 2x added x formed by titration.Total a t end of titration m - x. of bicarbonate and chloride diluted to the same volume. was added to the standard to make the final amount the same. I n both etandard and assay there are thus the same amounts When the experiniental liquid contained sodium chloride this Example : Preliminary titratioii 10 C.C. required 711 = 20.21 C.C. N j20-acid. x= 5.94 Standard 2(m - x ) = 28.54 True bicarbonate m - x = 14.27 Required to phenolphthalein 14.11 y = 0.16 This has to be added t o the titration t o get the true result. Final titration m = 20.21 x= 5.83 m - 2x = 8.4 = salt added. Corrected figure for x 5.83 + 0.16 = 5.99. 10 C.C. contain 20'21 X ] Z O total base Carbonate 2 x 5.99 = 11.98 Bicarbonate = 8.23 Carbonate 40-7 per cent.Bicarbonate 59.3 per cent STUDIES OF THE CARBONATES. PART 11. 149 Example 2 : Prelimiiaury titratioit 50 C.C. required in = 12.58 C.C. N/20-acid. X = 1.23 Standard 22.7 C.C. = 2(m - X) 11.35 m - x Required t o indicator 11.14 Correction 0.21 to be added. F i n d titration ?n = 12.58 X = 1.14 True value of x = 1-14 + 0.21 = 1.35. Total base on 50 c.c.=12'58 N/20 Carbonate 2 x 1.35 = 2-70 Bicarbonate 9.88 Carbonate 21.5 per cent. Bicarbonate 78.5 per cent-. Besults of Experiments Temp. 25". Bicarbonate Carbonate C. 1002. 390 (1 -x). [R,CO,]. kc. 101-025 x lo- 42.18 57.82 0.01173 x 5300 12.55 80.51 19.49 0.01173 7130 12.627 80-63 19.37 0.01173 7228 100.8 40.47 59.53 0.01046 5300 100.5 40.60 59.40 0.01052 5300 12-58 78.53 21.47 0.01049 6892 101.05 40.72 59.28 0.0 1066 5300 100.50 40.89 59.11 0.01072 5300 12.45 79.60 20.40 0.01069 7233 We have then for c=12.5 x 10-3: k.,.7134 7228 6892 7233 mean 7124 -We put on record some experiments with N/150- and N/200-solutions although here the titration with phenolphthalein is so small that the correction becomes comparable in magnitude with it 150 SEYLER ANT) IALOYD: However they were very carefully made by the same method : C. 100x. 100 (1-x). [ H,COJ. k,. 6.540 87.48 12.50 0.01 100 7270 6.800 x 87.84 12.16 0.01 102 x 10-3 7830 4.870 4.872 4.410 5.300 89-80 10.20 0.01173 6468 90.22 9.78 0.01173 6920 90.24 9-76 0.01 100 6680 88-65 11-35 0-01100 6697 The average of these is 7123 identical with that for N/80-solu-Even a t N/200 the concentration of the hydroxyl ion is too tions.small to affect the results materially. This is still not large compared with 0.50 x 10-3 equivalents of base as carbonate or 4.5 x 10-3 equivalents of bicarbonate. Efiect of Sodiii tti Ghloride. Concentra- Con-tion centra-of base tion of Total as car- sodium sodium con-bonates. chloride. centration. io0.00 x 10-3 - 100-0 100.0 1 00*00 -100~00 900.0 1000*0 100~00 900.0 1000*0 12.58 - 12.580 12.04 87.5 99.54 12.00 87.5 99.50 1002. 40-83 40-61 36.40 36.10 78.53 77-24 77.83 100 (1 -5%) 59.17 59-39 63.60 63.90 21.47 22.76 22.17 [H,CO:,1. E,. 0.01035 -0.01220 -0.01035 3869 0.01022 3836 0-01490 6892 0.01035 6100 0.01022 6417 Hydrolysis of Sodium Cnrbor,nte b y Hydrolysis of Eth?/l rl c e t o t e .The symbols have the follow-ing meaning: Shields's method was followed. c =original concentration of the ethyl acetate in the mixture. c2= original concentration of the sodium carbonate in the x = number of gram-molecules of carbonate changed to bi-t=time in minutes. k = velocity-constant of hydrolysis of ethyl acetate. About 200 C.C. of the sodium carbonate solution (made with boiled distilled water) were mixed with 200 C.C. of a solutioii of neutral ethyl acetate of known strength. The initial time was taken as halfway between the beginning and end of the mixing mixture. carbonate STUDIES OF THE CARBONATES. PART 11. 151 of the solutions and the final time the beginning of the titration; 20 to 50 C.C.were withdrawn from tJme to time and titrated with N/20- or N/40-hydrochloric acid. The titration was made with the usual precautions to a very faint pink with phenolphthalein. The temperature was about 25O the solutions being maintained a t that temperature before mixing. The value of k was obtained by the formula (3'132 + k)(4472 - 2') = 192'07, which was found to represent the values given by Shields in the neighbourhood of 25O. Thus a t 25O we have k=6.608 (Gold-Schmidt Ber. 1899 32 3396 gives 6.94 a t 25O). The value of k d is found from the formula C C C C t . kkd = 2 log 2 - - loge - ' c - - 2 C 2 - X 1 c - c 2 c - X I We give the full experimental data in three typical casea. N/ IO-Sodiz~m Garbonate.Conditions similar to those of Shields. Temperature 25 1 O. 1. c2 - x. X. c - x . kk,r. 0 4 * 9 3 5 ~ 1 0 - ~ - 49.871 x -10 3-160 1.775 48.096 8.736 x lo-' 15 2.875 2.060 47.811 8.340 20 2.635 2-300 47.571 8.250 30 2.285 2-650 47.221 7.990 40 2.000 2.935 46.936 7.970 Average kkCl= 8.45 x lo-'. The following results were obtained : Temperature. c2. C. khi- E . k d * 25.1 4.975 37-765 8.09 6.658 12.15 25.1 4.950 23.400 '7.81 6.658 11-73 25.0 4.925 23.750 8.37 6.608 12-67 251O 4.935 x 10-2 49.871 x 8-45 x lo-' 6.658 12.69 x 10-6 N / 8O-Sodizlm Carbonate. I n these experiments a correction was applied t o the results to allow for the effect of the sodium acetate formed on titration. This was made by partly neutralising a similar solution t o that being titrated by acetic acid and comparing the hydrochloric acid required to comp1et.e the titration with the carbonate actually present.Thus in the absence of acetate the carbonate was correctly estimated a t 12-95 x 10-3. When the acetate was 8.38 x 10-3 and the carbonate 4.57 x 10-3, 4.67 C.C. of acid were required an excess of 0.1 C.C 152 SEYLER AND LLOYD: When the acetate was 11-52 and the carbonate 1.43 1.57 C.C. of hydrochloric acid were required an excess of 0.14 C.C. By graphic means the value of this correction was found for each titration and the corresponding deduction made. Temperature 25O 200 C.C. of A7/40-carbonate mixed with 200 C.C. of ethyl acetate solution (c =493-6 x 10-3). 50 C.C. withdrawn and titrated with N/40-acid. t .c2 - x. 2. c - x . kkd. - - 6.3600 x - 246.80 x 10-3 10.00 1.6860 4.674 242- 13 15-52 x lo-' 14.75 1.2820 5.078 241.73 14.15 20.00 0.8780 6.482 241.32 14.60 30.00 0.4739 5.886 240.92 14.62 Mean kkCl = 14.72 x ExDeriments conducted in this way gave: Temperature. c2. 25.00" 6.360 x 24-95 6.183 25.10 5.820 Two experinients gave for excluding them. 24.95" 6.010 24.95 6.075 C. EE'I. k. k,i. 246.80 x 14.72 x 10-4 6.608 22.2 x 253.20 14.52 6-633 22.9 182.65 14.24 6.658 21.4 lower results but we could see no reason 194-40 11.18 6.633 16.8 191.95 10.80 6.633 16.3 It is possible that these lower results are due to the highly dilute solutions having accidentally absorbed some carbonic acid. If B is the concentration of the bicarbonate originally present in the solution then the formula becomes k .k . t = B+c ~- log 2%- - 10ge c . c - c 2 c 2 - x c - c 2 c - x Nj200-temperature. c,. C. kkd. k. kd -25" 2.5 x 10-3 90.8 x 10-3 15.2 x 10-4 6.608 2 3 . 0 ~ CoizcZusions.-( 1) The apparent variations of the second ionisa-tion constant of carbonic acid in the equilibrium equation [HI x [CO,]=k,[HCO,] are due to the ionisation of the sodium bicarbonate (a) and t h a t of sodium carbonate ( P ) . The variation of the hydrolysis constant of sodium carbonate, k d = 2 k p - in Shields's experiments and of k,= k.1 - p - in McCoy's k3 a k3 a2 experiments is due to the same cause. has been estimated a t 4.27 x 10-11 and ',= 19.2 x 10-5 2= 71'34. (2) By experiments a t high dilutions the value of k a t 2 5 O k k3 1% (3) The value of a the ionisation of sodium bicarbonate either alone or in presence of sodium chloride or carbonate may be take STUDIES OF THE CARBONATES.PART 11. 153 as equal to t h a t of sodium acetate a t the same molecular con-centration. (4) The value of j3 the ionisation of sodium carbonate (in respect to the CO ion) between equivalent concentrations 1000 x 10-3 and 100 x 10-3 (and probably a t higher dilutions) may be approximately represented by the empirical formula p= 1.104 -0.320 log c where c is the sodium concentration in milligram-equivalents per litre. (5) I n the presence of sodium chloride the apparent value of /3 is greater than for pure bicarbonate and carbonate solutions a t the same sodium concentration. If 1’ is the ratio of sodium as chloride to sodium as bicarbonate and carbonate then 1 - 0.1512 log (?” + 1) p = (1.104 - 0.320 log c) .- ~ 1 - 0.3096 log (Y + 1) ’ These values are considerably less than those estimated on the usual assumptions from conductivity of the analogous salt, sodium sulphate but they represent the “active mass” of the sodium carbonate molecule a t the given concentration and probably the concentration of the CO ion. (6) It is confirmed that’ the ionisation of sodium carbonate takes place i n two stages namely Na,C03= Na + NaCO and NaCO = Na + CO,. The value of the second ionisation constant,” J i b = x[c031 I N ~ C 0 i calculated and shown to be smaller and more constant than is the first. ADDENDUM. Frary and Nietz ( J . Amer. Chem. SOC.1915 37 2271) have recently published a series of experiments on the hydrogen con-centration of solutions of pure sodium carbonate. By similar experiments on sodium hydroxide (the hydrogen concentration being measured by the electrometric method) they arrived a t a very improbable figure for E,, namely 1*76xlO-l4 a t 25O. Johnston (;bid. 1916 38 954) considers t h a t this result is explained by the neglect of contact potentials and that the most accurate figure obtainable is 0.8 x 10-14 (Lewis and Randall ibid., 1914 36 1979). This agrees with the value we have adopted. Frary and Nietz’s value seems impossible since i t would lead t o a figure for k =28 x 1 O - f ~ with the ordinarily accepted value for k3 but nearer 40x 10-5 with our value for k3. No investigator has found values approaching these figures.Prary and Nietz themselves even a t extreme dilutions (A’/ loo), It. 154 SEYLER AND LLOYD: find only 1 9 . 7 ~ 1 0 - 5 in agreement with our observations on the rate of hydrolysis of ethyl acetate. Nevertheless in considering t,heir further results one is justified in using their value of kw with their own experiments. Their experimental constant represents what we call Using the ionisation const,ants a’ for sodium hydroxide a for sodium bicarbonate and P f o r sodium carbonate (with respect t.0 the CO ion) we have ., = kd ’ k* a a . Taking t.he limiting value f o r this a t high dilutions to be 19.7 x 10-5 we can calculate by the formula p = kd a’a. k W l k 3 [It is not necessary that a a’ and fl should be the value unity At high dilutions at = a a t infinite dilution but only that /3 = aa’.nearly so that P=a2 is the condition that kd = ”-.I. k, Frary and Nietz give the following data from which we calcu-late B. We follow them in using for a and a’ the values for the estimated sodium ion concentration but the results would not be appreciably altered by taking the values for the total sodium concentration. B 8 (S. and L.) Equivalents Na con- concentra-4000 0.738 0,462 3.60 0.060 - -3000 0.728 0.453 3.62 0.060 - -2000 0.768 0-490 3.90 0.073 - -1416 0-784 0.636 4.45 0.095 - -1000 0.807 0.590 4.80 0.116 0,144 0.20 400 0.849 0.711 7.00 0.214 0.271 0.33 200 0.889 0-757 9.10 0.311 0.368 0-38 100 0.916 0.797 11.10 0.411 0.464 0.50 40 0.926 0.848 14.80 0-590 - -20 0.931 0.877 17-60 0.729 - -10 0.935 0.917 19.70 [0*867] - -Concentration of (S.and L.) a t same sodium carbonate. a t same Na ion per litre x lo3 a’. a. kLtx lo5. 8. centration. tion. It is worthy of note that the values used by Frary and Nietz for the total sodium ion concentration agree very well with those which we find. We have shown that [ N a ] = c ( a + p ) where c is the concentration of the sodium carbonate in milligram-molecules per litre. The degree of dissociation of the carbonate as regards sodium ions (that is the fraction of the total sodium existing as ions) i STUDIES OF THE CARBONATES. PART 11. 155 therefore = = p’. JVe compare a+P __ with p’ calculated 2c 2 2 by Frary and Nietz from the conductivity (a is here assumed t o be the same as for sodium acetate at the same molecular con-centration) : aCB.2c. a. B. 2 8’ 1000 0.636 0.144 0.39 0.39 400 0.731 0.271 0.50 0.47 200 0.782 0.368 0.57 0.54 100 0.822 0.463 0.64 0.60 This agreement must. mean t h a t the mobility of the NaCO ion is not f a r removed from t h a t of the CO ion but judging from the lower dilutions is probably somewhat smaller. The conductivity therefore is a fair measure of the sodium ion concentration assuming t h a t a t infinite dilution the ions are Na and CO,. The results of Frary and Nietz for j3 are of the same order as those obtained by us a t the same total sodium concentration, although a little lower and therefore do not’ vary in the direction required by comparison a t the same sodium ion concentration.Azcerbnch c u i d Pick’s Results ( A r b . Kais. Cesuizdkeitsnmt 1911, 38 243).-These authors have investigated the hydroxyl concen-tration of carbonates and bicarbonates and mixtures by colori-metric methods and arrived a t values for E agreeing with previous investigators namely about 6 x 10-1’. They realised the import-ance of the degree of ionisation but were hampered by the diffi-culty of forming an estimate of this factor. They also investi-gated the theory of the subject but as we think neglected to introduce the degree of ioiiisatioii a t the right stage. They coil-cluded that the hydroxyl concentration of a pure bicarbonate is independent of the concentration a result which is opposed to our experience. For mixtures of carbonate and bicarbonate they obtained for / 1 o-solutions [H~xCPP.= 7 . 3 x 1 0 - 11. CNn IT GO:: [ H] x CIVR~CO,~ p For these mixtures k,= - - ~ -Cr;a tr C O ~ 0. x -. Inserting our values B = 0.464 a= 0.783 we get k,=4*32 x 10-11, For 1C’/5-soIutions they obtained Putting P=0-38 a=0*71 we obtain X.,=4*33 x 10-11. These are the most favourable results for accuracy. Pure bicarbonate solutions are difficult to prepare and keep since slight in very good agreement’ with our estimate. cK@!3 = 8.1 x 10 -11. ( h a HC0 156 SEYLER AND LLOYD: alterations of the free carbonic acid make large differences in the hydroxyl concentration. The authors themselves lay little stress on their colorimetric measurements for pure carbonates. For bicarbonates however, they find a value 6.5 x 10-11 in A7/5- as well as in I\’/lO-solutions, and state that the hydroxyl concentration is independent of con-cent r a tio n .Hydrosyl Co?tcentrcitio?L of Mixtures of Ccwbonates and Bicarbonates. Auerbach and Pick on the assumption that the salts are fully ionised deduce the formula JCy=[H]- + [ H ] 2 e where a is the amount of sodium bicarbonate and b that of the carbonate (in milligram-molecules per litre) originally present without regard-ing ths hydrolysis. F o r pure bicarbonates b=O we get k,k2=H2 so that the hydroxyl concentration appears to be independent of the concen-tration. This would still be the case if we introduced the values a and p into the above formula. However this appears t o be erroneous. b a nk, The values of a and If a and b represent the amounts of bicarbonate and carbonate regarded as fully dissociated then the hydrolysis is represented by 2NaHC03= Na,CO + H2C03 and the bicarbonate really present is C Sa~co3 =a - 2[H,C0,1 and the carbonate must be introduced from the beginning.CNs,C03 = b + [H,CO,]. If the concentration is altered we shall have [HCO,] = ~ C ~ H C O ~ = a(a - 2[R2c03]), so that [H,CO 3 3 - - cL - CK:I13C03 of [H2C0,] will be different. as before though the actual value 2 A h [COJ == P C N ~ ~ C O ~ = P ( b + [H2C03]). Putting these values for LHCO,] and [CO,] into the equations F o r b=0 that is -for pure bicarbonate this reduces to k&3 = H2B STUDIES O F THE CARBONATES. PART 11. 157 Hence the hydroxyl concentration [OHl2=X/3 is not in-k,k, dependent of concentration but varies as the square root of P.This formula ceases t o hold good for very dilute solutions. The full expression may be deduced from the following equations : (1) a+ b =[HCO,] + [CO,] + (1 -a)(.-2[H2C03]) + (1 - P ) ( b + [H2C03]) + [H,CO,I whence aa + b p = [HCO,] + [CO,] + [H2C0,](Za - P ) . (2) [H]*[HCO,l =k,[H,CO,] and (3) [H]-[CO,] = k,[HCO,]. (4) 3[CO,] + [ KCO,] + [NaCOJ + [OH] = [Na] + [HI. (5) [Na] = a(a - 2[1I€,CO,]) + 2P(b + [H,CO,]) + [NaCO,]. Combining (4) and (5) we have (6) 2[CO,] + [HCO,] + [OH] =aa + 2bP+ 2[H&OJ(P -a) + [HI. Substituting the values of [HCO,] [H,CO,] and [cos] from equations (a) (3) and (4) in (6) and simplifying we have finally, (7) k&,= For infinite dilution a = P = l this reduces to Auerbach and Pick's equation.When u and b are not so small as t o be comparable with k2 arid k we may neglect k in the expression fla(n+2b)+li2 and (2a - P)k in k,bp - (2a - P)kw and E, in [H]aa - [HI2 + li, and the factor [H]k,k,. Also we may neglect [HI4 and its coefficients and [HI2 in com-parison with [Hlaa. The formula then reduces to that previously obtained: It holds rigorously for all dilutions. k - [H]2--&- ( a + "b) . p + [H] bP -. k2a aa 3 -When [HI is very small (as in mixtures containing a moderate amount' of carbonate) this becomes k,= [HI - b P . -. CLa When b = 0 (as in pure bicarbonate) it becomes k,k,= [HI". By combining (6) with (2) and (3) we get (na + 2bp + [ H])[H]' - kw[ [ I ] H,CO -- Bk,k + k 2 p ] - a(p-,)LHl3 158 STUDIES OF THE CARBONATES. PART IT. At infinite dilution this becomes aa+ZbP is not the total sodium ion concentration but that corresponding with the [HCO,] and [CO,]. I f we take the first-stage ionisation of the sodium carbonate to be the same as that of the bicarbonate a t the common sodium ion concentration then we have [NaCOJ = ( b + [H2C03])(a - P ) whence from equation (5) [Na]=au+ZbP+ ( u - P ) ( b -[H,CO,]). The sodium ion concentration is therefore greater than aa + 2bP (compare Johnston Zoc. cit.). Since the above was written Kendall ( J . Anzer. Chenz. SOC., 1916 38 1480) has determined k (the first ionisation constant of carbonic acid) a t different temperatures and finds a t Oo 2.24 x 10-7 a t 1 8 O 3-12 x 10-7 and a t 2 5 O 3.5 x 10-7. The value 3.5 x 10-7 should therefore be used in conjunction with the experi-ments carried out a t 25O. This does not alter the ratio '2 found by us a t 25O namely, 7120 nor does i t alter the calculation of the degree of ionisation of sodium carbonate. It does however alter the value of li (the second ionisation constant of carbonic acid) and gives a figure of 4.91 x10-11 instead of 4-27 x 10-11. It would also give k, k!.! =16.7 x 10-5 instead of 19.2 x 10-5 if the value of Ic is taken '3 a t 0.82 x -14 at^ 25O. Further careful experiments are required t o determine t,he variation of 5 with temperature which would enable us to ascertain how k varies with t,his factor. k3 TECHNICAL INSTITUTE, SWANSEA. [Rewioed October 27th 1916.