CONTRIBUTIONS TO T H E STUDY OF IONISATION IN AQUEOUS SOLUTIONS OF LEAD ACETATE AND CADMIUM ACETATE. By ARTHUR JAQUES, B.Sc., late Fellow of Armstrong College, Newcastle-on-Tyne. ( A Paper read beforc the Favadny Socie fy, Tuesday, November 30, 1909, Mr. JAMES SWINBURNE, F.R.S.? PRESIDENT, in tlzc Chair.) A1 aterials used.-The lend acetate was once recrystallised. AnaEysis.-The lead was precipitated and weighed as sulphate. I. 1.2298 grms. salt gave 0.9823 grm. PbSO,= 54-56 per cent. Pb. 2. 2.0926 grms. salt gave 1.6641 grins. PbSO, = 51'32 per cent. Pb. Theory for Pb(C2H,02),, 3H20 = 54'61 per cent. Pb. The cadmium acetate was obtained from Kahlbaum, and was used as Analysis.- it was. I . 0.4716 grm. salt gave on ignition 0*2280 grm. CdO =48*34 per cent. 2. 0.8986 grm. salt gave on ignition 0'4337 grm.CdO = 48.26 per cent. Theory for Cd(C,H,02), 2H,O = 48.18 per cent. Silver acetate was obtained from Kahlbaum, and was used as it was. The A?zalysis.- salt was perfectly white and crystalline. I . 0.7758 grm. salt gave on ignition 0.5012 grm. Ag = 6460 per cent. 2. 0.6566 grm. salt gave on ignition 0.4235 grm. Ag = 64-50 per cent, Theory for AgC,H,O, = 64-67 per cent. Potassium acetate was obtained from Kahlbaum, and was used as it was. The ratio between the concentrations of the metal-ions in two solutions of The sodium acetate was once recrystallised before use. salts of the same metal can be found by measuring the e.m.f. of the cell- M I MA, xN I MA, yN I M, in which M represents the metal and MA its salt. and C, the respective ionic concentrations, for a divalent metal- If E be the e.m.f.and C, G. Ez50 = 0.0295 log - C , The same result can be found by measuring the two half-elements separately against a standard, e.g., the 0.1 N. calomel electrode. This formula does not include the potential at the liquid contact, which Cumming,:< however, has shown can generally be eliminated by interposing a saturated solution of ammonium nitrate between the two salt solutions. * Trans. Farad. SOC., 2, 213 (1907). 225236 STUDY OF IONISATION IN L4QUEOUS SOLUTIONS The following measurements were all made with cells of the type- M [ MA, xN. I NH,NO, sat. [ 0.1 N. cal. electrode. From measurements of cells of the type- M [ MA,xN, [ 1.0 N.cal. electrode, Abegg and Labendzinski"' found that the metal-ion concentrations in solutions of the acetates of the heavy metals were much smaller than in equally concentrated solutions of the corrcsponding nitrates, and concluded that this was due to extensive complex formation in the single solutions of the acetates.Abegg and Labendzinski's values contain the liquid potentials, and are therefore not quantitatively comparable with the measurements. given in this paper. That complex formation occurs in solutions of lead salts containing excess of an alkali acetate is evident from the fact that lead sulphate is much more soluble in solutions of alkali acetates than in water. It was therefore considered probable that in presence of a large excess of an alkali acetate practically the whole of the lead or cadmium would be pre- sent in the form of a complex ion.If this condition is fulfilled, the con- stitution of the complex can be found by the method of Bodlanderf as follows :- Let the complex have the formula M,Ac, (with Y - 2y negative charges) where M represents Pb or Cd. Applying the law of mass action, we have- whence, if two solutions are considered- First, making [Ac'], = [Ac'] 2, we get- If e be the e.m.f. of the concentration cell containing the two solutions-- whence- Next, making [M,Ac,], = [MqACr].12, we have- and- whence- * Zeif. f. Elektrockemie, 10 (1904). t Fests. 2. Dedckincl, Braunschweig, 1901.OF LEAD ACETATE AND CADMIUM ACETATE a27 Thus, assuming all the metal to be in the form M,Ac,, q and ?’can be A series of measurements of the e.m.f. of the cell found.M I ~~~~’~~ I NH,NO, sat. I 0.1 N. cal. electrode was made. The insulation of the whole of the apparatus was repeatedly tested during the measurements. The electrodes were platinum wires fused through the ends of glass tubes with fusible glass, and were coated electrolytically with lead and cadmium respectively from solutions of the acetates, using very small currents. Both kinds of electrode gave constant potentials immediately on being introduced into the solution, and these were maintained for several hours. Both metals were gradually dissolved by the acetate solutions, so that the potentials did not usually remain constant overnight. All the measureinents were made between 2;” and 25-84 The potentials were reproducible to within I milli- volt. Tables I.and 11. show the results obtained by applying Bodlinder’s method to the values found, putting the complex concentration equal to that of the total lead or cadmium. Putting q = I in Table II., the values of l i n column A are the powers of [Ma*] [Ac’]” Total coilcentration of the salt in solution’ The measuring apparatus was described in the previous paper. 4 [Ac’] in the equation- k = in which k remains constant over the alkali salt-concentration interval between [Ac’], and [Ac‘]~. The values of y for potassium acetate are taken from Kohlrausch’s values for the equivalent conductivity at ISO,:: and his temperature coefficient for the equivalent conductivity of 0.01 N. potassium acetate. The corresponding temperature coefficient for sodium acetate is almost constant over the range of concentration O.OOI-O*~ N.The temperature coefficient of the con- ductivity of potassium acetate is taken as independent of the concentration. A, is found from Kohlrausch’s values for ZK. and ZC,H,O,~ at 18’ and their temperature coefficients. The values for the equivalent conductivity of sodium acetate for concen- tration 0-5-2-0 are from Kohlrausch,::: those for concentrations below 0.5 N. are from 0stwald.f When y from the two sets of values is plotted against vc? a continuous curve is obtained. Arrhenius’ temperature coefficientsf were used, and Am was found as before. The effect of hydrolysis on the conductivity is very small, and has been neglected. The values of q for lead acetate in sodium acetate solutions approximate closely to I, while those for lead acetate in potassium acetate solutions and for cadmium acetate in sodium acetate solutions are a little greater than I.The values of vary rapidly, reaching vcry high values for the strong solutions, and falling to about 2.5 for the acetate ion concentration interval Q * Quoted in Whethain’s Theory of Solution, Table. t Zeif. Phys. Clzeni., vol. i. f From Landolt and Biirnstein, Plt3’sikalisclt-Cltei11ische Tabellen.TABLE 1. . 0'0221 0,0162 0.0074 1'21 1'10 I '20 Conc. NaAc = 1.922. -- Solution 11. Total Pb conc. - - ~ -- 0'003 0*004 0.008 0'01 2 0 '003 0~004 OW08 0'012 Total Cd conc. 0'002 0'004 0.008 Conc. NaAc = 2'792. Conc. NaAc = 0'673. Conc. NaAc = 0.279. Conc. NaAc = 1.153. Solution I. Total Pb COIlC. 0'016 0.016 Total Cd Conc.0.016 - -~ P.D. . - ~ P.D. -- 0.02 j8 0,0184 0.0089 0.0046 -- (1. 1 so4 1'03 1'01 I '12 P.D. ___- 0'0270 0.0163 0.0078 0.0024 P.D. 0.0256 0.0173 0*0088 0'0033 (1. -_ ___ I -03 0.96 I '00 0 -8 q. ~ - - I '02 I '05 0.95 I -05 P.D. 0'0222 0.0170 0~0092 0.00~0 4. 0' 0260 0.01~0 0'0093 0.003 j 0'99 I '09 1-13 1 '54 1'20 I -04 0.97 0.93 Conc. KAc = 0'633. conc. KAc = 1.810. Conc. KAc = 1.086. 0.0215 0.0145 0'0077 0.0033 0'0200 0.0140 0.0065 0*003 1.33 1.26 1'34 I '22 1'24 1'23 1.1; 1'12 o*o163 1 1.10 COllC. NaAC = 2'792. 0.0190 0.014 0~0086 I '03 I -26 I -13 1-17 0'0211 0.0158 0.0076OF LEAD ACETATE AND CADMIUM ACETATE 229 -_ 0'0210 0.0224 0.0240 0.0230 TABLE 11. I ~ 13'4 14.3 15-3 14.6 -- P.D. 0'0212 0.0234 0'0220 0.0230 0.0232 0.0151 0.0170 0.0152 0.0167 0.0156 0.0373 0.0395 0.0412 0.0404 0.0409 A.r Q -. 2'34 2-54 2 -58 2 *56 2'43 3 '2 3'6 3'2 3'5 3'3 B. rcalculated from bquation(Ig)(q= I). 2 '91 3 '59 3 '57 3-62 3'09 Mean = 3 -36 3-96 4-46 3 '91 4 '34 4-06 9'91 10.32 10.79 1052 10.71 Total Conc. of Pb in both Solutions. 0'002 0.004 0.008 0.016 0 012 0'002 0.004 0.008 0.016 0'012 0'002 0.004 0.008 0.016 0'012 [Ac'l 1. (NaAc 0'279 N.) 0.179 (NaAc 0.673 N.) 0.363 [Ac'l2' (NaAc 0.673 N.) 0'363 ~~ (NaAc 0.526 1.153 N.) (NaAc 2'792 N.) 0.729 8.9 9'45 9 '9 9'7 9 -8 (NaAc 0.526 1.153 N.) 18 23 23 22 22 0'002 0'004 0.008 0.016 0'012 0.0154 0.0185 0*0190 0.0188 0.0193 0'0205 0.0195 0'0193 0.0203 0.0190 0.0272 -___ 0.03 jo (NaAc 1-922 N.) 0.682 ( KAc 0.633 N.) 0'438 (KAc 1.086 N.) 0.67 P (NaAc 0.279 N.) 0.179 (NaAc 2'792 N.) 0.729 (KAc 1.086 N.) 0.67 I ( KAc 1.810 N.) 0.952 6.92 5 '22 5.10 4'46 4-26 3 '73 3 5 6 3'7 3'5 3'5 0'002 0.004 0.008 0.016 0'012 0.004 0.016 Total Conc.of Cd in both Solutions. 0'002 0.004 0.008 0.016 3 % 3 '2 2 '9 3'1 Mean = 3 '25 0.0270 0.0276 0.0265 0.0275 0'02 I 0 0.02 I 6 0.0225 0 '0220 (NaAc 0'837 N.) 0.425 0'002 0.004 0.008 0.016 (NaAc 1.674 N.) 0.645 (NaAc 0'837 N.) 0.425 (NaAc 0.64 j 1 -664) 5'1 5 '3 (NaAc 2'792) 0.729 0'002 0.004 0.008 0.016 15.1 16.1 The absolute potentials against the 0'1 N.E. are given in Tables X. and XI v.230 STUDY OF IONISATION IN AQUEOUS SOLUTIONS o.I&ca 0.4. If q may be taken as really I, it follows that at this acetate concentration a considerable part of each salt must be in the simple undis- sociated state, as PbAc, and CdAc,, or as PbAc' and CdAc'.Since the acetate concentration in these mixed solutions is certainly much greater than in, say, 0.05 N. single solutions of lead and cadmium acetates, it seemed probable that ionisation in these solutions leads chiefly to the formation of PbAc. and CdAc.. It was therefore thought worth while to see whether constant values for the dissociation constants would be obtained on the assumption that ionisation occurs in the single solutions according to the scheme- MAC, * MAC. + Ac', MAC. Q M.. + Ac'. A similar case has been worked out by W. K. Lewis ::: for lead nitrate. Following Lewis's method for the calculation of the constant for the second dissociation, we have, for lead acetate-. . . . . . . . . . (3) LAC'] = I(, [ P b Ac,] - . .. . . . (4) . . . . . . c=[Pb..] +[PbAc.] +',PbAc,] (5) where c = total lead concentration. Further, since the solution is electrostatically neutrd- . . . . . . . (6) 2 [Pb-] + [PbAc.] = [Ac'] From (4) and (6) by elimination of [PbAc-] we get- z[Pb-] K, K2-[ P b**] [Ad] = From (5) and (6)- [PbAc,] = c - [Ad] + [Pb..] . . . . . . . CPbAc.3 = [Ac'] - 2[Pb**] (7) From (3) and (4), and substituting for [PbAciI- Substituting for [Act]- c-lc, which reduces to Lewis's equation, viz- K: (c - rPb-1) - K, (c + -- 2[Pb.*] + [Pb.*]"(c + [Pb**]) = o . (8) "["1*) * Dissctd., Breslau, 1908.OF LEAD ACETATE AND CADMIUM ACETATE 231 4Pb-I: - is sufficiently small to be neglected in comparison with c, we KI If obtain- . . . (9) Substituting froin equation (7) in (3) and (4) we obtain- The value of [Ac'] in the single solutions can be roughly estimated from the depression of the freezing-point.Adding together the concentrations of all the molecules in solution we get, making the same assumption as in equation (5)- [Pb*.J + [PbAc.] + [PbAc,] + [Ac'] = ic . . . . (12) Subtracting (5) from this- [Ac'] = c(i - I ) . . . . . . . . . (13) A series of potential measurements in single solutioiis of lead and cadmium acetates was made. The values found are given in Table 111. The poten- tials in the single solutions were not quite so constant as those in the mixed ones, possibly owing to the higher resistance. They showed a maximum variation of about 2 millivolts, excepting in the case of 0.01 N. PbAc,, where the maximum variation amounted to about j millivolts. TABLE 111.C. 1P.D. against 0.1 N. cal. electrode. O ' j 0'1 0'0 I 0'536 05380 0.5368 0.5390 0'54T 0.7892 ::gg 0'8037 In the lead acetate cells the variation in the potential with change of concentration is remarkably small. This indicates that there is little change in the concentration of the lead ions even on diluting the 0.5 N. solution up to fifty times its original volume. This indicates that the value of K, is small, and the behaviour is similar to that found by Luther:: in the case of sulphuric acid, where the potential of a mercurous sulphate electrode only changed 3 millivolts over the range of concentration I*O-O'I N. * Zcit. f. Elcktrocltcniic, 1907, 294.232 STUDY OF IONISATION IN AQUEOUS SOLUTIONS In the cadmium acetate solutions the change is more rapid, and indicates In order to find the order of magnitude of K,, the freezing-points of thc ) for various Table IV.shows the values of i =- a higher value for K,. solutions in Table 111. were determined, or obtained by interpolation. ( molecule depression 1.85 solutions of the two salts. TABLE IV. Grm. Mol. 1,000 grams H,O Lead Acetate ... Litre Cadmium Acetate... .! to" I to's Freezing-point. - 0.13 - 0'34 - 0.54 - 0'20 - 0'31 - 1-16 -0.39 - 1'597 .__- i. -~ 2.32 1-78 1-51 1.189 1 *% I 26 1.726 2'1 I ~ [ i - I] = [Ac']. 0.0398 0-047 I 0.06 I 8 0'0455 0.069 0'13 0'111 0.363 For the present purpose, the gram molecule per 1,000 grams of water was taken as equal to the grain molecule per litre. Plotting c against c(i-r), the first three of Kahlenberg's values give a straight line, c(i -I) increasing with the concentration, while the fourth shows a sudden drop in i and c(i -I).The freezing-points of 0-1 and 0.5 N. solutions were determined, and the values found are shown in the table. Kahlenberg's fourth value was neglected. Table V. shows the values of K, and I(, obtained by inserting the experi- mental values in equations (13), (10) and (11). The values of [Pb-] are calculated from Lewis's value for the E.P. of Pb, viz., - 0'403 volt against the 1.0 N. cal. electrode at 25'. Taking the 0.1 N. cal. electrode as being 0'054 volt positive to this, we have E.P. of Pb against 0.1 N. cal. electrode For cadmium, the value quoted by Le Blanc,: viz., - 0.703 against the =- 0.457 Volt. 1.0 N. cal. electrode was used.TABLE V. 0.5 0.05 0'1 0'02 0'0 I 0.5 0'1 0'002 I 0 o*oo I 80 0*00197 0-00166 0'00142 [Cd-] 0.08 I 0.0566 Y 0'04.4 0.138 0.265 - - 0.335 l - 0'002 I7 0.0019 om02 16 0.0018 0'001 55 0'146 -- * Kahlenherg, Zeit. Pltys. Client., 17, 1895. t My observation. 1 I Interpolated from Kaldenberg. Lelzrbzich dcv Elektroclienzie, 4th edition, 1906.OF LEAD ACETATE AND CADMIUM ACETATE 233 From equations (10) and (11), it is seen that the values of K, and K, become unreliable when [Ac'] - 2 [r\lr**]= o or [Ac'] - (c + [M**]) = 0. In the 0.5 N. solutions these differences are relatively large, so that the values of K, and K, may be taken as indicating roughly the order of magnitude of the two constants. From Table V., therefore, it appears that for both salts 2[n/r'*1z ~ is small enough to be neglected in comparison with c.I t will now be convenient to consider the lead and the cadmium separately. K, A LEAD ACETATE. KI From equation (S), neglecting 'm, we may either (I) assume K, to be constant and calculate K, and [Pb-] by trial, using the relation- [Pb-] e = 0'0299log -- - f [Pb-I,' or (2) using the known E.P. of lead, calculate K,. I . From the P.D. measurements- whence- Inserting values for [Pb**] in accordance with this relation, we find that K2(0.5) = K2c0.01) when [Pb*.] (o'oI) = 0.00187 and K, = 000272. 2. Using Lewis's value for the E.P. of lead, we obtain the results given in Table VI. TABLE VI. C. 0.5 0.05 0'1 0'02 0'0 I - [Pb-J. 0'002 I 0 0'00 I80 0-00197 0.00166 0'00142 - K,. 0'002 I 0.00187 0-002 13 0wo I 89 0'0020 Mean =0~0020 K,, Corrected.0*002 I 8 0.00196 om0228 0*00203 0'002 I 0 0'002 1 The two values agree within the known limits of variation of the potentials. Putting K, = 0*0020 in equation (9) and solving for [Pb-] , we find- [Pb..] o'j = 0~00198, [Pb**],.,, = 0.0015, whence e = 0.0036, which is a sufficiently close approximation to the experi- mental value. The value 0*0020 may be taken as an approximation to K,. All these calculations contain the small error due to neglecting the term containing K, in equation (8). In order to find K,, the solubility of silver acetate was determined in solutions of sodium acetate, potassium acetate, silver nitrate, and lead acetate. This affords a quantitative means of determining the acetate ion concentra- tion in the mixed solution.Knowing this, we can calculate K,.234 STUDY OF IONISATION IN AQUEOUS SOLUTIONS 1'0 0'1 0 5 0.05 0'01 The values found are given in Tables VII. and VIII. The silver was precipitated and weighed as iodide. In the case of lead acetate the separation was effected by the method of Benedict and Gaus.*: Parallel analyses were made throughout. In solutions of the alkali salts and of silver nitrate the method gave concordant results withotlt difficulty, in the lead acetate solutions small differences between the two analyses were found. Whenever these approached I per cent. two new determinations were made with a fresh lot of solution. The solutions were shaken for at least 24 hours in the thermostat at 25'. They all darkened somewhat during shaking, excepting the silver nitrate solutions.For the lead acetate only the mean values are given, as these were taken in some cases from three or four values, the maximum difference never exceeding I per cent:t 0.03587 0'04349 0'01995 0.0566 0.06403 TABLE VII. Conc. (u) KC,H,O, = c. 2.262 1.131 0.2262 0.0226 2'403 0.2403 0*0240 (c) AgNO,. 0.1307 0.06535 0.03268 0'01634 (6) NaC,H,O,. 1'201 I. 0*01305 0'0 I 440 0.02654 0.05743 0.0 I 240 0.0 I 402 0.025 I 4 0.0349 0'0443 0.054 I 0'0594 0'05552 y for the added Salt. 11. 0.0 I 305 0.01443 0.02652 0.01238 0.01390 0.02 5 23 0.0346 0'0445 0.0539 0.0596 0.05758 0'05562 Mean. 0'01305 0'01442 0'02653 0'05750 0'01 239 0.01 396 0.025 19 0'05557 0.0348 0'044.1 0 ~ 5 4 0 0'0595 0~01os) 0'0209 0.0300 0.0572 0'0218 0.03 I 5 0'0579 0.03 69 o*o&o 0.0541 0'05945 0'02 I The fact that in the strong solutions of potassium and sodium acetates the calculated solubility is greater than the value found indicates that is lower than the true value of 7.A, TABLE VIII. Solirbiliiy of Silver Acetn ie in Lend Accinie Solziiioiis. C. I). 0.01 867 0.0263 I 0'03275 0.0394 0.0468 0' I297 0'092 I 0'0739 00614 0.05 I7 I 1 * Crookes, Selcct Methods, p. 324. t See remarks, Landolt and Bornstein, p. 518.OF LEAD ACETATE A4ND CADMIUhI ACETATE 235 Conc. o.oS64 (sat .) 0.05 Two independent determinations of the solubility in water gave the values The results for the alkali acetates and silver nitrate show that Its conductivity was measured at 0*0662,0*0665. silver acetate is a perfectly normal salt. 2jo, and the results are given below :- I I1 11 * Ye A.Y. 75'2 0.74 I 74.76 0'737 78.6 0'771 - - The values for the saturated solution show fair agreement with that found by Rudolplii ;:: (74'45). The first values were used in making the calculations. For A, Loeb and Nernst's value, 101.5, was taken. In the saturated solution [Ag.] = yti = 0'0492, and the solubility product [Ag.] [Ac'] = (yq)2 = 0'00242, and the concentration of the undissociated part which remains constant in all saturated solutions = 0.0664 - 0.0492 = 0,0172. The calculated solubilities given in Table VII. were obtained using the formula- We shall call this concentration A. in which x is the concentration of the common ion .in the added electrolyte, s is the solubility of silver acetate in water.In the mixed solution, in addition to equations (3), (4), and (s), adding together the acetate concentrations, we have- We are now in a position to calculate K, for lead acetate. q + 2~ = [AgAc] + [PbA4c*] + 2 [PbAc,] + [Ac'] . . . (14) [Ag-] + [PbAc.] + 2 rPb**] = [Ac'] . . . . * (15) and for electrostatic neutrality- From (4) and (15)- [Ac'] - [Ag] = [PbAc.] (I + s), 1.e.- . . . . . . . (16) Also- * Zcit. Phvs. Ckem., 17, 1895.236 STUDY OF IONISATION IN AQUEOUS SOLUTIONS [Pb-] 0.00167 0'001 37 0~00106 0*00068 0-000 I 7 From (14)- KI 0'0157 0.0133 0.0482 O'O* 0.044 I Mean = 0.033 From the values of [Ac'] in Table VIII. and equations (16) and (IS), and using the approximate value of K, already found, we can calculate K,. Since in equation (16), 2K, is always small compared with I, the error in K, can only produce a niuch smaller one in the value of K,.[Ac 1 [Ad] 0- I 297 0.0921 0.0739 0.0614 0.05 I 7 TABLE IS. (K, is calculated, also [Pb-] for comparison with the values given in Table VI.) [PbAc.] [PbAcz] -.- 0.1077 0.8906 0.0630 0.4356 0.0391 0.0599 0*0207 0'0286 o*oo+52 0*00530 Lend Acetate Solution saturated with Silver Acetate. C. 1'0 0'1 0'01 0'5 0.05 K, appears to vary over the range of concentration C = 1.0 to C = 0.1, but, for the purpose of making the small correction in equation (8) the mean value 0'033 was used. The corrzction is very small. The corrected values are given in Table VI. Solviiig equation (8) by trial without approximation, we find [ Pb*.],.,, = 0*00164, K2(o.5--oo,) = 0*00247. These values agree closely with those calcu- lated using Lewis's value for the E.P.of lead. Since Lewis's value rests upon a niuch bigger potential difference, the results given in Table VI. are probably the more accurate. From the fact that in relatively strong alkali acetate solution only amounts to 2.5, !l that K, calculated from the solubility of silver acetate is nearly constant, and of the same order of magnitude as the values calculated from the freezing- point determinations, and that K, Calculated from Lewis's value for the E.P. of lead is also constant and i n agrcciiieiit with the values found without assuming any value for the E.P., it appeared reasonable to conclude that the assumption that ioiiisation in the single solutions occurs normally according to the scheme- We thus find KZ = 0-0021, K, = 0.033.PbAc, = PbAc. + Ac' PbAc. = Pb.* + Ac' was justified. The real total concentration of the complexes in the mixed solutions can now be calculated. Calling this C, and the total lead concentration c, we have C = c - [Pb-] - [PbAc.] - [PbAc,]. Table X. shows the values of C in the solutions used in Table 11. Since for constant Ac' - concentration C is nearly proportional to c, the values of qOF LEAD ACETATE AND CADMIUM ACETATE 237 calculated from equation (I) on the assumption that all the lead was present as complex are practically unaffected. TABLE X. K, =0'033 ; K,=0~0021. '.D. against 0 1 X.E. [Pb"] C. 0.6232 0.612 j 0*6040 0.5985 0.5962 2*32*10-~ j.36' 10 - 1.60- I0 - 5 I -91 * I 0 - 5 I '04'10-5 0'000709 0'002212 0-001 0 I 7 0.003093 0.00; 3 6 8 1.87'10- 5 3'0 1.I 0 - 5 2'70' 10-5 2'97'10-5 2'04.10-5 Mean = 2'5'10-5 0'179 (NaAc) 0'002 0.004 0.008 0.016 0'012 0~00106 j 0-002127 0.004442 0.006 j47 0.0086 j 0'363 (NaAc) 0.6444 0.6355 0'6273 0.62 I 8 0.6 I 80 0.6594 O'Bj2 0.642 5 0.6382 0.6336 0'002 0.004 0.008 0.0 I 6 0'012 0.526 (NaAc) 0-00 I 406 0.00294; 0.00 578 0.008gO 0'01 1 56 0'002 0.004 0.008 0.016 0'0 I2 1 0.6967 0.69 I 5 0.6837 0.678 j 0'6745 7'50'10-9 I - 12' 1 0 - 8 2.07. I 0-* 3*10*10-* 4-21' I O - ~ 0'729 (NaAc) - 0.438 ( KAc) 0'002 0.004 0.008 0016 0'0 I2 - 0'002 o.ooL+ 0.008 0.016 0'0 I2 0.001939 0'003909 0.007832 0'0156j 0'01175 (O'oO03 2) 0~001~1 0.003 I 7 0.00 j90 0.00860 0.64 I ;* 0.63_53 0.6280 0.625 0.6225 5'j7'10-7 8-89. IO-' I .60.10- 2'02'10--s 2.4 j*10-~ 0.6620 06550 0.6482 0.6438 0.6410 0'002 0.004 0.008 0.0 I 6 0'0 I2 I * I ~ * I O - 7 I '94' I 0-7 3 '30' I 0 - 5*80*10-7 4'66.10- 7 0'00 I2 25 0.0026 j 8 0-00 j72 0.00878 0'0120 1 0-6822 0.6662 0'004 0.016 0*00370 0.0 2489 Assuming the concentration C to be that of a single complex, we can now calculate its constitution.As before-238 STUDY OF IoNIsxrIoN IN AQUEOUS SOLUTIONS Should the alkali metal enter into the complex as found by Lewis in the case of lead nitrate and potassium nitrate, let the complex have the constitution K9P bqA&. Then- Le., Y in the above equation would become p + r. Therefore- and- qe + 0.029 j log 2 - c, [AC’], . . . 0 6 . . . * * (19) - 0.0295 log - The corrected values of r calculated in this way, putting q = I, are given The effect of the correction is to raise all the values Taking 7 = 3 in 0.279 N.sodium acetate solution, which is also weak in Table II., column B. considerably. enough to be treated as “dilute,” we can now calcdate- [Pb**] [Ac’] 3. Ks= [PbAc,’] The values are given in Table X. The mean value is 2-5.10-5. It is now possible to test further the hypothesis made in calculating K, and K2, namely, that complex formation in single solutions within the concentration interval o*o~-o*~N. is of negligible degree. We now have- [ PI>**] [XC’] 3 K3 [PbAc‘,] = and- We thus obtain the following values for the concentration [PbAc;]- PbAc,. 0.126 0 1 000115OF LEAD ACETATE AND CADMIUM ACETATE 239 The hypothesis is therefore not quite true. The values of [PbAc,] cannot be taken as correct, since they are calculated on the assumption that [PbAc,'] =o.The error in K,, however, must be roughly proportional to [PbAc,'] in the above table, and must therefore be much less in OOI N. than in 0.5 N. solution. Since in Table VI. the values calculated for the different concentrations using Lewis's value for the E.P. of Pb are very nearly constant, it is evident that the error must be very small. This is further shown by the investigation of cadmium acetate. The error in I<, cannot be determined with certainty. From equations (4), (14), and (IS) we find that allowing for the formation of a complex anion of the type PbAc, in the solutions saturated with silver acetate would have the effect of raising K,. The value of K, found from the freezing-point of the single solutions is independent of complexes, since the term representing the concentration of the lead as complex in equations ( 5 ) and (12) disappears on subtraction.It seems safe to conclude that K, cannot be less than 0.04. Raising the value of K, has the effect of raising C and lowering the value of log 5 i.e., lowering the value of I-. As r cannot be less than 3, it appears from Table 11. that in dilute alkali acetate solutions the complex PbAc,' is formed in larger quantity than any other. Taking C = [PbAcJ and giving K, the limiting value 0.04, we find for K, in the same order as in Table X., 1*45,2'06, 1*90,2*03, 1'55 x 10-5. Mean value = 1*8010-5. Since raising K, lowers K,, it follows that K, cannot be greater . than 1*8*10-5= roughly 10-5.Three circumstances may possibly account for the extraordinarily rapid decrease in the ,lead ion concentration with increasing Ac'-concentration in the stronger alkali acetate solutions, namely : (I) departure from the laws of dilute solutions, including error in the values of y ; (2) the formation of one or more complex ions containing a large number of acetate groups in the ion ; (3) the formation of undissociated salts between the alkali metal ion and the complex ion. That the values of y are inaccurate appears certain from the values for the solubility of silver acetate. The presence of the alkali metal in the complex ion appears unlikely for the following reasons :- (I) Only one case has been found as yet where this occurs. This is in the ion KPbNO;' which Lewis:: found in solutions of lead and potassium nitrates. (2) While in the foregoing case the conditions in solutions of sodium nitrate and potassium nitrate were totally different, sodium nitrate giving no indication of complex formation, in the present case the behaviour of the two alkali acetates is very similar.c,' B. CADMIUM ACETATE. In this case the potential differences in the single solutions of concentra- tion O*S-O.OI N. were much greater than for lead acetate, and K, and the Cd--concentrations were calculated-without assuming a value for the E.P. From equation (S), neglecting 2[Cd"12 and [Cd**]3, we find- K* * LOC. cit.240 STUDY OF IONISATION IN AQUEOUS SOLUTIONS 0.6483 0-01205 0.00318 0.2486 0.0294 It was found that the only admissible values of I<, were obtained by taking the negative roots in this equation, and these agreed with the positive root of equation (S), when the same terms were neglected.Solving equation (20) with the value of e obtained with cadiniuni acetate (given in Table III.), we find K,= 0.0207. The solubility of silver acetate in solutions of cadmium acetate :it 25" is given in Table XI. 0.0183 0'0080 0.0019 0.0174 0'01 I 6 TABLE XI. Solubility of Silver Acetate iit Cadmitiin Acetate Solution at 25'. C. 1'0 0'1 0'0 I 0'5 0'05 ,I 0.02363 0*02592 0'0402 I 0.04852 0.06224 1 ) - ;\ = r.4g.1. 0.00043 0.00872 0*02301 0'03132 0.04504 L - [Ag'] - 0'37% 0.2776 0.1052 0.07729 0'05375 'l'ahle XII. shows the values of K, found, using K,=0-0207. Solving cquation (S), without approximation, using K, = 0.188, we find [Cd*.] o.5 = 0-0170, and K, = 0.0198.TABLE XII. C I '0 0'1 0'0 I 0.5 0.05 [Ac'] . 0'3765 0.2776 0.1052 0'07729 0.05375 [CdAc] . 0'3334 0'2340 0'0590 0.02994 0.00492 I I<, . 0'194 0.261 0.192 0.083 Mean = 0.188 0'21 I K, and [Cd-] were now calculated for the other concentrations, using the potential measurements, and the relation- The results are given in Table XIII. TABLE XIII. c. 0.5 0'1 0'02 0.01 [Cd-J. 0.0 I 70 0.01 19 0.00698 0.0054 8 0.0198 0.0161 0.0155 0.0198 Mean = 0.0178OF LEAD ACETATE AND CADMIUhf ACETATE 241 CdAc,. The values of [Cd-] give the E.P. of Cd = - 0.737 against the 0.1 N. cal. electrode at 25". This gives - 0.683 against the 1.0 N. cal. electrode at 25'. In order to find the probable error in this value, equation (8) was solved, allowing an error of 3 millivolts in the potential measurements between 0.j and 0.01 N.solutions. = 0.01 15 instead of 0.0145, we find [Cd..],., = o*o108 and K, =0~0119. This gives the E.P. - 0.7312 against the 0.1 N. cal. electrode. The error chosen was greater than the probable error. From these mea- surements the E.P. of cadmium is therefore - 0.737 & 0.006 volt against 0'1 N. cal. electrode at 25O, or - 0.683 & 0-006 volt, against the 1.0 N. cal. electrode. As in the case of lead, the complex concentration C was calculated for the solutions given in Table 11. The values are given in Table XIV., and the corrected values of r in Table 11. Putting eWj - TABLE XIV. (K, =0.188 ; K, = 0.018. E.P. of Cd against 0.1 N.E.= -0.737 volt.) [CdAcjJ. 0.645 0'729 C. 0'002 0*004 0.008 0.016 0.002 0.004 0.008 0.016 0'002 0'004 0.008 0'016 0.002 0.004 0.008 0.016 P.D. 0'857 O%jI 0.843 0.834 0.8840 0,8786 0.8695 0.8615 0.9055 0.8995 0.8915 0.8842 0.9265 0.922 0.916 0 7 [Cd-1. 8-gj.10-5 2-55'10-4 I '37'10'4 3'15'10-4 r '04' 10 - 5 3'23'10-5 6-02' 10-5 I '59' 10-5 I -94- 10 - 3.10.10-~ 1*02'10 - 5 3'79' 10' 3-77' 10-7 5*36*10-7 8.56*10-7 1'73'10'6 C. 0*0002548 0wo I 204 0.002795 0-005488 0-oOO860 0.0022 j7 0'004459 0.009400 0*001925 0.0 I 566 0.003894 OW07830 As before, K3 was calculated from the data for 0'279 N. sodium acetate solution, putting r = 3, and the values are given in Table XIV. The mean value, excluding the first one, is 5'7'10-4. Calculating the values of [CdAc,'] from this we obtaiii- c.0.5 0'1 0'0 I 0'414 0.0158 0.-335242 STUDY OF IONISATION IN AQUEOUS SOLUTIONS The error is thus much greater than for lead acetate. We shall probably remove nearly the whole of the error in K, by calculating it for the concen- tration-interval c = O*I--O*OI instead of c = 0'5-0.01. Kz,o.r4.0r, = 0~0097 = roughly, 0.01 & 0*002, [Cd.*],., = 0.0082, Doing this, we get- so that the values are reduced by about half. From the freezing-point of 0.5 N. cadmium acetate, and the solubility measurements, we may conclude that K, cannot be less than 0.2. Further, putting K, = 0.01, when K, falls below 0.3, C becomes small or negative for the three best data in Table XIV. for [Ac'] =0*179. Taking E.P. of Cd = - 0.732, however (see below), we get for the limiting value 0.13.K,, therefore, cannot be less than 0.13, and is probably greater than 0.2. The new value for the E.P. gives lower values for K,. K,, therefore, cannot be greater than 5'10-4. It follows, as in the case of lead acetate, that in dilute sodium acetate solution the complex CdAcj is formed in larger quantity than other complexes. 0.006 volt against the 0.1 N. cal. electrode or - 0.678 + om06 volt against the 1.0 N. cal. electrode. The correction in K, thus makes a change of 5 millivolts. It is probable that the reniaining error in this value due to complex formation in 0'1 N. cadmium acetate solution is of negligible magnitude. The limits of error for this value of the E.P. are rather wide apart, but it is given because it differs by much more than the probable error from the value accepted at present.The removal of the error due to the presence of a complex in the stronger solutions increases this difference. From the value [Cd**],., = 0.0082 we find the E.P. of Cd = - 0.732 SUM MARY. From measurements of the e.m.f. of cells of the types- p b I ;:$! I NH,NO, sat. I 0'1 N. cal. electrode, Cd 1 g:z;;{ 1 NH,NO, sat. I 0.1 N. cal. electrode, it was concluded that complex formation in sirigle solutions of lead acetate and cadmium acetate was small, and that the complex concentrations might be small enough to be neglected in calculating the two pairs of dissociation constants for the respective salts. From measurement of the e.m.f. of the cells- Pb I PbAc, xN I NH,NO, sat. I 0.1 N. cal. electrode, Cd 1 CdAc,, xN I NH,NO, sat. I 0.1 N. cal. electrode, the value 0'0021 was found for &, the second dissociation constant of lead acetate, and this value shows good constancy over the range of concentration 0-5-0*01 N. ; and it is probable that the value of I<, is greater than 0'04. On the assumption that sodium and potassium do not form complex ions with lead acetate or cadmiuiii acetate, evidence was given to show that in dilute alkali acetate solutions complex formation in the case of lead acetate leads chiefly to the production of the ion PbAci. K,, the dissociation constant for this complex, cannot be greater than 10-5. The small second dissociation of lead acetate is comparable with that found by Luther" for sulphuric acid. * I m . cif.OF LEAD ACETATE AND CADMIUM ACETATE 243 The most probable value for K, for cadmium acetate is 0'01 $-0*002, and K, is probably not less than 0.2. In dilute alkali acetate solutions the com- plex CdAcl is formed in larger quantities than other complexes. Its dissocia- tion constant, K3, cannot be greater than 5 x 10-4. The values of r, the number of acetate groups in the complex, rise very rapidly for both salts with increasing alkali acetate concentration. The E.P. of cadmium was calculated to be - 0'732 &coo6 volt against the 0'1 N. cal. electrode, or - 0.678 t_ 0.006 volt against the 0'1 N. cal. electrode, at q0. In conclusion, I wish to express my best thanks to Professor Dr. R. Abegg for kind assistance in the conduct of this research, and also to Professors Bedson and Thornton for the kind interest they have shown. ARMSTRONG COLLEGE, NE\~c~~sTI,E-o~-TY~E.