1138 J.C.S. DaltonThermodynamics of Complexing between (+)-Tartaric Acid and Lanth-anum(iii) Ion in Aqueous SolutionBy H. S. Dunsmore * and D. Midgley, Chemistry Department, The University, Glasgow G I 2 8QQThe stability constants of the lanthanum-tartrate complexes LaTar+, LaTar,-, and LaHTar3f have been determinedin 0.1, 0.2, and 0 . 4 ~ (Me,N)CI media t by potentiometric titration by use of a glass electrode. Thermodynamicconstants have been determined at 15, 25, and 35 "C by the same method and standard enthalpy and entropychanges obtained from the temperature variation of the constants. Some structural implications of the results arediscussed.THE closeness of the two dissociation constants oftartaric acid makes the determination of the stabilityconstants of tartrate complexes difficult, since protonatedTABLE 1Stability coiistants of lanthanum-tartrate complexesMedium (M) * log PI log Pz log Pl1 Method * Ref.t0.0597 (NaC10,) 3-75 6-02 A a0.1 (KNOB) 3.46 5-52 B b1 (NaC10,) 2.08 A cC 2.5 D d c 3.68 6.37 n e3.06 4.25 E f0.2 (KC1) 3.10 B g0.1 (NaC10,) 3.21 2.43 H iG 2.36 6.10 F h0.2 3.06 1.19 I3 i0.1 (KC10,) 6.72 x k* A, Distribution; B, glass electrode; C, uncontrolled; D,hydrogen electrode; E, e.m.f.; I;, solubility; G, saturatedsolution; H, pH titration. t a P. G. Manning, Canad. J .Chew,?., 1963, 41, 2566. b N. A. Dobrynina, L. I. Martinenko,and V. I. Spitsin, Izvest. Akad. Nauk S.S.S.R. Ser. khim.,1968, 2203. e K. L. Mattern, UCRL-1407, U.S.A.E.C., 1964.d I;. Brgzina and J.Rosickq, Monatsh., 1963, 96, 1025. R.Pastorek and F. Brgzina, Monatsh., 1966, 97, 1095. f U-Czin-Guan and Sjuj Guan-sjan, Kesue Tunbao, 1959, No. 10, 330.g N. K. Davidenko and V. F. Deribon, Zhur. neorg. Khim.,1966, 11, 99. h N. K. Davidenko, Redkozem. Elementy.Akad. Nauk S.S.S.R., Inst. Geokhim. i analit. Khim., 1963(Chem. Abs., 1964, 61, 5011g). i Wu Chin-Kwang and HSLIKwang-Hsien, Acta Chim. Sinica, 1965, 31, 58. f V. N.Kumok and N. A. Skorik, Zhur. neovg. Khim., 1970, 15, 291.k J. Star?, Analyt. Chim. Acta, 1963, 28, 132.and unprotonated species inay coexist in acidic conditionsand this greatly complicates the calculations. Previouswork on the lanthanum-tartaric acid system has usuallyconsidered only two complexes at a time, and no attemptt The nomenclature of A.E. Martell and L. G. Sill& ( I StabilityConstants,' Chem. SOC. Special Publ., No. 17, 1964) has beenadopted.1 H. S. Dunsmore and D. Midgley, J . Chem. Soc. ( A ) , 1971,3238.2 H. S. Dunsmore and D. Midgley, J.C.S. Dalton, 1972, 64.has been made to obtain thermodynamic values. More-over, the background media have usually containedconsiderable amounts of sodium or potassium ion, whichhave been shown 1*2 to form complexes with tartrate ion,Pastorek3 has reported i.r. spectra and thermalanalyses for a number of solid lanthanum-tartratecomplexes prepared from alkaline solution and finds alarge number of species in existence. Zvayagintsov andTikhonov and Katzin and Barnett have made spectro-scopic studies of lanthanide tartrates in alkaline solutionand find only one complex present.Gallett and Piiris 6have studied cerous and dysprosium tartrates by meansof thermometric titration and found three complexes ofthe type MTar+, M,Tar,, and MTar,-.We have carried out titrations at three different ionicstrengths, using background media containing tetra-methylammonium ion, which does not form complexeswith tartrate ion. We have also performed titrations indilute solutions a t three temperatures, activity co-efficients being calculated by means of equation (3).Constants are defined as in equations (A)-(E).p1 = [LaTar+]/( [La3+][Tar2-]) (A)p2 = [LaTar,-I/( [La3+] [Tar2-I2) (B)pll = [LaHTar2+]/( [La3+] [HT] [Tar2-]) (C>p12 = [LaHTar,]/( [La3+] [H+] [Tar2-I2) (D)Kll = [LaHTar2+] /( [La3+] [HTar-1) (ElEXPERIMENTALReagents.-Distilled water was obtained from an all-glassstill.Potassium chloride, potassium nitrate, potassium3 R. Pastorek, Monatsh., 1968, 99, 676.4 0. E. Zvayagintsov and V. P. Tikhonov, Zhur. neorg.6 L. I. Katzin and M. L. Barnett, J . Phys. Chem., 1964, 68,6 J.-P. Gallet and R. A. PAris, Analyt. Chim. Ada, 1968, 40,Khim., 1964, 9, 2789.3779.3211139hydrogen phthalate, and (+)-tartaric acid (AnalaR) wererecrystallised from distilled water. Tetramethylammoniumchloride (B.D.H., Reagent Grade) was recrystallised frommethanol-acetone 7 or methanol. Hydrochloric acid solu-tions were made up by dilution of the constant-boiling acid.8Sodium carbonate was prepared by decomposition of sodiumhydrogen carbonate (AnalaR) .Tetramethylammoniumhydroxide solutions were prepared by treating tetramethyl-ammonium chloride solutions with freshly precipitatedhydrated silver oxide and filtering the solution. Sodiumhydroxide solutions were prepared by dilution of a saturatedsolution made up from pellets (AnalaR) . Hydroxide solu-tions were stored in, and dispensed from, the usual syphonarrangement. The concentrations of the hydroxide solu-tions were determined by titration against potassiumhydrogen phthalate, with phenolphthalein as indicator,and by potentiometric titration against standard hydro-chloric acid solutions. Lanthanum chloride solutions wereprepared by dissolving lanthanum oxide (Johnson, Mattheyand Co.Ltd., Specpure) in a small excess of diluted constant-boiling hydrochloric acid. The chloride concentration ofthe solution was determined gravimetrically as silverchloride and the excess of acid by potentiometric titrationwith standard tetramethylammonium hydroxide solution.The lanthanum concentration was obtained by difference.The results for a batch are given in Table 2.TABLE 2Analysis of lanthanum chloride stock solution[Cl-l/M W + I / M [La1 /MTheoretical 0-1084 0.0085 0.0333Observed 0-1084 0.0085 0.0333Potentiowzetric Measurements.-Potentials were measuredon a Pye 7565 potentiometer, with use of an ElectronicInstruments Ltd. Vibron 33B electrometer as a null detector.The glass electrodes were of the type GC33 made by Elec-tronic Instruments Ltd.The reference half-cell consistedof a Wilhelm bridge 9 containing a silver-silver chlorideelectrode in either a tetramethylammonium chloride solu-tion of the same ionic strength as the test solution or anequimolar solution ( 0 . 1 5 ~ each) of potassium chloride andpotassium nitrate. The latter was chosen to reduce liquidjunction potentials lo with measurements made in dilutesolution.The glass electrodes were calibrated with solutions ofhydrochloric acid and by titration of hydrochloric acidsolutions with standard sodium hydroxide or sodiumcarbonate solutions. When the ionic strength was main-tained with tetramethylammonium chloride, Biedermannand Sillkn's l1 empirical liquid-junction potential correctionwas applied and a linear-relationship was obtained betweenthe corrected e.m.f.and -log [Hf]. Since no linearcalibration was obtained when the ionic strength was notmaintained] and no suitable liquid-junction correction wasavailable, the observed e.m.f., E, and the pH were fitted toequation (1) by the method of least squares. Here we defineE = a0 + adpH) + "2(PW2 + a3(pW3 + a,(Pq4 (1)pH = -log [H+] - log f, where f is the univalent ion' B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Trans.Faraday SOL, 1966, 62, 2738. * C. W. Foulk and M. Hollingsworth, J . Amer. Chem. SOG.,1923, 45, 1220; J. A. Shaw, Ind. Eng. Chem., 1926, 18, 1065;A. C. Titus and D. E. Smith, J . Amer. Chem. SOC., 1941,63, 3266.W. Forsling, S. Hietanen, and L.G. S i l k , Actu Chem.Scand., 1952, 6, 901.activity coefficient calculated by means of the Daviesequation.12 The validity of this calibration in the presenceof other ions was checked by repeating the calibrations withpotassium chloride added. No significant difference wasobserved. Calibrations and experiments were normalisedby reference to the e.m.f. observed with 0.05 mol kg-lpotassium hydrogen phthalate buffer before and after everyrun. The sensitivity of the electrodes was checked periodic-ally and found to be constant.Titration Procedure.-Series (I). Tetramethylammoniumhydroxide solution was added from a burette to solutionscontaining tartaric acid, lanthanum chloride, and tetra-methylammonium chloride. Tetramethylammoniumchloride solution was added from a second burette to main-tain the chloride concentration a t the desired level (0.1, 0-2,or 0 .4 ~ ) . Alternatively, lanthanum chloride solution wasadded to a partially neutralised solution of tartaric acid, theionic strength being maintained as before. The tempera-ture was 25 "C for all these titrations.Series (11). Tetramethylammonium hydroxide solutionwas added from a weight burette to solutions of tartaricacid and lanthanum chloride made up by weight. In someruns the lanthanum chloride solution was added to atartaric acid solution partially neutralised with tetra-methylammonium hydroxide. All weights were correctedfor the buoyancy of air. Titrations were performed a t 15,25, and 35 "C.Nitrogen from a cylinder was passed successively throughsolutions of hydrochloric acid, sodium hydroxide, and tetra-methylammonium chloride (twice) before being bubbledthrough the test solutions in order to mix them and toprevent the absorption of carbon dioxide.The saturatorswere at the temperature and ionic strength of the test solu-tions, except in Series (11) , where distilled water replaced thetetramethylammonium chloride solutions.The titration cell and Wilhelm bridge were immersed in awater-bath whose temperature was controlled to &O.Ol "Cby a mercury-toluene regulator operating a heating elementthrough a Sunvic relay (A.E.I. Ltd.). A Frigidaire re-frigerator unit with its coil in the water enabled measure-ments to be made at temperatures below ambient.Alloperations were carried out in a room maintained a t25 f 1 "C.Volumetric glassware was of Grade A and its calibrationhad been checked.CALCULATION AND RESULTSIn order to keep the calculations simple it is desirablethat no hydroxy-complex is formed. Biedermann andCiavatta13 reported that hydrolysis of La3+ ion does notoccur below pH 6.5. Since the titrations in this work do notreach pH 5 , hydrolysis of the metal ion presents no problem.The dissociation constants of tartaric acid were determinedin the same conditions as the lanthanum titrations, and havebeen reported.2Series (I).-The data were first treated as an LaTarf-LaTar,- system by the method of Gelles and Nancollas,l4lo K. V. Grove-Rasmussen, Actu Chem. Scand., 1949, 3, 445;1951, 5, 442.l1 G.Biedermann and L. G. SillCn, Arkiv Kemi, 1953, 5, 425.l2 C. W. Davies, ' Ion Association,' Butterworths, London,1962.13 G. Biedermann and L. Ciavatta, Acta Chem. Scand., 1961,14 E. Gelles and G. H. Nancollas, Trans. Faraday Soc., 1956,15, 1347.52, 981140but the resultant plots showed a pronounced upwardcurvature in the low pH region, indicating that protonatedcomplexes were also present. An estimate of PI was ob-tained from data a t higher pH’s and used to calculate plrfrom data in the low pH region.15 PI and p, were thendetermined by a modification of Gelles and Nancollas’method which allowed for the effect of the (known) pI1.Starting from the estimate obtained above, pll was variedsystematically until a good straight line was obtained,The values of p1 and p, given by this line, together with thecorresponding value of pl1, were taken as the ‘ best ’.Linear plots were obtained for all runs and, a t a given ionicstrength, gave good agreement between runs, except for onerun in 0 .2 ~ medium when there was a large ligand-metalratio a t low pH.Since the data cover a wide range of pH, metal-ligandratios, and absolute metal and ligand concentrations, andgood agreement was found between the various runs, withthe exception noted above, it is concluded that the systemcan be treated as consisting of three complexes, LaTar+,LaTar,-, and LaHTar2+, in most of the conditions studied.Further checks were made to see if the system could beexplained in terms of any other combination of complexes.Treatment of the data by Leden’s method16 gave noevidence for the formation of a (LaTar),2+ dimer.TheTABLE 3The stability constants of lanthanum-tartratecomplexesRun log p10 . 1 ~ Medium1 3.7332 3.6493 3.658Mean 3.6760 . 2 ~ Medium4 3.3995 3.3676 3.4037 3.4198 3.41410 3.420Mean 3.4109 t (3.410)0 . 4 ~ Medium11 3.09012 3.15713 3.11914 3.116Mean 3.108lo%,3.92.96.52.27.833.810.47.24.9108.53.42.46.46-32.31.61% (326.3766.1206-2666.1285.7295.0545.5465.6755.6485.7165.640(5.640)5.4865.7645.5415.559(5.559)102OZ4.40.87.80.710.469-25.96.34.610.22.92.63.21.41.11% P116.5336.3806.3956,4096.2406.9236.1396.2036.1496.1236.2066.225.8486.005(5.820)6.7695.820t log (312 = 9.0, 412 = 3.5 x 10-2.l02Oll2.01.05.50.93.332.453.32.74.738.41.95.91.05.61.30.8No. ofpoints2118151815162342273622151113assumption of an LaTar-+--LaTar,--LaTar33- system pro-duced only negative stability constants.Allowance for anLa,Tar, complex also produced negative constants. Thepossible existence of the neutral species LaHTar, was alsoinvestigated. There was no evidence for the presence ofthis complex, except in Run 9, in which the conditions wereparticularly favourable.The computer program GAUSS G17 was used to refinethe stability constants for each run in turn.Three con-stants, PI, Pa, and PI1 were refined simultaneously. When a15 G. H. Nancollas, ‘ Interactions in Electrolyte Solutions,’Elsevier, Amsterdam, 1966.16 I. Leden, Svensk kern. Tidskr., 1946, 58, 129.17 R. S. Tobias and M. Yasuda, Inorg. Chem., 1963, 2, 1307.J.C.S. DaltonTABLE 4Data for lanthanum-tartrate complexing at constantionic strengthsRun1234567891011121314103[HaT~] /YI3.9173.6723.5253.4363-3703.2644.1483.9183.7503.5973-4222.0762.0051.9391.8773.7053.5853.5103.4283.3693.3023.2383.1763-1173.0881.7501.6791.6451.6141.5983.9143-6923.5383.3943.2937.3916.9326.6536.3986.1625.9425.8375.7355.4845.2535.0404.8444.6634.4954.3314.1864,0503.8923.6553-5763.5013.4293.3603.2933.2993.1673.0742.9934.0083.9143.8243.5963.5203.4473.3603-3263.4973.3353.2573.1633.0762.9407.8267.4747.1526.7216.4603-8723.7843.6803.62011.6111.0910.409.985108[LaCl,]/N3.4683.2513.1213-0412.9832.8891.8381.7361.6621.5941-5171,8351.7721.7141,6593.7003.5803.5053.4333.3643.2973.2333.1723-1123.0831.7551.6841.6501.6181.6031.9611.8501.7731.7001-6503.7023.4723.3323.2043.0862.9762.9241.9161.8231.7551.6841.6181.5581.5021.4471.3991-3531.3000.3721.0791-7582.4053.0303.6334.2084.7635.6076.0590.4031.1731.9112.3392.9963.6244.3744.6634.5914.3794.2754.1534.0373.8592-5692.4542-3482.2072.1211.0181.9873.1393.7999.6879.0838.72110.14-log [H+] 103[Me,NOH]/~2.5112.7893.0133.1903.3543.7392.5862.8523.1143.4524.1382.7392.9803.3113.9092.5142.6662-7802.9043.0433.2033,3933.6454.0264.3062.7773.1763,4914.0244.7532.5872.9163.2263.6844.2803.3792.5922.7512.9203.1043-3203.4302.5553.6642-7802.9023.0323.1763.3313.5153.7193.9674.4213.0212.9382.8752-8232.7812.7442.7132,6852.6462-6683.8803.6923.5343.7383.6063.4963-4063.3502.5502.7582.8813.0533.2523.7332.7782-9363.1013.3733.5803.7293.5713.4233.3642.4282.5272.6712.769o*ooo2.2173.5444,3544.9495.908o*ooo1.9663.3964.7056.1940.0001.2112.3403.395o*ooo1.2902.1012.8813.6244-3385.0295.6936.3356-6480.0001.6182-3783.1043.4580.0002.2583-8275.2976.3240.0002.4773.9785.3576.6297.8188.3810.5101.4612.3193.1193-85:,4.5356.1675.7826-3276-8397.4330.97370-95280.93270.91360.89510.87730.86030.84390,81890.97585.8585.7215.5896.2116.0795.9535.8035.7450.0001.5992-3793.3004.1705.5154.0685,4416.6958.3779.3955.6385.5105.3585-2704,4245.7657.5628.6491O4[Hcl]/ar6.5435.1964.9884.8614.7684.6182.9382.7752.6562.5482.4242.9332.8322.7392-6519.4449.1398.9478.7628-5868-4178.2538.0967.9447-8704.4794.2974.2124.1304.0905.0054.7224.5254.3404.2119.4488.8618.5068.1797.8787.5967,4634.8914.6774.4804.2984.1313.9773.8333.6943.5703.4543.3190.9492.7554-4886.1407.7339.27210.7412-1614-3115.471.0302.9934.8796.9707.6489.25011.1611.909.2518.8238.6168.3688.1367-7765.1774.9444-7324.4464.2732-0504.0056.3257.65520.4319.5218-3017.51141fourth constant, pL2, calculated from the data of Run 9, wasincluded in the runs at 0 .2 ~ neither all four constants, norany three of them, could be refined simultaneously. Twoof the four could be refined, but the agreement betweendifferent runs was poor and the standard errors larger thanwhen only three complexes were taken into account.Thesame was true at the other ionic strengths when an estimateof Plz was made. The results for the individual runs, to-gether with the weighted means of results a t the same ionicstrength, are in Table 3. By a, is meant the standarddeviation in the logarithm of the ith constant. Theparentheses in Table 3 indicate that the particular constantwas not refined simultaneously with the others, but wasgiven the mean value from the other runs at that ionicstrength.The results were extrapolated to infinite dilution byplotting E, from equation (2) against I , where I is the ionicE, = log pc + Y .A . 1&/(1 + B . a . I:) =strength. A and B are the Debye-Hiickel parameters, a andb are adjustable parameters, Po and Poo are the stabilityconstants at the particular ionic strength, G, and a t infinitedilution respectively, and I is an integer characteristic of theequilibrium. As awas varied systematically, values of E, were calculated andfitted to the equation E, = p . I + q by the method ofleast squares. The a value which led to the best straightline for the plot of E, against I was assumed to be correct.The most precisely known constant, pl, was used in thecalculation of E, for obtaining the best value of a, which wassubsequently used in the extrapolation of the other twoconstants. The best fit resulted from a = 7 and gavelog p10 = 4.84.The corresponding values of log PBo andlog Pl10 w-ere 7.5 f 0.2 and 7.45 f 0.06 respectively. Aselection of the data from which the constants were calcu-lated is given in Table 4. The first and last points for eachrun are given, together with every fourth point. Run 4 isgiven in greater detail (alternate points).Series (11) .-Activity coefficients were calculated fromequation (3) for an ion of charge z. Activity coefficientslog pco + r . A . b . I (2)The value of Y for the constant P1 is 12.- logf, = A . z2 [Ii/(l + B . a . 14) - b . I] (3)had to be calculated iteratively and since the results inconstant ionic media indicate that only three complexes aresignificant in the conditions under study, the modifiedTABLE 5Thermodynamic stability constants of lanthanum-tartrate complexesxo.oft/"C log Pl0 103a1 * log PB0 102a2 * log Kllo points15 4.852 3 7.41 12 3.10 3325 4,604 3 7.59 4 2-48 4035 4.876 4 7.93 6 2.70 19* af is the standard deviation in the logarithm of the ithconstant.Gelles-Nancollas method was used rather than add yetanother iterative stage to the GAUSS G program. Atconstant ionic strength GAUSS G produced only small re-finements in the constants obtained by the former method.The values a = 7 [from Series (I)] and b = 0.3 were used incalculating the activity coefficients. The runs were firsttreated individually and the average value of Kilo found atthe particular temperature. This value was then used tocalculate PIo and p2* from the combined data a t thattemperature. The stability constants, in molal units, aresurnmarised in Table 5.TABLE 6Coefficients of the temperature variation ofthermodynamic stability constantsa b 103c1% P1° 235.06 - 1.647 2.6971% P2* 74.39 - 0.474 0.8401% K11° 382.66 - 2.530 4.210TABLE 7Thermodynamic quantities for lanthanum-tartrate complexing a t 25 "C- 10- AGO 10-~AHO ASOReaction J mol-1 J mol-l J K-l mot10.0 964-47 2960.56 66La3+ + Tar2- LaTar+ 2.63La3+ + 2Tar2-@LaTar,- 4-33La3+ + HTar- LaHTar2f 1.41TABLE 8Data for lanthanum-tartrate complexing at low ionicstrengthsRun t/"C15 1516 1517 1518 2519 2520 2521 2522 3523 3524 3525 35103[H,Tar]mol kg-l1.3241.3141.3100.84820.84320.83940.83520.83160.82750.82430.82331.6631.6491.6321.6111.5871.5611.5432.4282.4161.9051-8951.8891,8801.8761.8711.861143441.8311.8210.86720-86380.85750-85400.69720.69460.69150-68890.68530.68341.6761.6471-6351.6141.5991.5851.6181.5911-5781.5621.5511.5350.85450.84490.84121-8651.8431.832103[LaCI,]mol kg-l1.4501.4391.4351,0151.0091.0050.9990-9950.9900.9860.9850.13720.30590.50560,74881.0251.3361.5470.64190.63860-76980.76580-76350.75990.75820-75620.75210.74510.73990-73580.18550.26150.40400.48281-0251.0221.0171.0131.0081.0051.1521.1321.1241.1091.0991.0890.94230.92630.91880.90970.90340.89411.6931.6741.6670.65090.64340.6395103[Me,NOH] 1O4[HC1] 1O6[Me,NC1]pH mol kg-l mol k g l mol kg-13.4113-6803.8163.0403.1503-2543.3973.5573.8274.1954.3873.9643.8403.6953.5443.4193.3193,2602.8332-9012-8562.9342.9773.0543.0983.1453.2653.5283.7954.0673.4853.4343.3553.3233,0273.1143.2423.3773.6653.9232.8223.0213.1243.3693.6134.0532.8923.1253.2693.5053.7334-2573-1513.4453.6333.4273.7523-9721.9932.4002.5440.2280.5510.7941.0671.3021.5651-7701.8332.0762.0582.0372.0111.9821.9491.9260,06900.43560.0000.3720.5870.9221.0781.2611.6432.2992.7773.1570,62740.62490.62030-6178o*ooo0.2670.5810.8471.2181.413o*ooo0-9411.3382.0322.5142.9980.1981.1271.5652.0932.4602.9990.9181.5231.7582.0172-6262-9474.4824.4484.4363.1383.1203.1063.0903-0773.0623.0503.0460.4240.9461.5632.3153.1694.1304.7831.9851.9752.3802.3682.3612.3492.3442.3382.3252.3042-2882.2750.5740.8091.2491.4933.1703.1583,1453.1333-1163.1083.5613.5003.4743,4303.3983.3672.9132.8642.841243132-7932.7645.2355.1775.1542-0131.9891.977167920212143192.4464.4668.9898.2109613181490154317491733171616941669164116221.0576.675o*ooo5.7049.00314.1216.5219.3225.1735.2342.5648.389.6149.5769.5069.467o*ooo4.0988.90912-9818.6621.650.000792.21127171221172525166.6948.8131817632071252512831400169022012470772.1142 J.C.S.DaltonThe stability constants were related to the absoluteThe coefficients temperature by means of equation (4).log@ = a + b . T + C . T2 (4)are listed for the three constants in Table 6. The standardentropy change for each reaction was calculated fromequation (5) and the enthalpy change from equation (6).ASo = R(a + 2 b . T + 3c. T2)AGO = AH0 + T . ASo( 5 )(6)Table 7 summarises these thermodynamic quantities forthe three equilibria at 25 "C.Table 8 contains a selection of the data from which theresults of Series (11) were calculated. The first and lastpoints in each run are given, and alternate points between.DISCUSSIONMeasurements made over a considerable range of pH,metal-ligand ratio, and total metal and total ligandconcentrations at a number of ionic strengths andtemperatures show that the existence of three com-plexes, LaTar+, LaTar,-, and LaHTar2+ must be in-voked to account for the data.No other complex wassignificant, except in Run 9, where in conditions of lowpH and low metal-ligand ratios there was evidence forLaHTar,. Previous determinations of stability con-stants may be in error through neglect of one or otherof the three main complexes. For example, in Run 4,in which the total metal and ligand concentrations arevirtually equal, the approximate relationships (7)-(10)hold.In a titration of this sort neglect of one of thecomplexes cannot be justified.pH 2 - 5 : [La3+] N 10[LaTar+] N1000[LaTar,-] 21 5[LaHTar2+] (7)pH 3.0: [La3+] N_ 3[LaTar+] N120[LaTar,-] N 4[LaHTar2-+] (8)pH 3.5: [La3+] N [LaTar+] NlO[LaTar,-] N 5[LaHTar2'] (9)pH 4.0: [La3+] N [LaTar+] 2:5[LaTar,-] N 10[LaHTar2+] (10)Comparison of the stability constant of lanthanumtartrate at 25 "C and infinite dilution with that forlanthanum succinate in the same conditions,ls log pro =3.96, shows the increased stability of the tartrate com-plex caused by the co-ordination of the a-hydroxy-groups of the tartrate ion. Shevchenkolg has studiedthe i.r. absorption spectrum of solid La2(C4H406)3,9H20and found that some of the hydroxyl groups were co-ordinated and some not.Shevchenko found that lead-18 J. M. Peacock and J. C . James, J . Chem. SOG., 1951, 2233.l9 L. L. Shevchenko, Zhur. neorg. Khim., 1968, 13, 143.2O D. Grdenic and B. Kamenar, Acta Cryst., 1965, 19, 197.21 R. Larsson, Acta Chem. Scand., 1965, 19, 783.22 P. G. Manning, Canad. J . Chem., 1965, 43, 3258; J. E.Powell, A. R. Chughtai, and J. W. Ingemanson, Inovg. Chem.,1969, 8, 2216.23 J. Bjerrum, ' Metal -4mmine Formation in Aqueous Solu-tion,' P. Haase and Son, Copenhagen, 1941.Z4 P. G. Manning, Canad. J . Chern., 1966, 44, 3057.25 P. G. Manning, Canad. J . Chem., 1965, 43, 3258.(11), cadmium(Ir), and cobalt(11) tartrates exhibited thesame behaviour. Grdenic and Kamenar 2o studied(NH4),Sb,(C4H406),,4H,0 by X-ray diffraction andfound that both hydroxyl groups co-ordinate the anti-mony ion.For aqueous solution, Larsson21 has re-ported the coexistence of three types of complexing ofthe uranyl ion by glycollate ion : (a) by the carboxylategroup alone, (b) by both the carboxylate and hydroxylgroups, and (c) directly by the carboxylate group andindirectly by the hydroxyl group, which is hydrogen-bonded to a water molecule in the first co-ordinationsphere. The possibilities in the lanthanum-tartratesystem, where the ligand has two of each type of co-ordinating group, are even more varied.Attempts have been made2, to find the denticity ofligands from Bjerrum's formula23 (11) where P is theP = S . R . T (11)ratio, k,Jk, + 1, of two successive stepwise thermodynamicstability constants, S is a statistical term depending onthe co-ordination number of the cation and the denticityof the ligand, T is an electrostatic term, and R is the' rest effect,' a catch-all for any unconsidered factors.T has been calculated to be ca.6-5 for bivalent ligands inlznthanide complexes.24 The rest effect is commonlytaken to be equal to unity,25 although Bjerrum foundthat this need not be so. For lanthanum tartrate at25 "C, we have found P = 41, giving S . X = 6.2, whichis large enough to indicate that tartrate is more thanbident ate.Compilations of enthalpy and entropy changes forlanthanide complexing have been published,26 comprisingtwo main bodies : aminopolycarboxylate complexesin 0 - 1 ~ potassium nitrate or chloride media and mono-carboxylate complexes in 2~-sodium perchlorate medium.A few studies have been made at infinite dilution.Ofthese, lanthanum malonate 27 has a similar standardGibbs energy change at 25 "C (-2.8 x lo4 J mol-l)to lanthanum tartrate, but the enthalpy change is morepositive (2.0 x lo4 J mol-l). The more favourableenthalpy change of the tartrate complex may be ascribedto the effects of the co-ordination of one or both hydroxylgroups. The standard entropy change (160 J K-l mol-l)of the malonate complex is more favourable than for thetartrate. The same trends in the enthalpy and entropychanges have been observed in the rare-earth mono-carboxylates and their cc-hydroxy-deri~atives,~*~29 whereit has been suggested that the more favourable enthalpychanges found with the hydroxy-acids arise from the26 T.Moeller, D. F. Martin, L. C. Thompson, R. Ferrus,G. R. Feistel, and W. J . Randall, Chem. Rev., 1965, 65, 1; T.Moeller, E. R. Birnbaum, J. H. Forsberg, and R. B. Gayhart,Progr. Sci. Technol. Rare Earths, 1968, 3, 61.27 E. Gelles and G. H. Nancollas, Trans. Faraday Soc., 1956,5, 680.28 I. Grenthe, Acta Chem. Scand., 1964, 18, 283.28 A. Sonesson, Acta Chem. Scand., 1959, 13, 998; G. R.Choppin and J. A. Chopoorian, J . Inorg. Nuclear Chem., 1961,22, 97; A. D. Jones and G. R. Choppin, ibid., 1969, 31, 3523;G. R. Choppin and A. J. Graffeo, Inorg. Chem., 1965, 4, 1254;G. R. Choppin and H. G. Friedman, ibid., 1966, 5, 15991972 1143participation of the hydroxyl group in the complexingand that the reason for the smaller entropy changes,contrary to what is expected on chelation, lies in the co-ordination of the hydroxyl group via a water moleculein the first co-ordination sphere of the cation.In thiscase the normal entropy gain on chelation, caused by therelease of extra particles into the system, does not occur,although the loss of configurational entropy of the ligandstill does, resulting in a net lower entropy gain for thehydroxy-acid complexes than for unsubstituted ligands.The above interpretation ignores the contribution tothe entropy changes made by the release of watermolecules from the hydration sphere of the anion. Thecompilation by Christensen, Oscarson, and Izattshows that the entropy change of dissociation is morenegative for a monocarboxylic acid than for its CC-hydroxy-derivative , where hydrogen bonding between thehydroxyl group and the carboxylate group may reducethe number of water molecules entering the anion’s co-sphere, thus making the entropy change less negative] inspite of any loss of configurational entropy caused by thehydrogen bonding. The same phenomenon is observedin the first dissociation of a dicarboxylic acid when eitherthere is a hydroxyl group available for hydrogen bondingor the second carboxyl group is in a position to do thesame.The magnitudes of AS,O(diss) for various acidsare in the order maleic - oxalic > tartaric - malonic >malic > succinic > glutaric 1: adipic N pimelic 21suberic. The values of AS,O(diss) are much the samefor all the acids except tartaric, which has a secondhydroxyl group available and a less negative value ofAS;(diss) also. It is interesting to compare the dif-ference in ASlo(diss) for acetic and glycollic acids atinfinite dilution, 20 J K-l mol-l, with the difference re-ported by Grenthe 28 between the entropy changes oncomplexing of lanthanum acetate and glycollate, 28 JK-l mol-l, in a %-sodium perchlorate medium. Com-parison of literature values for lanthanum malonate andours for the tartrate gives a difference in ASo of 65 J K-lmol-l, perhaps reflecting a double effect from the twohydroxyl groups of the tartrate anion.The evidence from ratios of successive stabilityconstants and from the thermodynamic data is notstrong enough to confirm that a-hydroxy-acids chelateonly indirectly via a bound water molecule, or even thatsuch co-ordination is the most important of Larsson’sthree possible types.We thank the S.R.C. for a Research Studentship (toD. M.).[1/2185 Received, 18th November, 1971130 J. J. Christensen, J. L. Oscarson, and R. 11. Izatt, J . Amer.Chem. SOG., 1968, 90, 5949