J. Chem. Sac., Furaduy Trans. I , 1985, 81, 2333-2337 Measurements of Volume Changes on the Formation of Precipitates of Carbonates and Phosphates of Cadmium(I1) and Calcium(r1) in Aqueous Solutions BY MICHIHISA UEMOTO Department of Chemistry, Faculty of Science, Gakushuin University. Mejiro, Toshima-ku, Tokyo 17 I , Japan AND TAKUSEI HASHITAN* Faculty of General Education. Tokyo University of Agriculture and Technology, Fuchu-shi. Tokyo 183, Japan Received 23rd October, 1984 Changes in volume on the formation of CdCO,, CaCO,, Cd,(PO,), and Ca,(PO,), in aqueous solutions have been measured at 298.2 K. A dilatometer which has optically flat discs has been used for separating solutions. Values of the volume changes per mole of divalent metal ions have been determined. Volume changes on 'dehydration' have also been estimated from the measured data. The hydration of electrolytes in aqueous solutions can be studied by measuring partial molar and molal volumes.' Apparent molar volumes at infinite dilution have been determined and assigned to ionic values.These values have been interpreted quantitatively by reference to the intrinsic volumes of ions, ion-solvent interactions and the structure of water.* Here the volume changes were determined experimentally when hydrated water was liberated by chemical reactions (i.e. dehydration). The volume changes of the systems were measured when hydrated water of the cations and anions was liberated by the precipitation reaction for binary systems. The dilatometer used was designed by one of us3 and is characterised by optically flat discs for separating solutions.As it uses no mercury it is easier to use for electrolyte systems. EXPERIMENTAL THE DILATOMETER Fig. 1 ( a ) shows the dilatometer, which is made of Pyrex glass. In the centre of the vessel are discs A and B for separating the two solutions; the discs have optically flat surfaces. The outer edges of disc B, which has a central hole (ca. 1.3 cm in diameter), are fused to the wall of the dilatometer, and disc A is merely set on disc B. Each compartment of the dilatometer was calibrated with redistilled water, while the capillary was calibrated with mercury. The volumes of dilatometer compartments were 17-37 cm", and the inside diameters were 0.03-0.05 cm. The lengths of the capillaries were ca.40 cm. Before use, the distortion of disc B was tested. The constancy of the level and the absence of precipitate between the discs were examined while the two solutions were poured into and separated in the dilatometer. The method of filling was as follows: all solutions and solvent were previously outgassed and kept at 298.2 K. Solution I was poured into the vessel up to a level a few centimetres higher2334 VOLUME CHANGES ON PRECIPITATION Fig. 1. Dilatometer: A, B, optically flat discs for separating solutions; C, capillary; D, hole; E, groove; F, stirrer. than disc B. The two discs were not flush together at this time. Then the lower compartment of the dilatometer was immersed in a thermostat at 298.2 K. After thermal equilibration, disc A was gently placed flush onto disc B with tweezers.The solution in the upper compartment was sucked out with a syringe; the upper compartment was first washed with the solvent and then with solution 2. After this, solution 2 was injected and the vessel was stoppered to exhaust the excess of solution from the top of the capillary. To adjust the level of the solution in the capillary the stopper was turned so that groove E fitted into hole D, thus allowing the solution to flow out. The stopper has a ground-glass joint coated with sealant (e.g. petroleum). The stopper can be held tightly in place using rubber bands attached to glass hooks on the stopper and body. The method of mixing was as follows. The dilatometer was immersed in a thermostat and the level of the solution in the capillary was read with a cathetometer after thermal equilibration.Then the dilatometer was inverted, disconnecting the disc gravitationally [fig. 1 (b)], and the solutions were mixed. The dilatometer was returned with the two discs not flush, and the changed level in the capillary was read after stirring and thermal equilibration. K. The thermostat4(aca. 1 75-dm3 water bath) was maintained at 298.2 -+_ (3-4 x 1 0-4) K ; the temperature was monitored with Hewlett-Packard model 2801 A and 2804A quartz-oscillator thermometers. For such measurements, the temperature must be constant to better than 1 xM. UEMOTO AND T. HASHITANI 2335 Table 1. Volume changes on mixing for the system comprising aqueous solutions of M(NO,), and KnA (M = Cd2+ or Ca2+, A = C0:- or PO:-, n = 2 or 3), I = 0.1.V[M(NO,),I V(Kn A) A V A Vm/cm3 precipitate /cm3 /cm3 run /lop2 cm3 (MI1) mo1-I CdCO, 17.00 36.95 3 2.802 f 0.004" 50.2 18.88 34.76 1 3.232 49.9 CaCO, 17.00 36.95 4 3.091 &O.OlO" 56.5 18.88 34.76 1 3.573 56.8 Cd3(P04)2 17.00 36.95 3 3.141 +0.016" 56.3 Ca3(P04)2 17.00 36.95 3 3.066 f 0.007" 56.1 a Average deviations from the mean values. Aqueous solutions of cadmium(i1) nitrate and calcium(i1) nitrate at an ionic strength of 0.1 (0.033 mol drn-,) were poured into the lower compartment of the dilatometer, while aqueous solutions of potassium carbonate and potassium phosphate of the same ionic strengths (0.033 and 0.017 mol dm-3, respectively) were poured into the upper compartment. The volume of the upper compartment was ca. twice that of the lower, so potassium salts were present in excess after mixing.'The volume changes at the ionic strengths of 0.05 and 0.025 were also measured under the same conditions as described above in order to examine the ionic-strength dependence of the molar-volume changes. To examine the effect of hydrolyses of carbonate ions and phosphate ions, the solutions ( I = 0.1, K,CO, or K3P04 + I = 0.1 KOH, v/v = 4/ 1) were prepared as solutions of potassium salts under the conditions described above, where calcium hydroxide did not seem to precipitate. The values were compared with those at 'usual' conditions. In order to examine the effect of counter-ions in the systems, the volume change was also measured during a dilution of a potassium nitrate solution with an ionic strength of 0.1.MATERIALS A.R. cadmium(i1) nitrate, calcium(i1) nitrate and potassium carbonate were recrystallised from redistilled water. A.R. potassium phosphate and potassium nitrate were used without further purification. RESULTS AND DISCUSSION Volume changes on the formation of the precipitates are given in table 1. After mixing, the changed levels settled after a few hours in each system. The ionic-strength dependences of the volume changes are given in table 2; here volume changes per mole of divalent metal ions were almost constant within the experimental errors, over the range 0.025.4.1. The effect of hydrolysis of the carbonate and phosphate ions in the system containing CaCO, did not produce any significant difference; for the system containing Ca,(PO,), the volume change obtained by using the solution containing potassium hydroxide was ca.7% larger than when the latter was not present. Cadmium and calcium present in the supernatant solutions after mixing were analysed qualitatively with the chelating agent: they were not detectable. For normal mixing of binary solutions it is necessary to consider the effect of counter-ions (the potassium and nitrate ions in this case). However, the volume change on dilution of potassium nitrate solution ( I = 0. l), where the concentration of potassium nitrate after mixing was 0.054 mol dm-,, was extremely small2336 VOLUME CHANGES ON PRECIPITATION Table 2. Ionic-strength dependence of the volume changes ~M(N0,),]/cm3 = 17.00, V(K, A)/cm3 = 36.95 ionic strength precipitate 0.1 a 0.05 0.025 A v b A Vmc A v b A Vmc Avb A Vmc Avb A Vmc CdCO, 2.802 CaCO, 3.09 1 50.2 56.5 Cd3(P04)2 3.141 56.3 Ca,(P04), 3.066 56.1 1.441 51.6 58.0 55.6 56.1 1.586 1.552 1.533 0.748 0.789 0.775 0.758 53.6 57.7 55.5 55.5 a Taken from table 1.A V in the units cm3. AVm in the units cm3 (M") mol-l. Table 3. Calculations of the volume changes on dehydration from the observed molar volume changes ( I = 0.1) CdCO, 4.26 40.5 18.1 27.8 CaCO, 2.7 1 36.9 18.5 38.1 Cd,(PO,), 4.15 42.3 24.8 38.8 Ca 3 (PO 4 1 2 3.14 32.9 25.2 48.4 a Molar volumes obtained from the densities of precipitates. Molar volumes calculated from the ionic radii. In the units cm3 (M") mol-I. (- 0.18 cm3 mol-l) compared with those obtained on precipitation. Moreover, on precipitation, the volume change due to the counter-ions is expected to be smaller than this because of the lower extent of dilution.Thus the effect seems to be negligible in this case. Table 3 shows the procedure for calculating the volume changes on dehydration from the measured molar-volume changes ( I = 0.1). As precipitates have three- dimensional macroscopic structures, it is conceivable that a volume change occurs on precipitation not only on account of dehydration but also because of solidification. Differences between the molar volumes obtained from the densities of the precipitates5. and the molar volumes v2 calculated from crystallographic ionic radii7 and thermochemical ionic radii8* were subtracted from the observed molar-volume changes AV,. The molar volumes & were assumed to be the 'intrinstic' volumes of ions in the precipitates.The density of Cd,(PO,),, which could not be found in the literature, was measured using a Weld-type pyknometer.1° Consequently the last column in table 3 shows the volume changes on dehydration. If the volume change on dehydration is an additive property these values can beM. UEMOTO AND T. HASHITANI 2337 written as the sum of the corresponding values for the cation and anion as follows [eqn (1 j ( 6 ) in the units cm3 (MI1) molil] A Vm(Cd2+) + A Vm(COi-) = 27.8 AVm(Ca2+)+AVm(COi-) = 38.1 A Vm(Cd2+) +IA Vm(POz-) = 38.8 A Vm(Ca2+) +:A Vm(POi-) = 48.4. Subtracting eqn (1) from eqn (2) we get A V,(Ca2+) - A Vm(Cd2+) = 10.3 while subtracting eqn (3) from eqn (4) we get A Vm(Ca2+) - A Vm(Cd2+) = 9.6.The results of the same calculations for the data at ionic strengtlls of 0.05 anc 0.025 allows to make a first approximation that the volume change on dehydration is an additive property of this study. Further information is necessary when ionic-volume changes on dehydration are assigned. For systems containing phosphate salts it is probable that cadmium or calcium hydrogen phosphate is partly precipitated because of hydrolysis of the phosphate ions. Further investigations are necessary with regard to this point. However, it is interesting that Ca2+ and Cd2+, which have the same charge and almost the same ionic radii [r(Ca2+) = 1 .OO A; r(Cd2+) = 0.95 A],7 have markedly different values of the volume change on dehydration. The volume change on dehydration obtained in this study provides new information on the hydration of electrolytes and should be compared with limiting molar volumes and electrostriction volumes. We thank Dr S. Howell of Sophia University for help in preparing this manuscript. * F. J. Millero, Chem. Rev., 1971, 71, 147. J. W. Akitt, J. Chem. SOC., Faraday Trans. I , 1980, 76, 2259 and references therein. T. Hashitani, Bulletin of the Faculty of General Education, Tokyo University of Agriculture and Technology, 1978, 14, 84 (in Japanese). T. Hashitani, Bulletin of the Fuculty of General Education, Tokyo University of Agriculture and Technology, 1976, 12, 64 (in Japanese). Gmelins Handbuch der anorganischen Chemie, Nr. 33, Cadmium (Verlag-Chemie, Weinheim, 1925). Landolt-Bornstein Tabellen, II Band, I Ted, Mechanischthermische Zustandsgrossen (Springer-Verlag, Berlin, 1971). H. D. B. Jenkins and K. A. Thakur, J . Chem. Ed., 1979, 56, 576. A. F. Kapustinskii, Q. Rev. Chem. Soc., 1956, 283. Physical Chemistry (McGraw-Hill, New York, 7th edn, 1970), p. 98. ’ R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect B, 1969, 25, 925; 1970, 1046. lo F. Daniels, J. W. Williams, P. Bender, R. A. Alberty, C. D. Cornwell and J. E. Harriman, Experimental (PAPER 4/1812)