J. Chem. SOC., Faraday Trans. I, 1982, 78, 1071-1077 Thermodynamic Properties of Copper Sulphate in Dioxan + Water Mixtures from Electromotive-force Measurements BY RATAN L. BLOKHRA* AND SUDARSHAN KOHLI Department of Chemistry, Himachal Pradesh University, Simla- 17 1005, India Received 10th April, 1981 Electromotive-force measurements of the cell Cu-HglCuSO, (m), dioxan (X)IHg,SO,(s)lHg have been made at 288, 298, 308 and 318 K for solvent compositions X = 10, 20, 30 and 40% (w/w) of dioxan. These have been used to evaluate the standard potentials of the cell, the mean activity coefficient of copper sulphate (molal scale) and the thermodynamic functions of transfer of copper sulphate from water to the respective dioxan + water media. The results have been interpreted in terms of solute-solvent interactions.The activity coefficients of many typical 1 : 1, 2 : 1 and 2 : 2 ele~trolytesl-~ have been determined in various aquo-organic solvents and a few non-aqueous solvents. The thermodynamics of aqueous solutions of cadmium, copper, manganese and nickel sulphates have not been studied as comprehensively as those of aqueous solutions of zinc ~ u l p h a t e . ~ ? ~ A survey of the literature reveals that very little work has been reported on thermodynamic studies of 2: 2 electrolytes in aquo-organic and non- aqueous solvents. Recently Blokhra et ~ 1 . ~ 9 lo have reported on the thermodynamics of copper sulphate in diethylene glycol, aqueous diethylene glycol, ethylene glycol and aqueous ethylene glycol. The present investigations have been carried out using copper sulphate in order to determine (i) the activity coefficient of copper sulphate in various aqueous dioxan mixtures and (ii) the thermodynamic functions of transfer of copper sulphate from water to the respective dioxan +water media.The solvent systems chosen were 10, 20, 30 and 40% (w/w) dioxan+ water mixtures. EXPERIMENTAL Dioxan was of B. D. H. AnalaR quality and was purified by refluxing over sodium for 6 h followed by distillation. Water of specific conductance of ca. kg mol-l i2-l was used for making up, by weight, aqueous mixtures of dioxan. Copper sulphate (AX.) was used as such. Experimental solutions of the desired concentrations were prepared by weight. The e.m.f. cell used for the present study was as previously describedg except that a copper amalgam was used instead of the electroplated copper electrode in one of the limbs.Copper amalgam containing ca. 3 % copper (w/w) was prepared by electrolysing a copper(I1) perchlorate solution with a mercury pool as cathode, as described e1sewhere.l' At room temperature, a two-phase amalgam is formed between 0.0032 and 24.1 % copper (w/w).l29 l3 Within this range the potential will be independent of composition, and the exact composition of copper is therefore unimportant.14 A high copper content should be avoided, however, as the amalgam then becomes inconveniently stiff. The amalgam was stored under 0.1 mol dm-3 perchloric acid. Prior to use it was washed with dilute perchloric acid to remove traces of copper(1r). The e.m.f. measurements were made with an OSAW (Ambala) precision potentiometer 10711072 PROPERTIES OF CUSO, IN DIOXAN AND WATER having an accuracy of kO.1 mV.A d.c. spot-galvanometer was used in conjunction with the potentiometer. The potentiometer was standardised against a certified Weston standard cell maintained at a constant temperature. All measurements were made in a thermostat having fluctuations of < k0.2'. The cell attained equilibrium after 30-35 min in all the solvent mixtures. The concentrations of the solutions were occassionally checked following the experiments and no significant change was detected. Duplicate experiments were performed simultaneously in each case and the duplicates generally agreed within kO.5 mV. The densities (Po), dielectric constant (D,) and the Debye- Hiickel parameters for the various dioxan+water mixtures were taken from the work of Das et aL2 RESULTS AND DISCUSSION The e.m.f.(E) values of the cell are reported in table 1. Assuming copper sulphate to be fully dissociated, the standard potentials, E g , of the cell: Cu-HglCuSO, (m), dioxan (X)IHg,SO, (s)(Hg in different solutions can be estimated from an equation of the Hitchcock15 type: where I is the ionic strength of the solution, m is the molal concentration of the solution, A and B are the Debye-Huckel constants, a, is the ion-size parameter, Z+ and 2- are the valencies of the cation and anion, respectively, and k equals 2.3026 RTIF. B' is a constant quantity and it is a measurement of the interaction energy.16 The values of the activity coefficients, A,, - can be evaluated from the relation17 E = @ - k log mA+.- (2) should be a linear function of I when a suitable value of the ion-size parameter is chosen. The intercept of the plot at I = 0 then gives the value of E,e. The a, values for the various solvent mixtures at different temperatures are chosen in such a way that the deviation from linearity of the plot of Ei against I is minimum. A deviation of k 0.2 mV was observed when the a, value was vaned within k0.3 A of the chosen value. The following a, values were selected for the respective dioxan + water mixtures : From eqn ( 1 ) it is expected that dioxan (wt %) 10 20 30 40 aolA 5.0 5.2 5.2 5.5 a, is constant throughout the temperature range studied for a particular solvent composition.This agrees with the conclusions of LaMer et aZ.6*s The values of are recorded in table 2. The average standard deviation in is kO.2 mV and the values for each solvent system were fitted by the method of least squares to eqn (3) (3) where T is the temperature in K. The constants a, b and c are given in table 3. The mean activity coefficient A, of copper sulphate in various solvent media was calculated with the help of eqn (2), and these values at 298 K are listed in table 4. An error of kO.05 mV in the e.m.f. values results in an error of kO.001 in the value of 1,. - The values of the activity coefficient at a particular molality are found to = a- b(T- 298.15) - C( T - 298.R. L. BLOKHRA A N D S. KOHL1 1073 TABLE 1 .-ELECTROMOTIVE-FORCE MEASUREMENTS OF THE CELL USED (E/V) IN VARIOUS DIOXAN +WATER MIXTURES AT DIFFERENT TEMPERATURES T / K concentration/ mol kg-l 288 298 308 318 1 .oo 2.00 4.00 6.00 8.00 10.00 20.00 40.00 60.00 80.00 100.00 1 .oo 2.00 4.00 6.00 8.00 10.00 20.00 40.00 60.00 80.00 100.00 1 .oo 2.00 4.00 6.00 8.00 10.00 20.00 40.00 60.00 80.00 100.00 1 .oo 2.00 4.00 6.00 8.00 10.00 20.00 40.00 60.00 80.00 100.00 0.5204 0.5062 0.4929 0.4849 0.4799 0.4763 0.4652 0.4553 0.4506 0.4475 0.4452 0.5152 0.5016 0.488 1 0.48 14 0.4762 0.4723 0.4617 0.4522 0.4470 0.4434 0.4405 0.5070 0.4933 0.48 17 0.4741 0.4699 0.4658 0.4554 0.4450 0.4376 0.4319 0.4269 0.5005 0.4880 0.4769 0.4707 0.4664 0.4632 0.4541 0.4438 0.4358 0.4290 0.4228 10% dioxan 0.5227 0.5077 0.4940 0.4864 0.48 1 3 0.4772 0.4660 0.4560 0.451 1 0.4483 0.4467 20% dioxan 0.5170 0.5029 0.4893 0.482 1 0.4773 0.4739 0.4633 0.4536 0.4484 0.445 1 0.4426 30% dioxan 0.5077 0.4939 0.48 15 0.4748 0.4702 0.4666 0.4566 0.4472 0.4417 0.4377 0.4345 0.5029 0.4902 0.4788 0.4726 0.4682 0.4649 0.4564 0.4464 0.4392 0.4334 0.4282 40% dioxan 0.5247 0.5094 0.4954 0.4877 0.4826 0.4787 0.4670 0.4563 0.45 17 0.4490 0.4473 0.5185 0.5040 0.4907 0.4836 0.4783 0.4748 0.4639 0.4543 0.4493 0.446 1 0.4439 0.5099 0.4960 0.4833 0.4768 0.47 18 0.468 1 0.4579 0.4485 0.4429 0.4388 0.4357 0.5048 0.49 17 0.4803 0.4742 0.4700 0.4668 0.4582 0.4482 0.4419 0.4365 0.43 19 0.5266 0.51 13 0.4968 0.4889 0.4836 0.4795 0.4680 0.4573 0.4537 0.45 12 0.4500 0.5198 0.5046 0.49 14 0.4838 0.4786 0.475 1 0.4642 0.4555 0.4503 0.4473 0.4455 0.51 14 0.4970 0.4846 0.4775 0.4726 0.4688 0.4595 0.4498 0.4442 0.4402 0.4368 0.5064 0.4933 0.48 17 0.4757 0.4714 0.4683 0.4594 0.4504 0.4444 0.4394 0.43481074 PROPERTIES OF CUSO, I N DIOXAN AND WATER decrease with increasing dioxan content in the medium, as expected from Debye- Huckel theory, because of a lowering of the dielectric constant of the medium.The higher magnitude of the activity coefficient at lower dioxan contents suggests that the solute-solvent interaction increases as the dioxan content decreases. It is also seen that the activity coefficient at a particular molality decreases with increasing temperature. This may be attributed to a greater solute-solvent interaction at lower temperatures. TABLE 2.-sTANDARD MOLAL POTENTIALS OF THE CELL USED IN DIOXAN + WATER MIXTURES AT VARIOUS TEMPERATURES dioxan (wt %) 288 K 298 K 308 K 318 K ~~ ~ 0 0.3455 0.3420 0.3385 0.3350 10 0.3410 0.3370 0.3325 0.3280 20 0.3340 0.3295 0.3245 0.3190 30 0.3235 0.3 175 0.3130 0.3075 40 0.3140 0.3095 0.3040 0.2975 TABLE VALUES OF THE CONSTANTS a, b AND c IN EQN (3) b/ 10-4 v K T ~ c/ V K-2 dioxan (wt %) a/v 0 0.3420 10 0.3372 20 0.3294 30 0.3179 40 0.3095 3.00 4.25 4.72 5.25 - 4.98 2.50 1.70 2.40 0.20 2.60 The free-energy changes AGP accompanying the transfer of one mole of copper sulphate from the standard state in water to the mixed solvents were calculated on the mole-fraction scale using the relationls AGP = - 2F [(Efit), - (Efit),] - 2 x 2.3026 RT log (MJM,).(4) The corresponding entropy changes were calculated using the relation1* A@ = F(b, - b,) + 2F( T - 298.15) (c, - c,) + 2 x 2.3026 R log (M,/M,) ( 5 ) where the subscripts w and s refer to water and the mixed solvent, respectively.The corresponding enthalpy changes will be given by the equation AH? = AG?+ T A F . (6) The AGP, AH? and ASP values are listed in table 5. The probable uncertainties in AGP are f 19 J mol-l, those in AH? are &23 J mol-l, and those in A@ are k0.40 J K-l mol-l in 10 and 20% solvent composition and kO.70 J K-l mol-1 in 30 and 40% solvent composition. The standard Gibbs free energies of transfer, AGP, are positive for all the solvent compositions and increase with increasing temperature. The positive AGP values suggest that copper sulphate is in a higher free-energy state in dioxan +water mixtures than in water so that copper sulphate hasmore affinity for water than for dioxan + waterR.L. BLOKHRA AND S. KOHL1 1075 mixtures, and the transfer of copper sulphate from water to dioxan +water mixtures is not a spontaneous process with the solute in the standard state in either medium. Similar conclusions were drawn for copper sulphate in ethyleneglycol + water mixtures.l0 The values of A p and AH? are also positive for all the solvent mixtures. The enthalpy in dioxan+ water mixtures is, therefore, greater than that in pure water and hence the increase in order created by copper sulphate in dioxan + water mixtures is less than that occurring in pure water. It may be possible to split the AGP values TABLE 4.-MEAN MOLAL ACTIVITY COEFFICIENT OF CUSO, IN VARIOUS DIOXAN +WATER MIXTURES AT 298 K ~~ ~ dioxan (wt %) concentration/ mol kg-l 10 20 30 40 1 .oo 2.00 4.00 6.00 8.00 10.00 20.00 40.00 60.00 80.00 100.00 0.725 0.65 1 0.555 0.498 0.455 0.426 0.330 0.243 0.196 0.164 0.140 0.676 0.585 0.497 0.438 0.396 0.362 0.274 0.199 0.163 0.139 0.122 0.609 0.522 0.423 0.366 0.328 0.302 0.223 0.160 0.132 0.116 0.105 0.538 0.441 0.344 0.291 0.259 0.236 0.165 0.121 0.107 0.100 0.098 TABLE 5.-FREE ENERGY, ENTHALPY AND ENTROPY OF TRANSFER OF COPPER SULPHATE FROM WATER TO DIOXAN + WATER MIXTURES AT VAROUS TEMPERATURES T / K AGP/J mol-l AHp/kJ mol-l A P / J K-l mol-l 288 298 308 318 288 298 308 '318 288 298 308 318 288 298 308 318 469 55 1 73 1 910 1389 1552 1813 2170 2936 3373 3521 3861 424 1 43 70 4692 5207 10% dioxan 4.78 4.56 4.40 4.20 7.05 7.35 7.75 7.86 12.00 11.19 10.00 8.89 11.52 11.96 12.60 13.43 20% dioxan 30% dioxan 40% dioxan 14.98 13.44 1 1.90 10.35 19.66 19.47 19.28 19.08 3 I .46 26.25 21.04 15.83 25.29 25.48 25.67 25.871076 PROPERTIES OF CUSO, IN DIOXAN A N D WATER into two parts, as suggested by Roy et al.,19 a non-electrostatic or chemical contribution AG?,, and an electrostatic contribution AG?,, which has been calculated from the Born equation,20 eqn (7): where N is Avogadro's number and D, and D, are the dielectric constants of the mixed solvent and water, respectively; r+ and r- are the radii of the Cu2+ and SO:- ions, taken as 0.70 and 2.89 respectively.TABLE 6.-ELECTRICAL AND THE CHEMICAL PARTS OF THE THERMODYNAMIC QUANTITIES ACCOM- PANYING THE TRANSFER OF COPPER SULPHATE FROM WATER TO DIOXAN -I- WATER MIXTURES AT 298 K dioxan AG?el! AGfch/ A H r e l / AHrch/ A q e , / A q c h / (wt %) kJ mo1-1 kJ m o P kJ mol-1 kJ mol-l J K-' mol-l J K-l mol-l ~~ 10 1.92 - 1.37 - 2.8 1 7.37 - 15.87 29.3 1 20 4.53 - 2.98 - 5.34 12.69 - 33.10 52.57 30 8.00 - 4.63 - 8.50 19.69 - 55.38 8 1.63 40 12.92 -8.55 -12.93 24.89 - 86.77 1 12.25 The electrostatic part of the entropy of transfer may be obtained by differentiating eqn (7), whereby we have (8) where the values of d In D,/dT and d In D,/dT can be evaluated from the simple empirical eqn (9):2 dlnD 1 d T 8 in which 8 is a constant characteristic of the medium.Thus eqn (8) may be rewritten as 1 dlnD, - -- ----- - ~ ( ~ w d i ~ ~ w D, dT )(;+:) (9) -- -- - From the slopes of the linear plots of log D against T for the respective dioxan +water mixtures, the following values of 8 were calculated: dioxan (wt %) 0 10 20 30 40 8 220 202 194 187 181 From a knowledge of AGee1 and A T , , the electrostatic part of the enthalpy change AH?,l has been computed.The chemical contribution of the free energy of transfer AGFCh, entropy of transfer A T , , and enthalpy of transfer can then be obtained by subtracting the respective electrostatic contribution values from the molal quantities. These values so calculated at 298 K are presented in table 6. It is obvious that the chemical contribution of the free energy of transfer is negative and appearsR. L. BLOKHRA AND S. KOHLI 1077 to be a parameter of the solvent which measures the increase in basicity in the dioxan +water mixture. Hence, considering only the chemical contribution to the free energy AGP which has negative values, the dioxan +water mixture appears to be more basic than water.The electrostatic factors, however, predominate over the chemical contribution or the solvation, resulting in an overall unfavourable effect on the transfer process from water to dioxan + water mixtures. The electrostatic parts of the enthalpy and entropy have negative values, whereas the chemical contribution to the enthalpy and entropy is positive. We thank the U.G.C. (India) for financial support. S. K. thanks the D.A.V. Colleges Managing Committee, New Delhi, for sanctioning leave under the faculty improvement programme. P. K. 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