March, 1962
H E ~ T SO F FORMATION O F COMPLEX
ever it should be noted that the values of y+ depend upon the choice of the value of the ionization constant, K1, and the assumption yu = I. Using the estimated best values of the dissolved sulfur dioxide concentration, C, e 6 was employod t o obtain final best estimates for the horptivities a'. These estimatrs were made for six wave lengths below 260 rnr and the two wave lengths above 300 mp as well as for tho nine wave lengths used to estiinate p in eq. 8. The logarithms of these absorptivities are plol ted us. wave length in Fig. 3. The ionization constant, K 1 ,for aqueous solutions of sulfur dioxide decreases with increasing temperature.16 Tlencr, for u. fixed total sulfur concentration, CT,the concentration of the dissolved portion, C, and hence the absorbance, A , by uy. 6 , must increase with incrcasing temperatiire. Thia increase in absorbance with increasing temprrature is in accordance with the observations of DcMaine1O at tomperatures other than 25". (15) A. JL Rabe, Ph.D, Thesis, University of Wisconsin, 19%.
SULFATE IONS
519
It should be mentioned that Simon and Waldmann,16 working with Raman spectra and aqueous solutions of sulfur dioxide of coneentration greater than 1 M , detected lines attributable to &06*-, suggesting that another ionic eqililibriiim exists ih this system, namely 2HSOa- ~t S20a'HzO (13) As the concontration of sulfur dioxide is reduced, howcver, the equilibrium shifts sharply to the loft and for the dilute solutions employed in the present study (0.00327-0.0126 M),the number of S ~ 0 ~ 2ions - probably is negligible, just as the secondary ionization of the bisulfite ion HSOs- F? H + -tS01'(14) can be safely neglected. Evidence in the present study that the quantity of SZOS*-ions is negligible is the absence of any selective rtbsorpt>iona t 267 nipj the wave length charactoristie of the S,0s2- ion.
+
(18) A. Rimon and K. Waldmann, 2. nnoi-g. u. allgem. Ckcm., aa3, 359 (1950).
THE STANDARD EKTHALPY OF FORMATION OF COMPLEX SULFATE ION3 I N WATER. I. HS04-, LiS04-, NaS0,BY J. &/I. AUSTINAND A. D. MAIR Department os chenzistry, Vniversity of Canterbury, Christehurch, h'ew Zealand Received #ctobeT 1Y , 1961
The heat of dilution of perchloric acid, lithium perchlorate, and sodium perchlorate solutions in perchloric acid, lithium perchlorate, and sodium perchlorate solutions, respectively, has been compared with similar dilution in dilute fiolutions of sulfuric acid, lithium sulfate, and sodium sulfate, respectively. The differences between the observed heat effects have been used to calculate the standard heats of formation of the ions HSO,-, LiSO,-, and NaS0,-.
The thermodynamic functions associated with complex-ion formation may be found either from temperature coefficient studies of the free energy of formation or by direct calorimetric measurement at 2 5 O of the enthalpy change on forming that amount of complex determined by its free energy of formation a t 25'. Whereas there have been several investigations1-4 of the heat of formation of the T-ISO,-. ion by temperature coeficient methods in solutions of low ionic strength, the calorimetric data available has been obtained in solutiionsof high ionic strength. These observations involved measurement of thc heat of dilution of concentrated solutions of sodium sulfate in the presence of hydrochloric acid5 or perchloric acide at ionic strengths of one and two, respectively. A vah~cfor the standard heat of formation calculated from these observations can be in error as the result of heat effects associated with the reduced amount of NaS04present after dilution or by the inadequacies of activity coefficient expressions used t o correct heat effects observed a t such high ionic st)rcngths. As the NaSO1- and LiSO4- ions have bcen characterized only by their association constants determined from conductance data at a single temperature the heats of formation of these ions are not known. (1) V. S.I
