HENRYE. WIRTHAND FREDERICK K. BANGERT
3488 Analysis of the trifiuoromethyl hypofluorite by idiometric titration1' showed 89% purity. The nature of the experiments was ruch that only bistrifluoromethyl peroxide and c a b o n fluoride presented any difficulties as possible impurities. Since the measurements made for experiments wiLh trifluoromethyl hypofluorite were initial rate nwmirements, the presence of small (-1%) amounts of bistrifluoromethyl peroxide presented no problem. Since, in addition, these experiments were carried out with substantial amounts of added carbonyl fluoride, the presence of small amounts of carbonyl fluoride as :in impurity in the trifluoromethyl hypo-
fluorite was likewise not a source of difficulty. The procedure adopted was to use the trifluoromethyl hypofluorite, as received, and to correct for the fact that it was only 89% pure.
Acknowledgment. This work was supported by Grant No. AFOSR 70-1939 of the Air Force Office of Scientific Research, Office of Aerospace Research, USAF. The United States Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation hereon.
Apparent Molal Volumes of Sodium Chloride and Magnesium bhridie in Aqueous Solution
by Henry E. Wirth* and Frederick K. Bangert Department of Chemistry, Syracuse University, Syracuse, N e w York 13810 (Received .November 19, 1971) Publication costs assisted by Syracuse University
The apparent molal voluines of sodium chloride and magnesium chloride in aqueous solution at 25" were determined for the concentration range 0-4 m using a modified form of the Geffcken dilatometer. The data obtained at low concentrations (ionic strength less than 0.4) were treated by the extended forms of the Debge-IIuckel and Friedman equations. The calculated apparent molal volumes at infinite dilution of magnesium chloride were 14.47 (Debye-Huckel) and 14.52 cm3/mol (Friedman).
Introduction Preliminary t o the determination of the volume changes on mixing solutions of magnesium chloride and sodium chloride, the apparent molal volumes of magnesium chloride in aqueous solution were determined at concentrations ulp t o 4 m. As a check on the precision of the dilatometer method used, the apparent molal ium chloride were determined.
Experimental Section A. stock scilution approximately 4 m in sodium chloride (Fisher Certified) was made up and analyzed by evaporation and drying to constant weight a t 220". A similar stoclr solution of magnesium chloride (Baker and Adamsnn) was analyzed by precipitation of the chloride as silver chloride, All weights were corrected t o vacuum. The densities of the stock solutions were determined by the sinker method, using a "supplementary The sinkers used were made of Vycor and had approximate volumes of 300 cm3. The apparent molal volumes of dilute solutions were T h e Journal of Physical Chemistry, Vol. 76, N o . 23, 1972
determined using a modified Geff cken dilatometer.2-4 The apparent molal volume ( 4 ) is obtained from the observed change in volume (Av) when stock solution is added to water by means of the relation (1)
where n2 is the number of moles of electrolyte added, and $ref is the apparent molal volume of the electrolyte in the stock solution. The molality of the solution is 1000 nz/(m'l n z l ) , where ?n'lis the weight of the water to which the stock solution (containing n2 moles of salt and m1 grams of water) is added. With the Geffcken apparatus a series of additions can be made, so that a
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(1) H. E. Wirth and F. N. Collier, Jr., 1.A m e r . Chem. Soc., 72, 5292 (1950). (2) W. Geffcken, A. Kruis, and L. Solana, Z . P h y s . Chem., Abt. R (Leipzio), 35, 317 (1937). (3) €1. E. Wirth, R . E. Lindstrom, and J , N. Johnson, J. P h y s . Chem., 67,2339 (1963). (4) H. E. Wirth, ibid., 71,2922 (1967).
3489
L-".-
15.53
OS
0.3
0.2
04
U
0.5
1
Figure 1. Evaluaxion of for sodium chloride. The observed apparent m d a i volumes minus the limiting law plotted us. the ionic strength are compared with the results of Bruis6 and Miliero.0
number of data points are obtained from a single loading of the drlztdomrter. In Borne experiments a more dilute reference solution (WL N 1) was empIoyrd. The apparent molal volume of the electrolyte in these solutions was obtained from the dilution experirnonts with the stock solutions. The apparent molal volume of solutions between 2 and 4 712 mere obtained f n m Lhe volume change observed when water was added to IAPstock solution. The thermoetst used for both the density dcterminations and I h e dilatometer experiments was maintained a t 25.00 * 0. l o , and was held constant within .t.0.0005" during t h e course of a single series of observations.
S ~ d i ~ Chlortcle. nz The apparent molal volume a t infinite diilution (&") wa8 determined in the usual manner , ~ -- 1.86 1"' (where I = ionic by plotting c $ ~=~r,hobsd strength on a molal bagis) us. 1 (Figure 1). Based on 18 points ( I f 0.40), 4" == 16.610 f 0.006 cma/mol, where h0.006 is the "00: m a n square deviation (rmsd) between the observed and calculated values, assuming the slope of,,@,, vs. 1 is zero. The results are in good agreemeiit with values reported previously by Kruis,6 by 1Cilillero,6and b j Vi'~l,slo.~v.~ A deviation plot fur all the experimental points is given in Figure 2 . We were concerned that our present results are higher than those of Vaslow7 and previous results of Wirth* by appyoxima'tely 0.06 cma/mol a t concen trations above 2 m , although they do agree within the expcrinwntal error with the results of G e f f ~ k e n . ~An error of 0.02% in the censity or an error of 0.2% in the mofality is required to give this difference in the apparenz molal volume An error of 0.0270 in the density i s very unlikely, so it is possible that differences in the moiialil,y, perhaps due to impurities in the salts used, are the souroes of the discrepancy. Since in our procedure an error of 0 06 cm3/moi in the determination of the apparent riolai volume of the reference solution woulcl lead to an eqiaal error in the apparent molal volume of the dilute solutions (eq l), and since our v d u e s in diIule solution agree so well with other authors, we believe our new values are to be preferred.
0.5
1.0
1.5
2.0
m'/2.
Figure 2. Deviation plot of A ( = @o&d - (bobsd vs. the square root of the molality. For NaCl (upper plot), $ c a ~ c d= 16.61.0 f 1.8611/2 0.008481 0.0452~1~ - 0.008091a, an equation which represents all 47 experim.enta1points (0-41) with an rmsd of =kO.OIO cma/md. Data points were obtained by adding a solution (m = 1.12g2,cp = 18.64sj to water (X), by add'ng a solution (m = 0.7665, (b = 18.W1) t,o water (e))by adding reference solution (m = 4.1780, cp = 20.655) to wader (Jr), and by adding water to reference so'ution (0). For MgCh (lower plot), &lod = 14.517 3.951111/a- 0.562941 0.0847&312- 0.00474113, an equation which represents the 45 data points between 0 and 41 with an rmscl of rt0.028 cmZ/md, and q5aalod = 15.245 2.40721"' f 0.32951 0.00819812 0.00022761", representing the 35 observations between I = 0.6 and I = 12 with an rmsd of rt0.012 cm~/jmol, Comparison of experimental values with calculated values from the latter equation are given only for I > 4 ( m l / *> 1.15) in the above deviation plot. Data points were obtained by adding a solution (m = 1.011, 4 = 20.344) to water ( X ) , by adding a solut'on (nz = 1.000, 6 = 20.312) to water ( referenee solution (m = 4.1678, cp = 26.1ssj to waler (+), and by adding water to reference solution (e)).
+
+
+-
+
As h4illeros has pointed out, the partial molal volume of a 1-1 electrolyte should be given by the extended Debye-Huckel equation including the ion-size parameter 8
whereS, = 1.86 a t 2 5 O . l o The correspon for apparent molal volume (in terms of m ) ia
(3) The fact that the experimental results for sodium chloride at 25" would imply that R = 0 (and I1972
