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H. HAMMERSCHMID AND A. L. ROBINSON
VOl. 54
The fifth and sixth columns of Table IV contain the values of m, = mH = mOHcomputed by equation (8). The next two columns contain the values of YH YoH computed by multiplying K , by aH,O, and the last two columns y or 4 s . The values of y obtained by the two methods rarely differ by more than 1% or * 0.5% from their mean.
Summary 1. Measurements of the electromotive forces of the cells HZI Ba(0H)z ( m l ) ,BaClz ( m ~1 )Ba,Hg I Ba(0H)Z (mo) I HZ have been made, and the activity coefficient of barium hydroxide in aqueous barium chloride solutions has been computed. 2. From these and other suitable results previously determined, the ionic activity coefficient of water in barium chloride solutions has been computed. 3. Thecells HZ 1 Ba(OH)Z (mol, BaC12 ( m ) I AgCl I Ag
have been measured and the ionic activity coefficient of water has been computed from the results, and compared with the values obtained from the amalgam cells. 4. The dissociation of water in barium chloride solutions increases, passes through a maximum and then decreases with increasing ionic strength, a behavior similar to that observed in solutions of the alkaline halides. The maximum dissociation occurs a t 1.5,~. NEW HAVEN,CONNECTICUT [CONTRIBUTION FROM THE DIVISIONOF PHYSICAL CHEMISTRY, CHEMICAL LABORATORY BAVARIAN ACADEMY OF SCIENCES, MUNICH,GERMANY, AND THE DEPARTMENT OF CHEMISTRY, UNIVERSITYOF PITTSBURGH, PITTSBURGH,PENNSYLVANIA ]
OF THE
INTEGRAL HEATS OF DILUTION AND RELATIVE PARTIAL MOLAL HEAT CONTENTS OF AQUEOUS SODIUM BROMIDE AND POTASSIUM BROMIDE SOLUTIONS AT TWENTY-FIVE DEGREES* BY H. HAMMERSCHMID AND A. L. ROBINSON RECEIVED APRIL 1, 1932
PUBLISHED AUGUST5, 1932
Introduction The measurement of heats of dilution of strong electrolytes a t concentrations low enough to permit an unambiguous extrapolation of the results t o infinite dilution makes possible a combination of such measurements with data obtained a t higher concentrations to calculate the relative partial molal heat contents of the components of the solutions. These are the partial molal heat contents referred to the molal heat contents of
* Communication Number 37 on Thermochemical Investigations by E. Lange and co-workers.
Aug., 1932
THERMOCHEMISTRY OF SODIUM AND POTASSIUM BROMIDES
3121
the reference state, the infinitely dilute solution.‘ A knowledge of the partial molal heat contents and the partial molal specific heats of the components of solutions is necessary for the calculation of thermochemical and thermodynamic properties of solutions, such as heats of reaction and their temperature coefficients, temperature coefficients of activity coefficients and partial molal free energies, temperature coefficients of solubility and ionic entropies. Measurements are presented here of the heats of dilution of aqueous sodium bromide and potassium bromide solutions from 0.1 M to infinite dilution a t 25’ and these measurements are combined with data of Wiist and Lange2 to calculate relative partial molal heat contents from infinite dilution to saturation. Experimental A differential adiabatic calorimeter, developed by Lange and co-workers, already described3 was employed. All details of manipulation and calculation were the same as in previous investigations. The potassium bromide was a guaranteed preparation of de Haen, several times recrystallized. For the sodium bromide measurements two different 0.1 M stock solutions were used; one was a solution prepared by Dr. W. Geffken for density determinations and kindly furnished by him, which contained sodium bromide prepared from pure sodium carbot ~ a t eand , ~ solution two was made from a Kahlbaum preparation that had been recrystallized twice. Both solutions were standardized by titration with two different silver nitrate solutions using phenosafranine as an indicator.6 The first two columns of Table I give the initial and final concentrations of a dilution, respectively. The third column of the table gives the heat effects of individual measurements (negative values of AH indicate heat evolved) in this concentration interval calculated per mole of salt, and the fourth column gives the average of the individual measurements and the probable error, exclusive of any systematic errors. The reproducibility of the measurements is better than two per cent. Discussion The data of Table I are plotted against the square root of the molality (weight and volume concentrations differ inappreciably in this concenLewis and Randall, “Thermodynamics,” McGraw-Hill Book Co., Inc., New York, 1923, p. 88. Wiist and Lange, 2.physik. Chem., 116, 161 (1925). Lange and Monheim, ibid., 149A,51 (1930); Lange and Robinson, Chem. Rev., 9, 89 (1931). Baxter, THISJOURNAL, 38, 70 (1916). Fajans and Wolff, 2.anorg. allgem. Chem.,137, 221 (1924).
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H . HAMMERSCHMID A N D A.
VOl. 54
L. ROBINSON
TABLE I MEASURED HEATSOF DILUTION AT 25' Initial concn., mole/liter
0.1 .1 .05 .05 ,025 .025 .0125 .0125 ,00627 .00627
0.1 .1 .05 .05 .025 .025 .0125 ,0125
End concn mole/liter"
AH, calories/mole Prep. 1
Prep. 2
0.0026 .0052 ,0013 .0026 ,00065 .0013 .00065 .000328 ,000164 .000325
Sodium Bromide -51.3 49.7 51.9 -45.5 45.9 45.3 -49.9 49.4 49.3 -44.1 44.1 44.0 -43.0 43.1 43.6 -38.5 38.4 39.2 -31.5 32.3 30.2 -34.4 35.0 33.6 -22.4 24.3 24.4 -21.7 22.7 22.6
0.0026 ,0052 ,0013 ,0026 .00065 0013 ,000329 .00065
Potassium Bromide -44.6 43.0 43.5 -37.0 36.0 37.0 -40.5 41.0 41.1 -35.7 35.9 37.2 -38.1 41.0 37.9 -33.8 33.2 33.8 -30.9 31.1 31.4 -28.9 29.0
52.3 46.3 50.0 43.9
30.6 34.7
43.5
36.2 38.7 30.6
Average AH, calories/mole
-51.3 -45.8 -49.7 -44.0 -43.2 -38.7 -31.4 -34.4 -23.7 -22.3 -43.7 -36.7 -40.9 -36.3 -38.9 -33.6 -31.0 -29.0
* * +t
0.3 .15 .1
* .o * .1 * .2 * .3
*
*
* +t
* * * * * *
.2 .4 $2 0.2 .2 .1 .2 .3 .2 .1 .05
tration range) in Fig. 1. Below 0.01 M the integral heats of dilution are proportional to m'/* within the limit of experimental error and can be extrapolated to infinite diluMolality. 0.01 0.04 0.09 0.16 tion with an uncertainty of not 3 -80 more than one calorie. In Fig. i 2 the results below 0.1 M have been combined with the data ,.$ -60 of Wiist and Lange which ex0 tend to saturation for both ."id salts. The error involved in 4 3 -40 coordinating the two sets of Quo measurements is not more than +.' -20 five calories and is probably less. In Table I1 are given the 1 integral heats of dilution for $ H 0 0 the two salts a t various con0.1 0.2 0.3 0.4 centrations from infinite dilu(Molality)'/'. tion up to saturation; these 0, NaBr; 0, KBr. values have been interpolated Fig. 1.-Integral heats of dilution a t 25". from Fins. 1 and 2. UD t o 0.01 M the integral heat of dilution (heat absorbed-when a solution^containing one mole of the salt is diluted with an infinite amount of water)
3 Y
' 1
3 Y
Aug., 1932
3123
THERMOCHEMISTRY OF SODIUM AND POTASSIUM BROMIDES
of sodium bromide is represented by A H i n t . = -359 ml/'; for potassium bromide m i n t . = -350 ml/'. The individual nature of these curves for salts of the same valence type has been discussed beforeO6 0.0625 0.25 0.5625 1.0
0
4.0
6.25
9.0
0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5 2.75 3.0 (Molality)'/'. 0,NaBr; 0, KBr. Curves to A, these measurements. Fig. 2.--Integral heats of dilution at 25'.
INTEGRAL Concentration moles/1000 g. HnO
0.0000 ,0001 .0004 .0016 .0025 .0064 .Ol .04 .09 .16 .25 .64
Molality. 2.25
TABLEI1 HEATSOF DILUTION AT 25'
&Hint.,
calories/mole salt NaBr KBr
0.0 3.5 7.0 -14.5 - 18 -29 -36 -60 -70.5 -72 -66 -19.6
-
-
0.0 3.5 - 7.0 -14.0 -17.6 -28 34 -52.8 -61.3 -61.5 52 23.5
-
-
-
Concentration, moles/1000 g. H20
1.00 1.44 2.25 3.24 4.00 4.84 5.68 (satd.) 5.76 6.25 7.29 7.84 8.41 9.16 (satd.)
AHint
calories/mole salt NaBr KBr
39 116 256 396 484 566
106 201 353 521 633 743 841
636 664 695 701 700 694
4 Lange, Z. Elektrochem., 36, 772 (1930); Lange and Robinson, Chem. Rev., 9 89 (1931).
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VOl. 54
H. HAMMERSCHMID AND A. L. ROBINSON
The integral heat of dilution7 is related to the relative partial molal heat contents of solute and solvent by - H i n t . = n&, where nl moles of water are associated with one mole of salt a t a given concentration. Values for and 1,are most readily obtained from heat of dilution data by the method of Rossini,' using the slopes of the curves of Fig. 2. Figure 3 shows a plot of for sodium bromide and potassium bromide and
zz +
0.09
Molality. 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29
9.0
1.5 1.8 2.1 2.4 2.7 3.0 Molality'/'. Fig. 3.-Relative partial molal heat contents a t 25'. = g1". ZZ= 2 2 - @z0. Curve 1,ZZNaBr; Curve 2,12, KBr; Curve 3, Lt KBr; Curve 4 , z 1NaBr. 0
0.3
0.6
0.9
1.2
& z1-
solutions so obtained and the values of Table I11 are interpolated from these curves. L, is the relative molal heat content of the solid salt (referred to the standard state of infinite dilution) and is calculated from the data of Wiist and Lange on integral heats of solution; L, for sodium bromide is for the anhydrous salt, although the saturated solution a t 25' is of course in equilibrium with NaBr.2H20. Rossinia has shown that a t 25' up t o concentrations of 2.5 M the partial molal specific heats of sodium bromide solutions are represented by Cpp = -24.3 20.4 ml/' for the sodium bromide and Cpl = -0.123 for the 16.2 ml/'and water and for potassium bromide solutions E,, = -29.5 cpl = -0.097 m8/'. These values can probably be used up to saturation 7 This is the negative of the function @h - 4 ; used by Rossini [Bur. Stand. J. Res.,
+
+
6, 791 (1931)]and called by him the relative apparent molal heat content of the solute.
Rossini, Bur. Stand.
J. Res., 7,
47 (1931).
Aug., 1932
THERMOCHEMISTRY OF SODIUM AND POTASSIUM BROMIDES
3125
TABLE I11 RELATIVE PARTIAL MOLALHEATCONTENTS OF AQUEOUSSODIUM BROMIDE AND POTASSIUM BROMIDESOLUTIONS AT 25"
La
z a
calories/mole Hz0 NaBr KBr
Concentration, molesjlOO0 g. H10
0.0 .OOl ,005 .Ol .05 .1 .2 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 5.68 (satd.) 6.0 6.5 7.0 7.5 8.0 8.5 9.16 a
0.0 .0004
0.0 .0005 - ,0016 ,0031 - ,0132 - ,0138 .05 .7 3.0 6.8 11 4 15.7 20.4 25.8 30.6 34.5 37.7 38.9
-
-
-
-
,001
.0019 .0104 ,0098
.08 1.0 3.6 8.2 13.6 19.8 26.5 33.3 40.3 46.4 52.0 56.6 58.9
calories/mole salt
NaBr
0.0 11 38 55 79 76 56 - 32 - 208 - 384 - 540 656 753 834 - 899 - 947 - 983 - 1003
-
-
37.2 30.0 20.3 10.0 0.8 - 5.7 -18.5
994 938 858 775 706 - 662 - 576 L, = 44
KBr
0.0 9 30 46 71 68 37 - 91 - 311 - 509 - 680 - 825 - 958 -1078 -1183 - 1271 - 1347 -1394 - 1414 L, = -4727
-
Negative values indicate heat evolved.
concentrationsg and are useful in conjunction with the values of the relative partial molal heat contents reported here. The experimental portion of this work was kindly supported by the Notgemeinschaft der Deutschen Wissenschaft, the Kaiser Wilhelm Institute for Physics and the Munich Univeritatsgesellschaft.
Summary The heats of dilution of aqueous sodium bromide and potassium bromide solutions have been measured a t 25' from 0.1 M to 0.0002 M and extrapolated to infinite dilution. These measurements have been combined with the data of Wiist and Lange, wmch extend to saturation concentrations, to obtain values for the integral heats of dilution and relative partial molal heat contents of solvent and solute for the entire concentration range. PITTSBURGH, PENNSYLVANIA
For example see Harned and Nims, THISJOURNAL, 54, 423 (1932).
