T H E VAPOR PRESSURES OF AQUEOUS SOLUTIONS OF SODIUM NITRATE AND POTASSIUM THIOCYANATE J. N. PEARCE
AND
H E R S C H E L HOPSON
Division of Physical Chemistry, The State University of Iowa, Iowa C i t y , Iowa Received November 13, 1956
This paper presents briefly the results obtained in a study of the vapor pressures of aqueous solutions of sodium nitrate and potassium thiocyanate a t 25°C. The apparatus and the technique are the same as that employed in our previous work (3, 2). Large samples of the “analyzed” salts were further purified by recrystallization, twice from distilled water and once from conductivity water. All solutions were made up on a weight molal basis. Solutions of sodium nitrate were made by direct weighing of the dry salt, previously heated to constant weight a t 140°C. The saturated solution was prepared by first filling the saturators with a solution of the salt saturated at a temperature a few degrees higher than the temperature of the bath. The saturators were then transferred to the constant-temperature thermostat and the electrolytic gas was allowed to pass for two days while the solution was coming to equilibrium with the solid crystals a t 2 5 T . d= 0.005’. Concentrated stock solutions of the thiocyanate were prepared and stored in glass-stoppered, mercury-sealed flasks in the dark. The thiocyanate content of each was determined gravimetrically as silver thiocyanate. The experimental solutions were made by diluting definite weights of these solutions to the desired molality. The densities, dit0, are the mean of at least three determinations and are accurate to 1 part in 300,000. The final experimental and calculated data are collected in tables 1 and 2. In these m is the molality of the salt solution, c is the molarity, and p1 is the vapor pressure of the solvent. Each value of p l is the mean of at least three values whose deviation from the mean does not, except in one case, exceed 0.007 mm. The activity of the solvent was obtained directly by the relation, al = p l / p ; . The change in free energy accompanying the transfer of one mole of water from pure solvent to a solution of concentration m was calculated by means of the relation, AFl = RT In al. The remaining symbols possess their usual significance and will be mentioned later. Perhaps no graphic method illustrates better the deviations of solutions 535
536
J. S . PEARCE AND HERSCHEL H O P S O S
TABLE 1 Experimental a n d calculated data Tor solutions o j sodium nitrate at 2 b ' O C . -AF,
m
calcd. mm.
0.0 0.1 0.2 0.4 0.6 0.8 1.o 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 10 8300'
0.997074 1,002711 1,008245 1.019128 1 ,029723 1,040108 1.050308, 1.074970' 1,098511 1.121130 1.142706 1.183332 1 ,220751 1.255220,
* Saturated. 'p
= 27.5078
0.0000 0,0994 0.1983 0.3942 0.5878 0.7791 0.9680 1.4301 1,8778 2.3116 2.7315 3.5323 4.2533 4.9875
23 752 23 674 23 596 23 446 23 299 23 152 23 006 22 650 22 332 21 998 21 691 21 092 20 534 19 999 19 484 18 987 18 448 17 957 17 554
'Pobsd
cc.
1 0000 0 9967 0 9934 0 9871 0 9809 0 9747 0 9686 0 9534 0 9402 0 9261 0 9132 0 8880 0 8645 0 5420 0 8203 0 7904 0 7767 0 7560 0 7391
cc.
27 571 1 93 28 393 28 362 3 91 25 749 28 689 7 69 29 151 29 153 11 42 29 552 29 506 15 17 29 857 29 803 18 92 30 100 30 062 28 17 30 626 30 608 36 54 31 076 31 060 45 54 31 430 31 450 53 81 31 783 31 795 70 41 32 369 32 390 86 30 32 880 32 892 101 9 33 314 33 326 117 4 33 716 33 709 132 7 34 048 3-1 050 34 3.52 34 357 149 8 165 8 34 637 34 636 34 851 34 847 179 2
CC.
27 28 29 29 30 30 31 32 32
33 33 34 35 35 36 36 36 37 37
571 757 249 911 467 905 287 081 728 279 758 562 217 761 236 632 981 312 513
+ 2.1968ct + 0.03597~.
TABLE 2 Experi?iiental a n d calculated data f o r solutions of potassium thiocyanate at 26°C. m
711ni
0 0000 0 1000 0 2000 0 4000 0 6000 0 8000 1 0000 1 5000 2 0000 3 0000 4 0000 4 9865 5.9785 6 9786 7 9712 8 9693 10 0000 'p
a1
Pl
1 024202 1 032707 1 041001 1 060773 1 079491 1 113790 1 144565 1 171667 1 196605
0 0 0 1 1 2 3 3 4
5807 7666 9488 3888 8077 5872 2969 9357 5252
1 277894 6 4811
= 49.2123
.
23.752 23 672 23 597 23 439 23 283 23 131 22 969 22 598 22 246 21 533 20 807 20 143 19 438 18 737 18 120 17 486 , 16 827
+ 1.8382~1-I- 0.01018~.
___
--GI
calcd.
(cobsd
2 00 3 88 7 87 11 83 15 71 19 87 29 53 38 83 58 15 78 47 97 00 118 8 139 9 160 4 181 5 204 3
__
49 797 50 051 50 357 50 594 50 830 51 016 51 447 51 723 52 204 32 582 52 957 53 227 53 454 53 664 53 847 53 995
cc
CC
CC
1 0000 0 9966 0 9934 0 9868 0 9802 0 9738 0 9670 0 9514 0 9366 0 9066 0 8760 0 8480 0 8184 0 7897 0 7629 0 7362 0 7081
L'Z
'peq
__
49 49 50 50 50 50 51 51 61
52 52 52 53 53 53 53 54
212 793 033 369 624 836 021 405 718 218 613 931 210 1-19 659 841 016
49 50 50 50 51 51 51 52 52 53 54 54 54 53 j5 55 j!5
212 083 441 940 315 623 889 433 867 535 036 426 746 012 234 424 593
VAPOR PRESSURES OF SALT SOLUTIONS
537
of strong electrolytes from the laws of perfect solutions than does the plot of the fractional lowering of the vapor pressure against the molality. If we assume complete dissociation and that the ions behave as perfect solutes, the experimental fractional lowering curve for binary electrolytes should coincide exactly with the slope of the curve of the molality plotted against 2n2/(nl + 2 4 . Here nl is the number of moles of solvent and 2n2 is the number of moles of ions from n2 moles of salt. With all of the salts previously studied the experimental fractional lowering curve for a given salt of a given type lies below the theoretical curve up to a characteristic concentration. Above this concentration the experimental curve lies above the theoretical curve, and its deviation from the theoretical curve increases more or less rapidly with further increase in concentration. For similar salts with a common anion the concentration a t which the two curves intersect is lower the smaller the radius of the bare cation. Potassium thiocyanate behaves in a similar manner. The concentration a t which the two curves intersect is higher than for any binary salt studied thus far. ilt both high and low concentrations it deviates but little from the theoretical curve representing complete dissociation. Sodium nitrate, however, presents a striking relation in that the experimental curve lies below the theoretical curve a t all concentrations. The apparent molal volumes of the salts are very sensitive to errors in density measurements. To eliminate these errors in the calculation of the apparent molal volumes we first plotted the values of
F = [1000(di - d ) ] / c against the square root of the molar concentration, c1I2. Here d l and d are the densities of the pure solvent and solution, respectively. In no case did the experimental value of y & s d deviate from the smooth curve by more than 0.1 of an F-unit. Using the apparent molal volumes thus calculated from the densities, we derived by the method of least squares an equation for the dependence of the apparent molal volume upon the concentration. That is, peq.
= a
+ Pc”* + YC
The final equations for the two salts are inserted below their respective tables. The agreement between the values of Yobsd. and y e s is excellent throughout; in no case do they differ by more than 0.06 cc. The partial molal volumes of the salts for each concentration have been calculated by means of the relation derived by Gucker ( l ) ,namely,
The values of Bz thus calculated are incorporated in the accompanying tables.
538
J. N. PEARCE AND HERSCHEL HOPSON
It would be interesting to compare these volume relations with those calculated on the basis of the Debye-Huckel theory. From this theory Redlich and Rosenfeld (4) have deduced an equation which they claim satisfactorily reproduces partial molal volumes for dilute solutions. The lack of definite knowledge of the ionic radii, and of the dielectric constant and its dependence upon the pressure and the concentration, preclude for the present a t least the employment of Debye-Huckel equations for the calculation of partial molal volumes in the high concentrations which we have studied. SUMMARY
The vapor pressures of aqueous solutions of sodium nitrate and potassium thiocyanate have been determined a t 25°C. The apparent and partial molal volumes of the salts in these solutions have been calculated. REFERENCES
(1) (2) (3) (4)
GUCKER:J. Phys. Chem. 38, 307 (1934). PEARCE AND BLACKMAN: J. Am. Chem. SOC.67, 24 (1935). PEARCE AND NELSON: J. Am. Chem. SOC.64, 3544 (1932); 66, 3075 (1933). REDLICHAND ROSENFELD: 2. Elektrochem. 37, 705 (1931); 2. physik. Chem. 166A, 65 (1931).
