LIQUID AMMONIA AS A SOLVENT. IV OF AMMONIUM NITRATE, IODIDE,BROMIDE, AND CHLORIDE ACTIVITIES AT
25OC.
W. E. LARSEN' AND HERSCHEL HUNT Department of Chemistry, Purdue University, Lafayette, Indiana Received October 19, i934
The aLtivities of solid non-volatile solutes in liquid ammonia may be obtained by measuring the vapor pressures of their solutions at various concentrations. Vapor pressure data also furnish an excellent means of testing the theories of concentrated solutions, since the measurements can be made over a very wide range of concentration. The vapor pressure data used in this paper have been reported in a previous article (3). The values used in calculating the activities were taken from a smooth mole ratio versus vapor pressure curve. Ammonia gas deviates considerably from the behavior of an ideal gas; therefore the fugacity rather than the vapor pressure must be used in calculating the activities and showing deviations from Raoult's law. The fugacity was calculated from the vapor pressure using the equation ( 5 ) Inf = In P -
4' SdP
f is the fugacity, P is the vapor pressure, and
The last term in equation 1 was evaluated from the known data for ammonia gas at 25OC. (4), using the equation
PV = RT
f
aP
f
bP2
(3)
a and b are constants. This equation becomes
1
(1
-
g)
=
a -A - B P = RT
(4)
This paper is a part of a thesis submitted by W. E. Larsen to the Faculty of Pur& University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. a77
878
W. E. LARSEN AND HERSCHEL HUNT
or
f - A P + B2P
2.3026 log -
P-
(5)
A and B (Pin cm.) were found to be -1.356 X lo4 and -2.578 X respectively. The relationship a1 = f/fogives the activities of the solvent, f0 being the fugacity of liquid ammonia, andf the fugacity of the solution. Our value of the vapor pressure, although lower than that reported by Cragoe (l), was used in calculating the fugacity of liquid ammonia, because our manometer gives the same per cent lower value for the vapor pressures of the solutions. The activity of the solute was calculated from that of the solvent by equations resulting from the Gibbs-Duhem equation, namely, dlnaz =
- NNz -i ddnal
(6)
az is the activity of the solute, and N1 and N z the mole fraction of the solvent and solute, respectively. Upon integrating and changing to common logarithms
The value of the integral was obtained by a graphical method. Measurements could not be made for solutions dilute enough to allow extrapolation to i n h i t e dilution; consequently this method gave only relative activities. This necessitated giving a n arbitrary value to a [ at some concentration used as a reference point. A concentration of 1 molal was chosen as the reference point. This arbitrary assumption amounts to placing a = 1a t 1molal, and consequently log a: = 0; then by measuring the area between this point and any other point we have log Icaz =
- area
(8)
Using this equation a series of values was obtained proportional to the activity. Assuming that the ammonium salts dissociate into two ions, the relative mean ionic activity coefficient is given by
M is the molality. This series of k'y values is plotted against the molality in figure 1, which brings out the differences between the ammonium halides.
879
IV
LJQUID AMMONIA AS A SOLVENT.
TABLE 1 k'y for
ammonium nitrate
~
nr
P
f
a
85.3 101.8 135.9 182.6 228.2 281 .O 354.7 456.3 527.1 586.8 626.1 643.5 653.9 659.4 661.9 664.0 666.2 667.8 668.7 673.0
0.1270 0.1512 0,2019 0.2713 0.3391 0.4175 0.5270 0.6779 0.7831 0.8719 0.9303 0.9562 0.9715 0.9797 0.9835 0.9866 0.9899 0.9923 0.9936 1.0000
1.17 1.20 1.19 1.14 1.05 0.936 0.779 0.601 0.510 0.452 0.483 0.550 0.677 0.825 0.930 1.05 1.25 1.49 1.69
f
a
k'r
73.1 96.7 156.5 190.5 253.6 342.3 444.8 549.5 584.0 609.3 630,6 647.0 658.3 661.5 663.7 666.0 667.4 668.7 669.6
0.1086 0.1437 0.2325 0.2830 0.3767 0.5086 0.6609 0.8165 0.8678 0.9054 0.9369 0,9613 0.9782 0.9828 0.9861 0.9895 0.9917 0.9936 0.9950
11.5 9.14 5.66 4.45 2.96 1.81 1.13 0.743 0.676 0.645 0.644 0.706 0.869 0.966 1.06 1.21 1.41 1.63 1.87
k'Y
cm. H g
48.9 42.8 34.5 27.2 22.8 18.9 15.2 11.2 8.63 6.38 4.19 2.94 1.97 1.40 1.14 0.917 0.683 0.508 0.411 Pure NHD
86.3 103.2 138.5 187.4 235.8 292.7 373.8 489.1 572 .O 643.8 692.0 713.6 726.5 733.4 736.6 739.2 742.0 744.0 745.1 750.6
k'y
M
P
TABLE 2 for ammonium iodide
cm. H g
25.4 22.6 18.0 16.4 14.3 12.0 9.32 6.45 5.21 4.19 3.19 2.20 1.33 1.07 0.883 0.675 0.521 0.399 0.309
73.8 98.0 160.0 195.7 263 .O 360 .O 475.8 598.8 640.4 671.3 697.5 717.9 732.1 736.0 738.8 741.7 743.5 745.1 746.3
880
W. E. LARSEN AND HERSCHEL HUNT
TABLE 3 )r ammonium bromide M
P
f
I
a
cm. Hg
24 8 21.3 17.3 13.5 10.5 7.70 5.23 3.40 2.39 1.78 1.2p 0 979 0.766 0.587 0.455 0 369 0.280
162.0 221.3 319.7 446.1 550.4 634.2 688.2 714.8 725.4 731.6 736.9 740.0 742.1 743,8 745.1 745.9 747.3
158.4 214.6 306.7 418.8 508,s 578.9 623.1 644.5 653 .O 658.0 662.2 664.6 666,3 667.7 668,7 F69.3 670.4
0 ,2354 0.3189 0.4543 0.6223 0.7560 0.8602 0.9258 0.9576 0 ,9702 0.9776 0.9839 0.9875 0.9900 0.9920 0.9936 0.9945 0.9961
.*
1.26 0.993 0.714 0.500 0.401 0.360 0.380 0.464 0.577 0.696 0.857 1.01 1.19 1.42 1.68 1.93 2.19
TABLE 4 k'r for ammonium chloride 'U
I
P
a
h'y
cm. H g
24.4 21.8 18.9 16.3 13.7 10.7 8.76 7.40 5.49 4.00 2.61 1.96 1.47 1.06 0.850 0.667 0.506 0.390
314,O 379 .O 453 .o 535,O 591.8 653.4 684.3 700 0 717 3 727,l 733.9 737.2 739.7 742.2 743.4 744.6 745.9 747.7
300.5 359.4 424.9 487.2 543.7 594.7 619.9 632. S 646.5 654.4 659.8 662.4 664.4 666.4 667.4 668.3 669.3 670.8
0.4465 0.5339 0.6313 0.7239 0 ,8079 0.8836 0.9211 0.9399 0.9606 0.0723 0.9803 0.9842 0.9872 0,9901 0.9916 0.9930 0.9945 0 9966
0.239 0.213 0.192 0.177 0,171 0.176 0,190 0.209 0.256 0.324 0.462 0.585 0.740 0 958 1.14 1.38 1.68 1.89
LIQUIU AMMONIA AS A SOLVENT.
88 1
IV
The method of Randall and White, if it could be used, would give absolute activities. Although their method has been used successfully for aqueous solutions by Pearce and Nelson (6),the extrapolation involved in the case of liquid ammonia is much more difficult, Their method was used to give an approximate value of the activity coefficient. Using these activity coefficients the value of k' for each concentration of the more exact series was obtained. These values of k' vary within the maximum limits of 0.65 per cent, showing that the two methods run parallel to a reasonable extent. The fact that k' is constant does not mean that the extrapolation is necessarily correct, but only that the two methods run parallel. The average value of k' for ammonium nitrate is 37.7, am-
._.
FIG. 1
FIG.2
FIG.1. VALUES OF k'Y FIG.2. DEVIATIONS FROM RAOULT'S LAW
monium iodide 31.8, ammonium bromide 50.6, and ammonium chloride 83.5. These values show that the activities of these salts are low in liquid ammonia. DEVIATIONS FROM RAOULT'S LAW
If the vapor is not ideal and the solute is a non-electrolyte, the fugacity depends on the concentration in the following manner;
f = foNi or fo-f-
fo
M
N2= 58.71 + M
(11)
882
W. E. LARSEN AND HERSCHEL HUNT
The left side of equation 11 is really the fractional lowering of the fugacity. If we consider that binary salts, such as the ammonium salts, are 100 per cent ionized, and that the ions resulting still behave as ideal solutes, then a relation similar to equation 11 is
fo -f 2M fo 58.71 + 2M The deviations from the ideal are shown in figure 2, where two of the curves were made by plotting the right-hand side of equations 11 and 12 against the molality, and the others were made by plotting the fractional lowering of the fugacity against the molality. These solutions do not behave as ideal solutions either in the dilute or concentrated region. Such deviations in the concentrated region are not unexpected, but the trends of these curves in the dilute solutions are more unusual, since all but ammonium iodide show a smaller lowering of the fugacity than is predicted for a non-electrolyte. This effect is most marked for ammonium chloride, which does not cross the non-electrolyte curve until above 12 molal. The interpretation of these resultsmay be made from several viewpoints, as Hepburn (2) has shown. A possible explanation is that some form of association takes place, thus lowering the mole fraction of the solute. The relative positions of the curves for the different halides are what would be expected from this explanation. The results in the concentrated region indicate that some of the solvent molecules have lost their fugacity, which may mean that they are attached to some of the solute ions. Although the solvation per ion is greater in the dilute solution, in the concentrated solution the number of solvent molecules that are bound up comprises a significant part of the total present, and the mole fraction of the solute increases faster than it otherwise would. The extent of solvation indicated makes it appear probable that both anion and cation are highly solvated. SUMMARY
1. From the vapor pressures of solutions of ammonium nitrate, iodide, bromide, and chloride a quantity k’r has been calculated using the GibbsDuhem equation, and a plausible value of k’ determined using the method of Randall and White. 2. The deviations from Raoult’s law are shown, and it is suggested that these deviations can be explained if the solutes are partially associated, and there is considerable solvation between the ions resulting and the molecules of the solvent.
LIQUID AMMONIA AS A SOLVENT.
IV
883
REFERENCES CRAQOE, MEYERS, AND TAYLOR: J. Am. Chem. SOC.42,206 (1920). HEPBURN:J. Chem. SOC.1932, 566. HUNTAND LARSEN:J. Phys. Chem. 38,801 (1934). International Critical Tables: Vol. 111, p. 11. McGraw-Hill Book Co., New York (1928). (5) LEWISAND RANDALL: Thermodynamics, p. 195. McGraw-Hill Book Co., New York (1923). AND NELSON: J. Am. Chem. SOC.34,3544 (1932). (6) PEARCE (7) RANDALL AND WHITE:J. Am. Chem. SOC. 48,2514 (1926).
(1) (2) (3) (4)
