HEAT CAPACITY AND DENSITY O F SOLUTIONS
959
However, the actual depression obtained so far depends entirely on the extent to which the lyophilic anion compensates for this tendency. The results reported offer further proof for the importance of the lyotropic series of anions in colloidal systems. Further work on the aging of surfaces of the solutions discussed in this paper until equilibrium is established and an extension of this work to include soaps with varying anions will be reported on an early occasion. REFERENCES (1) .ISDRE~S, J. M.,HAESER,E. .i., . ~ N DTUCKER, 11- B: J . Phys. Chem. 42, 100119 (1938). (2) BORS, M.: Ber. deut. physik. Ges. 21, 679 (1919). (3) HARTLEY,G. S.,COLLIE,B., . ~ N DSAMIS,C. S.:Trans. Faraday Soc. 32, 975 et seq. (1936). (4) KXIGHT,G. 9., AND SHAW,B. D.: J. Chem. Soc. 1938, 682-3. ( 5 ) MACOVSKI, E.: Bull. soc. chim. MBm. 151 3, 495-500 (1936). (6) O,gai$ic Syntheses, Volume XV, pp. 29-30. John Wiley and Sons, Inc., S e v York (1935).
HEAT CAPACITY AXD D E S S I T Y O F AQVEOUS SOLUTIOKS OF POTASSIUM IODATE, POTASSIUhl ACID SULFATE, IODIC ACID, AND SULFURIC ACID AT 25°C.' MERLE RAKDALL A K D U 4 R I O K D. TAYLOR* Department of Chemistry, 1-nzverstty of Calzfornza, Berkeley, Calzfornza
Received March 16, 1041
The heat capacity of a n ideal solution is, by definition, the sum of the heat capacities of the various constituents in their pure states a t the same temperature and pressure. In any actual solution, this ideal heat capacity will be modified by the intermolecular and electrostatic effects which each constituent exerts upon the heat capacities of the other constituents. If a reaction,-for example, the dissociation of bisulfate ion into hydrogen and sulfate ions,-is more complete a t a higher temperature than a t a lower, then the heat corresponding to the additional fraction of bisulfate ion dissociated at the higher temperature >$ill be measured as though it were a part of the heat capacity of the solution 1 Clerical assistance of the Work Projects Administintlon 1s gratefully acknowledged, Official Project KO.165-1-05-73 (Unit C-2). * Present address. Shell Development Company. Emeryville Californid
960
MERLE RANDALL AND MARION D. TAYLOR APPARATIJS, MATERIALS, AND CONSTANTS
Calorimeter The calorimeter was essentially the one used by Randall and Rossini (3). A few minor changes were made to eliminate contact of metal with the solution and to prevent evaporation along the shaft of the stirrer. A thin metal sleeve was mounted, with de Khotinsky cement, on the glass shaft above the liquid level. The lower end of the sleeve was machined to fit a metal socket which was soldered to the main frame B (see figure 1). This
FIG.1. One unit of the calorimeter joint was lubricated with stiff vaseline and was practically air-tight under small pressure heads a t the used speed of 135 R.P.M. The heating element was constructed in the following manner3: A piece of lead-glass tubing (external diameter 6 mm., internal diameter 4 mm.) 16 cm. long was heated in the center until quite soft, and drawn to form a capillary tube 31 cm. long and 1 mm. in diameter, with walls about 0.3 mm. thick. Inasmuch as very little glass was used in the construction of this capillary, the 6-mm. tubing left a t each end was approximately 8 cm. long. A piece of bare, No. 32 manganin wire (diameter 0.02 cm.,) 31.5 cm. long was thrust through the capillary until the ends, which had been coated with solder, extended 0.25 cm. into the 6-mm. tubing. One end of Heaters of similar design have been used by Lange (1)
HEAT CAPACITY AND DENSITY O F SOLUTIONS
961
the tube was now connected to a vacuum pump and the other was closed with a cork; then, while the pressure within the tube was about 0.1 mm. of mercury, a small flame was run down the capillary until it collapsed and formed a solid rod, about 0.8 mni. in diameter, with the manganin wire sealed in the center. By careful heating and manipulating it was then bent in the forrn shown, I, and mounted on the German-silver tubes N , N’. The leads were KO.24 double-silk-covered copper wires (0.5 mm. diameter) soldered to bare No. 30 copper wires (0.25 mm. diameter). Connection to the manganin wire was made by fusing a drop of solder on the end of one of the copper lead wires, coating with rosin as a flux, thrusting it through the German-silver and 6-mm. glass tubes, and heating the tube a t the junction of the copper and manganin wires until the drop of solder melted. With a current of 0.5 ampere and a resistance of approximately 10 ohms, the heat lag of the heater was Less than 1 min. The calorimeter units were cooled when necessary by passing dry air, which had previously been cooled to approximately 9O0K., through a glass coil, H, immersed in the solution contained in the unit. When not in use, the German-silver tubes leading to this glass cooiing coil were closed to prevent convection. The lieat capacity of water a t 25°C. was taken as 0.9979 calorie per gram per degree, The weight of the water wa.s determined to 1 mg. and corrected to vacuum. Water redistilled from alkaline permanganate solution,-“conductivity” water,---was used. The same precautions were observed in the measurements as were discussed4 by Randall and Rossini (3).
Materials Sulfuric acid was prepared by boiling conlmercial C.P. acid for 3 hr. in a quartz vessel to expel sulfur dioxide, cooling in quartz, and storifig in a Jena-glass bottle. Samples were added to flask 2 (through the large entry tube, C, figure 1) from n weight buret, the tip of which almost touched the surface of the liquid already in the flask. (When not in use this entry tube was plugged with a neatly fitting cylinder of balsa wood which had been coated with Duco varnish.) Potassium acid sulfa,te was commercial C.P. quality which was fused to expel excess sulfuric acid, ground, and dried. Iodic acid was recrystallized from commercial C.P. quality iodine pentoxide. Considerable difficulty was experienced in this recrystallization, owing to a tendency for the solutions to supersaturate. By placing saturated solutions in a desiccator over solid potassium hydroxide for several Additional detailed description and data are t o be found in t h e thesis of Marion D. Taylor, University of California, Berkeley, California, 1931.
962
MERLE RANDALL AND MARION D . TAYLOR
weeks, beautiful plates were obtained, which, when washed and dried, analyzed better than 99.99 per cent iodic acid. Potassium iodate was recrystallized from commercial C.P. quality salt, ground, and dried. TABLE 1 Densities of some aqueous salt solutions at 25'C.
I
m
I/
di?
II
HI08 '
0.1888 0.9760 2.2540 3.6132 10.051
I
m
KIOa 0.06279 0.1985 0.2387 0.2846 0.3989 0.40645
1.0256 1.1349 1.2984 1.4547 2.0209
~
d25° 4"
1.0082 1.0320 1.0387 1.0468 1.0669 1,0680
KHSOi
1
2.4310
1.1922
TABLE 2 Heat capacities of some aqueous salt solutions at 25°C. KIOa
HIOa m
CP
m
KHSO, CP
H~SOI
m
CP
0,0498 0.1017 0.2483 0.5547 1.0151 2.2442
0.99720 0.99725 0.99919 1.00595 1.01884 1.06272
m
CP
0.0444 0.0704 0.0713 0.1748 0.3722 0.5515 0,8054 0.9941 1.2423 1 ,4580 1.4580 1.8771 2.2300
0.99821 0.99857 0.99854 0.99921 1,00249 1,00483 1.00921 1.01334 1.01808 1.02310 1 ,02374 1.03374 1,04252
d
0.0658 0,1888 0.2313 0.3774 0.5296 0.6583 0.6795 0.9760 1.0311 1.4501 1.9580 2.2572 2.3287 3.6020
0.99646 0.99648 0.99646 0.99739 1.00022 1,00344 1 ,00258 1.01162 1.01291 1,02547 1.04345 1.05744 1.05928 1.11368
0.0434 0.0521 0.0628 0.0973 0.1089 0.1840 0.2814 0.2845 0.3774
0.9968 0.9967 0.9966 0.9962 0.9963 0.9962 0.9970 0.9973 0.9985
The molalities of the solutions were computed from the weights of solute and water added. These were checked a t several points by analysis of samples taken from the calorimeter. The sulfuric acid and potassium acid sulfate solutions were analyzed with standardized sodium hydroxide; the iodic acid both with sodium hydroxide and iodimetrically with stand-
TABLE 3 Apparent and partial molal heat capacities of the constituents of some aqueolls salt solutions at 25T.
-
-
CPZ
CPl
m
%
ACP
0.00 0.05 0.10 0.15 0.20 0.30 0.40 0.50 0.75 1.00 1.25 1.50 2.00 2.50 3.00 3.50
0.99780 0.99677 0.99629 0,99617 0.99629 0.99689 0.99785 0.99952 1.00538 1.01231 1.01961 1,02798 1.04663 1 ,06731 1,08812 1.10928
0.0 -0.0010 -0.0015 -0.0016 -0.0015 -0.0009 0.0001 0.0017 0.0075 0.0145 0.0218 0.0302 0.0488 0.0695 0.0903 0.1115
-36.95 -20.56 -15.06 -10.83 -7.53 -3.04 0.12 3.44 10.35 14.51 17.46 20.11 24.41 27.81 30.11 31.85
-36.95 -13.73 -6.10 -0.55 3.85 9.54 13.61 17.89 25.13 29.10 32.02 34.91 39,29 41.61 42.54 42.59
17.976 17.970 17.960 17.949 17.935 17,908 17,878 17.846 17.773 17.714 17.648 17.576 17.680 17.355 17.304 17.299
KIOa
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.3774
0.99780 0.99677 0.99629 0.99613 0.99625 0.99660 0.99725 0.99804 0,99852
0.0 -0.0010 -0,0015 -0.0016 -0.0015 -0.001 1 -0.0005 0.0003 0.0007
-33.24 -20.56 -15.06 -11.17 -7.77 -4.78 -1.86 0.69 1.91
-33.24 -13.96 -6.19 -0.22 5.55 9.42 13.73 17.55 19.39
17.976 17.971 17.960 17.946 17.930 17.912 17.892 17.870 17.857
H&OI
0.00 0.05 0.10 0.15 0.20 0.25 0.50 0.75 1 .oo 1.50 2.00 2.25 2.40
0.99780 0.99821 0.99868 0.99921 0.99978 1 ,00041 1 ,00385 1 ,00820 1.01303 1 ,02434 1,03685 1 ,04304 1 ,04682
0.0 0.0004 0.0009 0.0014 0.0020 0.0026 0.0060 0.0104 0.0152 0.0265 0.0390 0.0452 0.0490
-67.43 8.13 8.85 9.40 9.92 10.43 12.10 13.87 15.23 17.69 19.51 20.11 20.42
-67.43 9.06 10.14 11.07 11.86 12.58 15.47 18.41 20.66 24.70 25.66 25.27 24,63
17.976 17,975 17.974 17.972 17.969 17.967 17.946 17.915 17.878 17.787 17.756 17.766 17,795
KHSO,
0.00 0.05 0.10 0.15 0.20 0.25 0.50 0.75 1.00
0.99780 0.997W 0.99725 0.99770 0.99837 0.99923 1 ,00454 1.01105 1.01848 1,03553 1.05373 1,06286
0.0 -0.0005 -0.0005 -0.0001 0.0005 0.0014 0.0067 0.0132 0.0207 0.0377 0.0559 0.0651
-63.96 -11.96 -5.50 -0.65 2.87 5.74 13.49 17.67 20.68 25.16 27.95 28.91
-63.96 -1.27 6.17 10.93 14-25 16.81 24.13 28.26 31.09 35.56 37.76 38.79
17.976 17.967 17.955 17,945 17.935 17.927 17O S!. 17.833 17.789 17.695 17.823 17.577
HIOa
1.50 2.00 2.25
963
4
964
MERLE RANDALL AND MARION D. TAYLOR
ardized sodium thiosulfate; and the potassium iodate iodimetrically with standardized sodium thiosulfate. The heat capacity of flask 2 was found to be 51.44 calories per degree. The heat capacity of the unit was increased 0.038 st 0.001 calorie per degree when the amount of liquid was increased by 1 ml. with 1160 to 1120 ml. in the flask. DENSITIES OF THE SOLUTIONS
The change in volume of solution within the calorimeter when solute was added was determined from a weight balance of the material in the calorimeter, together with the density of the initial and final solutions. The densities were obtained so far as possible from the International Critical Tables. In order to extend the range of densities, the densities given in table 1 were measured, using a 25-ml. pyknometer. HEAT CAPACITIES
The values of c, (in calories per gram per degree) a t the various molalities are given in table 2. When plotted against the square root of the molality, these values of c, define smooth curves with sufficient accuracy. Making this plot on a large scale and reading values of c, a t even molalities from the curve, the round values are given in the third column of table 3. The fourth column gives the values of the apparent molal heat capacities, the fifth the value of e,, (in calories per mol per degree), calculated by the equation of Randall and Rossini (3): The slopes were read from large-scale plots of the apparent molal heat capacity against the square root of the molality. The last column gives the partial mol heat capacity of the water calculated from the expression
@,,,= C,,O - m(Cp, - 4)/55.508
(2)
DISCUSSION
When the values of C,, for potassium iodatr, given in table 3, were plotted against the square root of the molality, and the curve obtained was extrapolated to infinite dilution, the value of C,e0(K103) found was -33.24 calories per degree per mol. Values taken from a survey by Rossini (4) are C,,,O(HCl) = -32.04 and C,,O(KCl) = -28.57 calories per degree per mol. By proper combination of these data, the value of C,,,O(H103) was found to be -36.71 calories per degree per mol. Using the data of the above survey (4)for ~p,o(K~SO~),-namely, -60.50 calories per degree per mol,--in conjunction with the above values for E,,’(HCl) and CpZo(KC1)the values of Cpzo(H2S04)and e,,o(KHSO,) have
965
H E A T CAPACITY AND D E N S I T Y O F SOLUTIONS
been calculated as -67.43 and -63.96 calories per degree per mol, respectively. Plots of E,, for iodic acid, pot,assium acid sulfate, and sulfuric acid against m1/2 are given in figure 2. The curves so obtained are extended to the calculated values of C,,’ given above. In all three cases these curves show a marked increase in slope as m’” approaches zero. This behavior can be explained by assuming that iodic acid and bisulfate ion are moderately weak acids. If n e denote the measured partial molal heat capacity of a strong acid, such as hydrochloric acid, by E,, (strong), and the partial molal heat capacities of the ions by c,,(H+) and CP2(Cl-),we may write:
e,.,
0
(strong) = c,,(H+)
0.5
1.0
+ CpX(Cl-)
15
(3)
2.0
m 12’ FIG. ‘2 Partial molal heat capacity of aqueous solutions of pohssium iodate, potassium arid sulfate, iodic acid, and sulfuric acid a t ‘25°C.
The increase of E,,, (strong) for hydrochloric acid against ml”is gradual, as may be seen from data recalculated by Rossini (4) from the measuremenk of Richards, c t . al., Randall and Ramage, and Marignac. This slow increase of C,, (strong) indicates that the heat capacities of
the ions are increasing in some regular fashion as the molality is increased, owing to the interionic effects considered by Debye and Huckel. If we denote the measured value of the partial molal heat capacity of a moderately weak, monobasic acid, such as iodic acid, by e,,, (weak), the degree of dissociation of the acid by a, and the heat absorbed due to the ionization which takes place as the solution is heated one degree by H,, we may write, E,, (weak) = aC,,(H+)
+ aC,,(IO,-) + (1 - a)C,,(HI03) + H i
(4)
966
MERLE RANDALL AND MSRION D. TAYLOR
To account for the rapid change of E,, (weak) with molality (shown in figure 2) in the dilute region, we must assume a value for the dissociation constant, K, such that the variation of a and of Hi in this region is rapid, since, as shown above, no rapid change in the heat capacities of the solute particles is to be rxpectcd. The curves given in figure 2 diow that the rate of the variation of a with molality is most rapid in the dilute range, especially when the value assumed for K is small. The curves for H, are obtained from calculations made on the assumption that 4H for the ionization reaction is about 500 calories per mol, and the equation" d(R In K)/d(l/Y) = AH (5) The rapid change of the measured value of the partial molal heat capacity of a moderately weak acid with the molality, in the dilute region, is therefore due to two effects: (a) the nature of the solute particles is dependent upon the concentration, and ( b ) the heat absorbed by the increase in ionization as the temperature is raised is a maximum and varies rapidly in this region. As may be noted in figure 2, the rapid increase in the slope of the curve for iodic acid begins when the molality is larger than the molality a t which the curve for potassium acid sulfate starts to increase rapidly. This can be explained by assuming that the dissociation constant for bisulfate ion is smaller than the dissociation constant for iodic acid. (Such an assumption is in accord with the values ordinarily given for these constants.) I t may be noted, from figure 2, that the value of c,,'(KHSO,) is much lower than the value of E,,'(HIO3), although the values of the partial molal heat capacities of the two substances are nearly equal in the more concentrated solutions. This means that the value of AEP2for the ionization of bisulfate ion, i.c.,
+
[E,, (H+) e,, (SO4--) - E,, (HS04-!I is larger, in ail absolutc sense, than the value of A E , , for iodic acid. The curve obtained \vhen the measured partial molal heat capacity of sulfuric acid is plott,ed against, m1'2(see figure 2) shows no rapid increase in slope until thc molality is less than 0.05. This is to be expected, as thc dissociation of bisulfate ion is repressed by the presence of thp hydrogen ion formed from the dissociation of sulfuric. arid. In concentrated solutions the partial molal heat capacity of sulfuric acid is extremely abnormaL6 This peculiar behavior is probably dnc. to the formation of hydrates. R is taken as 8.316 joules per degree. 5 Lewis and Randall (refcrence 2, page 298). The equation is integrated. assuming I H coilstant, between T o = 297.6%. and 298.6%. G The plot of t,he data obtained by Biron, given 011 page 87 of reference 2, exhibits three maxima and two minima.
HEAT CAPACITY AND DENSITY OF SOLUTIONS
967
The explanation given above for the type of curve obtained in the dilute region when E,, is plotted against m”*,-namely, a rapid increase in slope as m is decreased,-can be applied to the data for acetic and citric acids obtained by T. tl-. Richards and his collaborators and recalculated by Rossini (4). In all four cases (Le., acetic acid and the three citric acids) the curves are straight lines down to the lowest molality measured, but they must necessarily drop down rapidly in very dilute solution in order to reach the calculated values of Cpzo. The dissociation constants of these acids are so small that the break must come in extremely dilute solution, and the slope must increase very rapidly. In his plots of these data Rossini (4) indicates an increase of slope by means of a dotted line, but the true curve must lie closer to the 1-ertical axis than is indicated by his curve. SUMMARY
1. The heat capacity has been measured for solutions of iodic acid between 0.05 and 3.5 molal, potassium iodate between 0.05 and 0.3774 molal, sulfuric acid between 0.05 and 2.4 molal, and potassium acid sulfate between 0.05 and 2.25 molal. 2. An explanation, based on the assumption that iodic acid and bisulfate ion are moderately weak acids, has been given for the type of curves obtained when the partial molal heat capacity of iodic acid, sulfuric acid, or potassium acid sulfate is plotted against the square root of the molality. The explanation seems applicable to the data for other partially JT-eak acids. 3. The value of E p z o for potassium iodate has been determined from an extrapolation of the data obtained in solutions of finite concentrations. This permits the calculation of the heat capacities of many other salts of iodic acid. 4. The densities, not given in the International Critical Tables, for solutions within the ranges specified in the first part of this summary, have been measured. REFERESCES (1) LANGE:Z. physik. Chem. 133, 129 (1928). (2) LEWISAND R-~KDALL: Thermodynamacs and the Free Energy of Chemical stances. -McGraw-Hill Book Company, Inc., New York (1923). (3) RANDALL AND ROSSINI:J. Am. Chem. SOC. 61, 323 (1929). (4) ROSSIXI:Bur Standards J . Research 4, 313 (1930).
Sub-
