152
W. .E. WALLACE
(6) HUSTRULID, A., I~USC P., HA,N D TATE,J. T.: “The ,Dissociation of HCN, CzHz,and CzH4 by Electron Impact,” Phys. Rev. 62, 843-54 (1937). (7) HUSTRULID, A., I~USCH, P., A N D TATE,J. T.: “The Dissociation of Benzene (CeH,), Pyridine (C&N), and Cyclohexane (CsHl2)by Electron Impact,” Phys. Rev. 64, 1037-44 (1938). (8) KOVARIIC, A. F., AND NICICEEHAN, L. W.: Radioactivity, p. 72. Bull. Natl. Research Council No. 61, Washington, D . C. (1929). (9) LIND,S. C . : The Chemical Effects of Alpha Particles and Electrons. Reinhold Publishing Corporation, New York (1928). (10) LIVINGSTON, M. S., AND BETHE,H. A , : ‘‘Nuclear Physics, c-Nuclear Dynamics, Experimental,” Rev. Modern Phys. 9, 246-390 (1937). (11) MOTT,N. F., AND MASSEY, H. S. W.: The Theory.of Atomic Collisions. Oxford University Press, New York (1933). (12) RICE,F. O., AND RICE,K. K. : The Aliphatic Free Radicals. The Johns Hopkins Press, Baltimore, Maryland (1935). (13) ROLLEFSON, G. IC., AND BURTON, M.: Photochemistry and the Mechanism of Chemical Reactions. Prentice-Hall, Inc., New York (1939). (14) RUTHERFORD, E., CHADWICK, J., AND ELLIS,C. D . : Radiations from Radioactive Substances. The Macmillan Company, New York (1930). (15) SMITH,L. G. : “Ionization and Dissociation of Polyatoniic Molecules by Electron Impact. I. Methane,” Phys. Rev. 61, 263-75 (1937). ( l G ) SMYTH, H. D. :“Products and Processes of Ionization by Low Speed Electrons,” Rev. Modern Phys. 3, 347-91 (1931). (17) WILLIAMS,E. J . : “Concerning the Scattering of Fast Electrons and of Cosmic Ray Particles,” Proc. Roy. SOC.(London) 169, 531-72 (1939).
HEATS OF SOLUTION AND DILUTION OF CALCIUM SULFATE DIHYDRATE IN AQUEOUS SODIUM CHLORIDE SOLUTIONS1.2 *a W. E. WALLACE
Deparbment of Chemistru, University of Pittsburgh, Pittsburgh, Pennsylvania Received October 22, 194.5
The heat of dilution of electrolytes has been the subject of many investigations in recent years (12). I n practically all cases, however, the data were obtained for simple binary systems consisting of a single electrolyte in pure water. The extension of such studies to systems with several solutes seems both logical and desirable. Analytical examination of the dissolved material in sea water has shown ( 5 ) that, sodium and chloride ions being excluded from consideration, calcium and Contribution No. 451 from the Department of Chemistry, University of Pittsburgh. This research was supported by grants from the Carnegie Institute of Washington and the Buhl Foundation, Pittsburgh, Pennsylvania. The material in this paper was presented before the Division of Physical and Inorganic Chemistry a t the 103rd Meeting of the American Chemical Society, Memphis, Tennessee, April, 1942. 1
2
HEATS OF SOLUTION AND DILUTION
153
sulfate ions are two of the more abundant constituents. By choosing as the solutes to be studied calcium sulfate and sodium chloride, this investigation permits the evaluation of some of the thermodynamic quantities of interest in the study of the physical chemistry of ocean water. I. EXPERIMENTAL
Measurement of the heats of dilution and solution was accomplished by use of a Lange-type adiabatic differential calorimeter, the characteristics and details of operation of which have been described (6, 8, 18). The ready adaptability of such a calorimeter to the study of heats of solution has been demonstrated by the earlier work of Lange and Monheim on calcium sulfate (11). The only change necessary is the replacement of the pipets used for dilution by a device for introducing the sample to be dissolved. It was essential that this device should have the following characteristics: (1) rapid and complete discharge of the solid sample into the solvent, ( 2 ) negligible (or reproducible) thermal effect on opening, and (3) easy withdrawal from the calorimeter at the conclusion of an experiment. The second characteristic was particularly important in this investigation, since the experimental heat effect was often less than 0.1 calorie. The design adopted is shown in figure 1 and consists essentially of four parts: A, a short piece of 7-mm. glass tubing which contained the sample; B, a hard rubber support for A; C, a plunger of hard rubber; and D, a basket of 40-mesh gold-plated copper gauze. E is a glass tube which projects through the top of the calorimeter. By means of it the entire device can be lifted from the calorimeter and prepared for the next experiment. The operation of the device proceeded as follows: The glass tube, A, was closed with a snugly fitting plug of paraffin approximately 1 mm. thick a t 2 (see figure 1) and a definite amount of calcium sulfate dihydrate plus water (vide infra) was introduced. A second plug of paraffin was inserted at 1 and sealed to the glass’by touching with a warm glass rod. The plug a t 2 was not sealed by heat for fear that an appreciable thermal effect might result in the process of discharging the sample. Instead, it was sealed by a thin layer of an electrolyte-free vaseline spread at the paraffin-glass j ~ n c t i o n . ~ After the sample had been enclosed in A, the tube was inserted in the holder B. The entire assembly was then placed in the calorimeter and allowed to stand approximately 30 min. for the system to reach temperature equilibrium. At the end of that time, the plunger C was lowered, forcing plug No. 1 ahead of it and discharging the sample from A. The first experiments were performed without the use of basket D, under which circumstance there mas a tendency for the sample to emerge as a compact cylinder which often fell to the bottom of the calorimeter and there dissolved very slowly. The basket obviated this difficulty, To insure against the possibility of a “heat of discharge” of the sample, an Under these conditions plug No. 2 began to emerge from A almost simultaneously with the downward movement of plug No. 1. When a heat seal was used a t 2, a n undesirably large compression was necessary for its expulsion.
154
W. E. WALLACE
apparatus, similar in every detail to the one just described except that it contained no sample, was opened in the side opposite that in which the experiment occurred so as t o balance out the thermal effect of discharging the sample. Blank experiments performed with neither side discharging a sample confirmed the efficacy of this method for eliminating such effects. Mention has been made above of addition of water t o the sample t o be dissolved. Lange and Durr (10) first indicated the desirability of such a procedure.
FIG.1. Device for introducing sample of calcium sulfate
The presence of excess water (or solvent) has the threefold advantage of (1) guaranteeing the degree of hydration t o be maximal, (2) relegating the contribution of soluble impurities to a heat of dilution rather than a heat of solution, and ( 3 ) increasing the rate of solution of the sample. I n this research the weights of water and sample were roughly equal. The heat effect accompanying the dilution of the resultant saturated solution was always practically negligible and in many cases absolutely so. However, correction was made in all cases for which the dilution was appreciable. ,
I
HEATS OF SOLUTION AND DILUTION
155
The sodium chloride used was a Merck C.P. reagent, used without further purification. The water was doubly distilled and had a specific conductance of 3 x 10-6 mhos or less. The calcium sulfate was a Mallinckrodt analytical-grade reagent. For some of the measurements a sample of gypsum was used which had been prepared by allowing the Mallinckrodt reagent to stand overnight in contact with conductivity water. The sample so prepared when properly dried gave results which agreed with data obtained using the calcium sulfate directly from the bottle. Spectroscopic examinations of the purified material showed that it contained no metallic impurities in amounts greater than about 0.01 per cent. To confirm the degree of hydration of the calcium sulfate, several dehydration experiments were performed. The water content found TV&S 20.92 f: 0.03 per cent, a value which compares favorably with the theoretical value of 20.93. 11. RESULTS O F MEASUREMENTS
I n table 1 are given results of the measurements of the heats of solution of calcium sulfate dihydrate in water and in aqueous solutions of sodium chloride, first without and then with calcium sulfate already in solution. Column 2 in table 1 gives the amount of sample dissolved during an experiment. Columns 3 and 4 show the calcium sulfate concentration in moles of CaS04 per kilogram of solvent before and after the solution, respectively. In column 5 is the observed heat of solution (in calories) of the amount of solute listed in column 2; in the last column the integral heat of solutione in calories per mole of solute. The negative sign denotes an evolution of heat. Results of the heat of dilution experiments in pure water and the various sodium chloride solvents are exhibited in table 2. Columns 1 and 2 give the initial and final concentrations, respectively. The remainder of the table indicates the number of experiments, the experimental heat effect, and the heat of dilution in calories per mole. The quantities in parentheses in column 6 are taken from the results of Lange and Streeck (13). Agreement between the two sets of determinations is about what should be expected. 5 Thanks are due t o D r . Mary E. Warga and Mi-. Harvey Worthington of the Physics Department, University of Pittsburgh, for making this investigation. 8 The intpgral heats of solution, AHm,, listed correspond t o the reaction:
CaSOI.2H20
+ solvent
-+
solution (solvent containing 1 mole CaSOl at the final concentration, m,)
AHm, is related t o the observed heat of solution, q , by the following expression: AHmf =
q
+ nl AHmi nI + n2
Where n1= moles of calcium sulfate initially present, n2 = moles of calcium sulfate being dissolved, aud AHmi = integral heat of solution per mole when the concentration changes from zero t o the initial concentration, mi.
TABLE 1 Heats of solution of calcium sulfate dihydrate CONCENTRATION
CaS04.2HzO
SOLVENT
USED
Initial
1
HEAT OF SOLUTION
Final
moles per Rg. wafer
grams
0.000701 0.000740 0.001180 0.001259 0.001384 0.001405 0.002280 0.002346 0.002373 0.002403 0.004477 0.004587 O.OO7106 0.007115
+O. 0682 0.0893 0.1273 0.1371 0.0973 0.1142 0.1963 0.2104 0.347 0.413 0.525 0.523 0.862 0.830
+98 121 108 109 135 130 143 148 147 173 200 190 254 239
0.000000 0.000000 0.000583 0.000000 0.000000 0.001103 0.001156 0.000000 0.000000 0.002350 0.002348 0.004569 0.004541
0.000583 0.000612 0.001050 0.001103 0.001156 0.002169 0.002207 0.002348 0.002350 0.004541 0.004569 0.006733 0.006843
0.1033 0.1033 0.1397 0.2120 0.2072 0.2312 0.2494 0.504 0.499 0.582 0.585 0.697 0.676
176 168 195 190 178 203 205 213 211 236 236 262 254
0.000000 0.000000 0.000000 O.OO0541 0.000539 0.000614 0.000000 0.000000 0.001768 0.001741 0.003671 0.003752
0.000539 0.000541 0.000614 0.001100 0.001120 0.001481 0.001741 0.001768 0.003671 0.003752 0.005798 0.005830
0.0576 0.0551 0.0608 0.0642 0.0726 0.1021 0.2167 0.2126 0.2390 0.2858 0.334 0.339
106 101 99 1os 116 109 124 120 123 133 135 142
0.000550 0.000564 0,001152 0.001192 0.001720 0.001734 0.001751 0.003355 0.003448
0.1205 0.1272 0.2029 0.2165 0.1108 0.1212 0.1893 0.1870 0.4082 0.4133 0.3568 0.3808 0.4521 0.4347
0.000000
0.000000 0.000000 0.000000 0.000701 0.000740 0.001180 0.001259 0.000000 0.000000 0.002403 0.002373 0.004477 0.004587
0.2 m sodium chloride..
0.1013 0.1062 0.0801 0.1915 0.2005 0.1849 0.1825 0.4076 0.4079 0.3801 0.3854 0.3756 0.3995
0.7 m sodium chloride.. . . . . .
0.0932 0.0935 0.1061 0.0964 0.1002 0.1499 0.3006 0.3053 0.3287 0.3473 0.3673 0.3589
0.05 m sodium chloride..
.
zloriespermole
- 182
0. ooooO0 0.000000 0.000564 0.000550 0.000000 0.000000 0.000000 0.001751 0.001734
HzO.. ..................
calories
-0.1002 -0.0914 +0.0184 $0.0086 -0.0699 -0.0497 -0.0674 0.2486 +0.2828
0.0948 0.0971 0.1011 0.1106 0.2860 0.2983 0.3014 0.2761 0.2951
156
+
- 162 -63 -77 -41 -29 -38 +54 +68
157.
HEATS O F SOLUTION AND DILUTION 111. TREATMENT O F RESULTS
A . Apparent relative molal heat contents of calcium sulfate In evaluating the apparent heat contents of calcium sulfate in aqueous sodium chloride solvents, it proved necessary to resort to both heat of solution and heat of dilution data. The heats of dilution were so small that solutions appreciably weaker than saturation could not be effectively studied. Therefore, between 0.015 and 0.0002 molal, wherein no dilution data could be obtained, use had to be made of the heat of solution results. It was not feasible to,attempt a coverage of the entire concentration range by heats of solution data alone, since above about 0.007 molal the heats of solution became too large t o be properly handled. TABLE 2 calcium sulfate Heats of dilution
SOLVENT
1 1 1 mi
Mf
moles ger kg. wader
mBEROF RUNS
9
AB
calories
calories ger mole
HzO, , . . . . . . . , . . . 0.01323 0.0000896 0.0001778 0.0000896
7) -0.0557 f 0.0008 -620 f 8 (-607 -0.0044 f 0.0001 -24 f 1 ( -29 f 7)
0.05 m sodium chloride.. . . . . . . . 0,01506 0.0001052 0.0002096 0.0001052
-0.0290 f 0.0007 -0.0006 =t 0.0006
-285 f 7 -3 f 3
0.2 m sodium chloride.. . . . . . . 0.01458 0.0000978 0.0001949 0.0000978
-0.0129 f 0.0005 -130 f 4 -5 f1 -0.0010 =t 0.0003
0.7 m sodium chloride.. . . . . . . . 0.01400 0.0000946 0.0001878 0.0000946
-0.0047 f 0.0004 -0.0007 f 0.0004
-48 f 4 -4 I 2
The apparent heat contents have in the past been determined from the measured heats of dilution by the method of Young (20, 21), the so-called chord-area method. Unfortunately, the necessity of using both solution and dilution data precludes the possibility of its application in this case. The heat of solution data contained in table 1 were assumed' to be expressible by an equation of the type AH = a b m ' f cm .. (1)
+
+.
7 In this case, since the ionic strength does not approach zero with decreasing calcium sulfate concentration, one can obtain little assistance from theoretical considerations. The function chosen has none other than empirical significance. The decision t o develop the equation in powers of rnt instead of m was based upon two factors: ( I ) better linearity i n the low concentration range and (2) better reproduction of the experimental data. The use of m* is undesirable in t h a t it may lead some, who are accustomed t o associate a square root of concentration with coulombic interaction and a n ion cloud, t o expect a justification in some molecular kinetic picture. The occurrence here of mi is perhaps not unlike t h a t i n the case of volumes (15) and heat capacities (16), where a n approximate linearity persists into a concentration region such t h a t the ion cloud is clearly not the dominant influence.
158
W. E. WALLACE
where AH is the integral heat of solution of calcium sulfate at a molality m of calcium sulfate. Using the method of least squares, the following equations were derived : Solvent: 0.05 m sodium chloride Solvent: 0.2 m sodium chloride Solvent: 0.7 m sodium chloride
+ 2509m' AH = 139 + 1443mf + 84m AH = 88 + 676m' AH = 30
(2) (3)
(4)
By use of equations 2 to 4 heats of dilution can readily be calculated in the concentration range covered by the original experimental data. If it is assumed that these equations are valid for extrapolation into concentration regions not included in the experimental study, heats of dilution can be calculated and compared8 with those recorded in table 2. I n table 3 is presented such a comparison. Deviations of the heats of solution from a smooth curve (see figure 2) are sufficiently large to suggest,that heats of dilution computed from equations TABLE 3 Comparison of measured and calculated heats of dilution
I
1
iLI (meas- A B (cal- ANmaaad.
SOLVENT
wed)
culated)
AfIcieaIod.
-
moles per kg. water
0.01506 0.0002096
0.0001052 0.0001052
-285 -3
-282 - 10
.
0.01458 0.0001949
0.0000978 0.0000978
-130 -5
- 161 -6
0.7 m sodium chloride., , . , , . . . , . . . ,
0.01400 0.0001878
0.0000946 0.0000946
-48 -4
- 83
0.05 m sodium chloride., , , , , . , . , , , . , 0.2 m sodium chloride.. , . . . . , . . ,
, , ,
-3
-3
7 31 1 35 -1
2, 3, and 4 are not reliable to better than 5 to 10 calories per mole. Accordingly, table 3 indicates that equation 2 is applicable for all concentrations up to about 0.015 molal. Equations 3 and 4 seem t o be satisfactory for extrapolation t o concentrations lower than those studied but unsatisfactory for extension t o higher concentrations. Hence, new equations must be developed for the 0.2 m and 0.7 m sodium chloride cases, equations which will be consistent with the heats of dilution a t the higher concentrations. As an illustration of the scheme used, consider the data obtained in 0.2 m sodium chloride. Equation 3 has been shown to be capable of a valid extrapolation t o concentrations below those actually studied, so that from it we calculate the heat of solution at a concentration of 0.0000978 m to be 153 calories 8 More precisely, the equations allow calculation of the heats of dilution of calcium sulfate dehydrate, whereas table 2 contains data for anhydrous calcium sulfate. However, the differences between these quantities are small, 3 calories per mole or less f o r the low concentrations studied, and are obscured by the experimental error of the measurements, amounting t o 5-10 calories per mole.
HEATS OF SOLUTION AND DILUTION
159
per mole. From the heat of dilution given in table 2 the heat of solution at 0.01458 m is found t o be 283 calories per mole. By including this one extra
FIG.2. Plot showing the variation of hea.t of solution of calcium sulfate dihydrate with calcium sulfate concentration in solvents of pure water (O), 0.05 niolal sodium chloride (e),0.2 mold sodium chloride ( A ) ,and 0.7 molal sodium chloride (X). The points indicated by 0 were obtained by combination of the heat of solution and heat of dilution data. The smooth curve for pure water was taken from the results of Lange and Streeck (13). The other smooth curves were calculated from equations 2, 5 , and 6.
point a t 0.01458 m with the data contained in table 1, a new equation was derived : Solvent: 0.2 m sodium chloride
AH = 124
+ 2092m’ - 6272m
(5)
160
W. E. W A L L A C E
A similar treatment for the data obtained in a solvent of 0.7 m sodium chloride yields : Solvent: 0.7 m sodium chloride
AH = 80
+ 1084m'
- 4776m
(6)
Graphical representation of equations 2, 5, and 6 together with the data from which they were obtained is given in figure 2. Equations 2, 5, and 6 lead *immediately to analytical expressions for the apparent relative heat contents of calcium sulfate in the various solvents. Solvent: 0.05 m sodium chloride
(PL2= 2509m*
Solvent: 0.2 m sodium chloride
- 6272m @L2 = 1084ma - 4776m
Solvent: 0.7 m sodium chloride
(PLz = 2092m*
(7)
(8) (9)
TABLE 4 Standard heats of s o h t i o n of calcium sulfate dihydrate SOLVENT
Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
This research
Lange and Monheim
Lange and DUrr
calories-per mole
calories per mole
cslories per mole
f6 f 25 f 25 i 10
-289 =!= 40
-273 =k 50
-341 0.05 n t sodium.chlorido.. . . . . . . . . . . . . . . . . . +30 0.2 nh sodium chloride.. . . . . . . . . . . . . . . . . . . +121 0.7 m sodium chloride., . . . . . . . . . . . . . . . . . . +80
B. Standard heats of solution The heat of solution of calcium sulfate in pure water (given in table 1) can be combined with the heats of dilution of Lange and Streeck (13) t o provide a value for the heat of solution at zero calcium sulfate concentration. Corresponding quantities for the saline solvents can be calculated from equations 2, 5, and 6. These data and their estimated precisions are given in table 4, together with the results of measurements of Lange and collaborators on the heats of solution in pure water. The datum of Lange and Durr (10) has been included, although a relatively insensitive calorimeter was used in their work. The lack of agreement between the results of this investigation and that of Lange and Monheim (11) is less easily dismissed. Lange and Monheim apparently have obtained their result on the basis of just two determinations. The utilization of nine experiments in securing the value reported in this investigation perhaps indicates that it is more reliable.
C. Relative partial molal heat contents In evaluating the partial molal quantities, the following terminology (chosen to correspond as nearly as possible with the Lewis and Randall (14) notation for binary systems) will be used:
HEATS OF SOLUTION AND DILUTION
161
1 refers to water 2 refers to calcium sulfate 3 refers to sodium chloride ni = number of moles of ith component m2 = molality of calcium sulfate (this has been designated heretofore as simply “m”) m3 = molality of sodium chloride Ri(rn2,m3)= partial molal heat content of the i t h component a t a calcium sulfate concentration of m2 and a sodium chloride concen. tration 1113, where i = 1, 2, or 3 Bi(0,m3)= partial molal heat content of the i t h component in a solution m3 molal in sodium chloride but infinitely dilute in calcium sulfate Ri(m2,0)= partial molal heat content of the i t h component in a solution m2 molal in calcium sulfate but infinitely dilute in sodium chloride (Edm3= E;ii(m2,m3) - E;i,(O,md Ei = Ri(m2,m3) - R~(o,o) a
2
= ~ni/n2(Zi)m8
integral heat of solution of calcium sulfate in a solution infinitely dilute in both calcium sulfate and sodium chloride (m2= m3 = 0 ) AH& = integral heat of solution of calcium sulfate in m3molal sodium chloride, the calcium sulfate being infinitely dilute Rossini (17) has developed equations for obtaining partial molal heat contents from the corresponding apparent quantities for two-component systems : AH:
=
- I Z - -m@Lz L 55.508
m’ a(mLz) 2(55.508) dml
(10)
L 2 = - 1 a(maL2) ____ 2m4
ami
A similar treatment when applied to three-component systems gives :
Numerical evaluation of equations 12, 13, and 14 requires determination of two slopes : aaL2 a a ~ ~ and am! ami ~
162
W. E. WALLACE
The first of these is obtained by differentiation of the analytical expressions given above (equations 7, 8, and 9). To determine the second slope, equations 7, 8, and 9 were solved at some particular mz and these three points, together with one taken a t the same calcium sulfate concentration from the data of Lange and TABLE 5 Relalice partial molal heat contents
I12
m2
SOLVENT
calories per mole Ha0
calories er mole Cahr
NaCl
0.00 0.025 0.055 0.085 0.115
0. ooooo* -0.00103* -0.00999* -0.0247* -0.0439*
0. 00000* - 0.00103* - 0.00999 * -0.0247* -0.0439*
O* 274* 583* 754* 859 *
O* 274* 583* 754* 859*
0.05 m sodium chloride ...
0.00 0.03 0.06 0.09 0.12
0.000000 -0.000373 -0.00243 -0.00647 -0.0133
-0.020 -0.020 -0.022 -0.026 -0.033
0 113 226 339 452
371 484 597 710 823
0.00 -0.27 -2.7 -11.1 -28.5
94 94 91 83 66
chloride ... .
6
0.00 0.03 0.06 0.09 0.12
0.000000 -0.000106 0.000108 t0.00320 f0.0141
0 83 143 181 196
465 548 608 646 66 1
0.000 -0.088 -0.69 -2.63 -6.4
85 85 84 82 79
5
0.00 0.03 0.06 0.09 0.12
0,000000 0.000095 0.00079 0.00560 0.0208
0 40 63 69 57
421 461 484 490 478
0.000 -0.023 -0.14 -0.56 -1.57
-63 -63 -63 -61 -65
0.2
0.7
712 sodium
‘in sodium
chloride ....
-
0.009‘4 0.0093 0.0093 0 * 0097 0.0235 1.20 1.20 1.20 1.21 1.22
*From the d a t a of Lange and Streeck (13).
Streeck (13) (ma = 0), were used to plot @Lzagainst mi at a constant value of
a@Lz
was determined graphically. By the use of these m. From this curve 7 am3 slopes and the 3 L ’ s calculated from equations 7 , 8 , and 9, the values for (&),,,8, (Ez),, and (Ea),,,,shown in table 5 were obtained. It is apparent from the definitions of (Ei)m3and ti that there exists between them the simple relation:
-& =
-k [Hi(O,ms)
- Ri(o,o)l
(15)
For i = 1 or 3, the quantity in brackets is the relative partial molal heat content of a component of the simple binary system sodium chloride and water. The El’s and zs’s listed in table 5 were obtained from the corresponding (Z),,’s by employing the thermal data of Gulbransen and Robinson for aqueous sodium
H U T S O F SOLUTION AND DILUTION
163
chloride solutions (8). When i = 2, it becomes necessary t o resort to the heat of solution data presented in this communication t o determine the quantity in brackets in equation 15. The process of dissolving a mole of calcium sulfate in an infinite amount of solvent of either pure water or aqueous sodium chloride can be expressed in equation form as follows: CaS04.2Hz0 (solid) ---t CaS04 [in AH:,
00
NaCl (m3)]
= Wz(O,m3) - Hz(so1id)
CaS01.2Hz0 (solid) ---t CaS04 [in AH: = H2(0,0) - Hz(so1id)
(16)
HzO] (17)
Subtracting equation 17 from 16 gives: B2(0,m3) - Rz(O,O) = AH’,,
- AH:
(18)
Now AH: and AH:, are just the quantities which have been listed in table 4; in this way the L2’s of table 5 have been calculated from the (ZZ)~,’s listed therein. IV. DISCUSSION O F RESULTS
The results of the measurements of heats of dilution and heats of solution are summarized in figure 2. It is of interest t o show that the general features of these curves are consistent with currently accepted views regarding the behavior of solutions of electrolytes. The ionic strength is so great as t o prohibit a quantitative comparison between the experimental heats of dilution in sodium chloride solutions and the predictions of the Debye-Huckel (2,4) theory. However, the principles of the theory can be employed in a qualitative interpretation of the results. It is customary to regard the thermodynamic properties of electrolyte solutions as dependent largely upon the electrical environment which prevails throughout the system. Any process which results in a substantial alteration of the electrostatic conditions within the solution will produce a relatively large change in the various thermodynamic properties of the solution; on the other hand, if a process occurs in which the electrostatic effects remain nearly constant, one expects activity coefficients, heat contents, and related quantities to exhibit very little, if any, variation. These ideas are consistent with the results shown in figure 2. Upon comparing the results in pure water with those in salt solutions it is seen that the heat effects diminish rapidly as the concentration of solvent salt is increased. Such a trend is to be expected, since for a given dilution the electrical environment changes considerably more when the solvent is pure mater than it does in solvents containing sodium chloride. Indeed, in 0.7 m sodium chloride the contribution of calcium sulfate, even in a saturated solution (approx. 0.02 m), to the electrical environment is so small that it is no surprise t o find the heat of dilution in that solvent t o be extremely small. I n connection with these results it is of interest to recall some investigations by Bronsted (3) on mixed electrolytes. He found that when the concentration of
.
,
1G4
W. E. WALLACE
solirent salt was very large compared with that of the solute electrolyte, the activity coefficient of the latter remained constant over a rather wide range of concentration. For example, in 2 molar magnesium sulfate the activity coefficient of cadmium sulfate v a s found to be essentially constant over the range of 0.05 molar to about 0.001 molar. On the basis of this and other studies Bronsted concluded that if the solvent salt had a concentration considerably greater than the solute salt, the latter’s behavior would be nearly ideal. Clearly this ideality is due not to the absence of ionic interaction but rather to the fact that such interactions as are present do not vary with changing concentration of solute salt. Accepting the Bronsted concept of an approach to ideality with increasing concentrations of solvent salt, it follows that the heats of dilution should approach zero at high solvent salt concentrations. Such an approach is clearly apparent i n the curves of figure 2. However, it remains for subsequent investigations to determine whether vanishingly small heats of dilution mould actually be attained at sufficiently high sodium chloride concentrations. The curves of figure 2 show that the dissolved sodium chloride not only affects the heats of dilution of calcium sulfate but also exerts considerable influence on its limiting heat of solution. Obviously, the change in heat of solution results from an alteration of the heat content of the dissolved sulfate by virtue of the presence of sodium chloride. And since such an alteration a t low concentrations is caused almost exclusively by electrostatic interaction between the dissolved ions, it should be possible to make an estimate of the magnitude of the change by use of the Debye-Huckel theory. The limiting law for this particular case reduces to
where Z = =t2 = the valence number ol the calcium or sulfate ion, and the other symbols have their usual significance. With the aid of dielectric constant data of Wyman and Ingalls (19) and appropriate values for the universal constants ( l ) , equation 19 reduces for aqueous solutions a t 25°C. to Ifi(0,ma) -
R,(O,O)= 2862mi calories per mole9
(20)
Results calculated from equation 20 are shown in figure 3, together with the corresponding experimental quantities taken from table 4 (see equation IS). A quantitative comparison of theory and experiment is beyond the scope of this investigation, but the trend of the experimental data in figure 3 suggests the possibility that complete agreement between theory and experiment may obtain a t vanishingly small sodium chloride concentrations. The disparity between theory and experiment a t sodium chloride concentrations greater than zero seems to conform qualitatively to present conceptions of the nature of solutions of electrolytes. I n this connection it is of interest Q
At very low concentrations the difference between mi and ca is negligibly stnall.
165
HEATS OF SOLUTION AND DILUTION
t o consider the results shown in figure 3 in terms of the influence of the charges on the medium (water) in which they reside. Frank and Robinson (7) have concluded from studies involving the partial molal entropies of water that the degree of organization of waterla in electrolyte solutions shows an initial increase with increasing electrolyte concentration, often passes through a maximum, and subsequently decreases. The initial increase is attributed by them to polarization of the water molecules as a result of the increasing average,electric field strength in the solution. Superimposed on this ordering process are disruptive
2-
I Yl I
I
0
I
1
0,4
I
44
I 1
I
I
+ r
I
0.8
3
FIG.:3. 0 ,plot showing the variation of heat content of calcium sulfate with concentration of sodium chloride. 0 ,variation of partial molal entropy of water i n sodium chloride solutions. The straight line is calculated from equation 20.
effects arising from inabilities of ions to fit smoothly into the water because of size, shape, or some other factor. This effect is unimportant a t low concentrations but becomes the dominant factor a t high concentrations, giving rise to the observed behavior. I n the process of solution the incoming ions (calcium and sulfate) must satisfy their solvation tendencies in competition with the arrangement already existing Frank and Robinson draw the distinction between"enve1ope water", the layer of water molecules immediately surrounding a n ion, and "average water", those further removed fromsnion. In thisdiscussion"m7ater" will be usedinthe sense of"avera.gewater."
166
W. E. WALLACE
in the solvent. Hence, when order is high within the solvent, the heat liberated in solvation will be low, since solvation will be strongly opposed by tendencies of the solvent to retain its original arrangement; on the other hand, when order is low, the ions can more successfully compete with the structural tendency of the solvent, and solvation should diminish as the order of the solvent increases. Alterations in the heat of solvation are, of course, transmitted directly to the heat of solution so that a change in the degree of organization of the solvent will be revealed by a corresponding modification of the heat of solution. If the conclusions of Frank and Robinson regarding the variation of order of “average water” with electrolyte concentration are accepted, it is to be expected that the amount of heat liberated in the process of solution would show an initial decrease. At higher sodium chloride concentrations the amount of heat liberated would decrease to a minimum (or even change from a liberation to an absorption of heat) and then begin to increase. This is the behavior exhibited in figure 3 . I L
100 m,
FIQ.4. Plot slionying the variation of heat content, of calcium sulfate with concentration of calcium sulfate in sodiuiii chloride-calcium sulfate mistures of constant ionic strength 0.05.
Included in figure 3 are values for the negative of the relative partial molal entropy content of water in aqueous sodium chloride solutions taken from the data of Frank and Robinson (7). It, of course, is at a minimum when order is best, so that -(& - 8:) should show a concentration dependence somewhat the same as the heats of solution. At least the maxima of the curves should occur at about the same concentration, as is actually the case in figure 3. The determination of activity coefficients in mixed electrolytes has been the subject of many investigations in recent years, particularly by Harned and coworkers (9). As yet there has been no corresponding study of the heat contents of mixed electrolytes. The data of this research provide information of this nature. As a typical case figure 4 shows the variation of heat content of calcium sulfate with concentration of calcium sulfate a t a constant ionic strength of 0.05. Should 11 It is unnecessary to consider the influence of “envelope water” in this case. the hydration of calcium and sulfate ions be accomplished with the aid of some water e s . tracted from the envelopes of sodium and chloride ions, that “enz-eEope water” would be immediately replenished from the supply of “ a m r a g e water”. Therefore, efleectizjely all the water used in hydration of the solute ions is obtained from the supply of “atwage water”.
HEATS OF SOLUTION AND DILUTION
167
V. SUMMARY
Measurements have been reported for the heats of dilution and solution of calcium sulfate dihydrate in solvents of pure water and 0.05, 0.2,and 0.7 molal sodium chloride. Relative partial molal heat contents have been evaluated for the three components over the concentration ranges studied. The heats of solution have been extrapolated t o zero concentration with the aid of the heats of dilution to give values for the standard heats of solution in the four solvents. The heat of dilution results indicate that, in agreement with some conclusions of Bronsted, the presence of high concentrations of sodium chloride causes the behavior of calcium sulfate to approach that of an ideal solute. The Debye-Hiickel theory has been used t o compute the heat effect associated with the transfer of a mole of infinitely dilute calcium sulfate from water into solvents of varying sodium chloride content. The few experimental data for comparison with theory suggest an agreement between theory and experiment in the limit similar to that observed for solutions of single electrolytes. At higher concentrations of sodium chloride the divergence of theory and experiment has been attributed t o weakening and disorganization of the liquid water structure as a result of the finite size of sodium and chloride ions. The data have been used to show for a typical case the variation of heat content with concentration in electrolyte mixtures of constant ionic strength. The author is pleased t o acknowledge the continued interest and many helpful criticisms offered by Professor A. L. Robinson during the course of this investigation. REFERENCES (1) BIRGE,R . T.: Rev. ModernPhys. 13,233 (1941). (2) BJERRUM, N.: Z . physik. Chem. 119, 145 (1926). (3) B R ~ N S T EJ. D ,N.: (I) Medd. K . Vetenskapsakad. Nobelinst. 6, No. 25, 1-19 (1919); (11) Kgl. Danske Videnskab. Selskab., Math.-fys. Medd. 3, No. 9 (1920). (4) DEBYE,P., A N D H ~ ~ C K E E.: L ,Physik. Z. 24, 185 (1923). (5) DOIWEY, N. E.: Properties of Ordinary Water Substance, p. 655. Reinhold Publishing Corporation, New York (1940). (6) DUNKELBERGER, T. H., AND ROBINSON, A . L.: ,J. Am. Chem. SOC.60,1301 (1938). (7) FRANK, H . S., AND ROBINSON, A. L . : J . Chem. Phys. 8, 933 (1940). (8) GULBRANSEN, E., A N D ROBINSON, A. L . : J. Am. Chem. SOC.66, 2637 (1934). H. S.: J . Am. Chem. SOC.67, 1865 (1935). See, also, Harned in Taylor’s (9) HARNED, Treatise on Physical Chemistry, 2nd edition, Vol. 1,p. 801, D. VanNostrand Company, New York (1930). (IO) LANOE, E., A N D DURR,F.: Z . physik Chem. 118,129 (1925). J.: Z. physik. Chem. 16OA. 319 (1931). (11) LANGE,E., AND MONHEIM, (12) LANGE, E., AND ROBINSON, A. L.: Chem. Rev. 9, 89 (1931). See YOUNG,T. F., AND SELIGMANN, P.: J. Am. Chem. SOC.60, 2379 (1938) for reference t o more recent studies. (13) LANGE,E., A N D STREECK, H . : Z . physik. Chem. 167A, 1 (1931). (14) LEWIS,G. N., AND RANDALL, M . : Thermodgnamics and the Free Energy of Chemical Substances, p. 83. The McGraw-Hill Book Company, Inc., New York (1923).
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(15) MASSON, D . 0 . :Phil. Mag. 8 , 2 1 8 (1929). (16) RANDALL, M., AND ROSSINI,F. D.: J. Am. Chem. SOC.61,323 (1929). (17) ROSSINI,F. D.: Bur. Standards J. Research 4, 313 (1930). (18) WALLACE, W. E., AND ROBINSON, A. L.: J. Am. Chem. SOC.63,958 (1941). (19) WYMAN, J., A N D INQALLS, E. N.: J . Am. Chem. SOC.60, 1182 (1938). (20) YOUNG, T. F., AND VOGEL,0. G. : J. Am. Chem. SOC.64,3030 (1932). (21) YOUNG,T. F., A N D GROENIER, W. L. : J. Am. Chem. SOC.68,187 (1936).
NEW BOOKS
+
Fluorochemistry. By JACK DEMENT. 6 s 92 in.; svii 796 pp. Brooklyn, New York: Chemical Publishing Co., 1945. Price : $14.50. The author presents a summary of the facts and to a lesser estent the theories of luminescent phenomena, ranging from the methods of preparing solid phosphors t o Gurwitsch’s mitogenetic rays and the “Plotnikow-Plait scattering.” Probably as a result of the attempt to make the book all-inclusive, certain aspects of the subject (especially the fundamental theories) are treated in a rather superficial manner. The author uses a surprising number of newly coined words. While for the greater part this is only a minor nuisance, in a few cases where terms well established in physics are used with unfamiliar meanings i t is more confusing. As an example of the latter, on pages 35 and 53 “quantization” is identified with “excitation.” A number of old ideas appear in the guise of new and somewhat grandiose principles, as the following quotation (page 2) will illustrate: “ I n 1942, J . DeMent enunciated the fundamental principle underlying all processes of a luminescent nature. Based on theoretical considerations alone, the first law of fluorescence states t h a t before emission can occur from a luminescent system, absorption must Jirst take place. DeMent’s rule is the analog of the Grdtthuss Draper law of photochemistry.’’ It should not be assumed from the foregoing t h a t the book is without merit. I n spite of the curious and unnecessarily complex terminology, the basic facts of fluorescence and phosphorescence are presented with reasonable clarity. The more obscure phases of the subject are discussed with unusual completeness. The bibliography is extensive and appears t o be unbiased, if in part uncritical. However, the subject of luminescence is st.ill in great need of a sound, modern monograph. The book is clearly printed on glazed paper. The diagrams fall far short of the standard set by most American publishers. I t is perhaps unnecessary t o point out t h a t the price ($14.50 for an 800-page book with 30 poor’illustrations) is outrageous. ROBERTLIVINGSTON. Bioenergetics and Growth. By SAMUEL BRODY. 1033 pp. New York: Reinhold Publishing Corporation, 1945. Price: $8.50. “The primary purpose of this book is to present quantitative analyses of metabolic processes of the organism as a whole i n relation t o the energetic efficiency of agriculturally productive transformations.” To achieve this end Professor Brody has written a compilation and appraisal of the vast experimental data on energy relations i n growth and animal production and has very capably presented new interpretations. He has devoted a chapter t o the principles of energetics and the relation of thermodynamics to, biology and agriculture; another t o experimental methods; twelve chapters t o energy and nitrogen metabolism, growth, aging, and such productive processes as milk secretion, egg production, and muscular work. Factors which influence productive efficiency-nutrition, enzymes, hormones, seasonal and diurnal rhythms, and temperature-comprise the material for eight additional chapters; and three interspersed chapters serve t o introduce, integrate, and summarize the
