RAYMOND W.BREMNER
444
Vol. 66
tent, errors in the weighing9 and temperature other causes should be small in relation to these readings. Of these, the first probably caused two. the largest errors, since runs in which the vacuum Acknowledgment.-We wish t o express our was poor gave very erratic results (runs 9 and 12). appreciation to the Brush Beryllium Company Thinner oxide films would not stop the evapora- for the pure beryllium sample, and to Prof. H. G. tion, but still might slow it down appreciably. Heil of the Mendenhall Laboratory of Physics, However, early in the work it was recognized that for the use of the high temperature equipment this might be the main source of error; accord- and for instructions in its use. ingly, special care was observed in all the work to summary reduce this error to a minimum. For results on The vapor pressures of metallic beryllium in films of nickel oxide on nickel, see the results on nickel oxide by Johnston and Marshall.a~loTL; the range from 1170 to 1340'K. have been detertemperature control of the furnace was not all mined by the Langmuir method. The results are that could be desired, and a considerable error given in Table I, and a plot of log P as, 1/T is have been calcumight have been caused by temperature varia- given, Fig. 1. Values of tions; however, this source of error was mini- lated and found to vary some with temperature, mized by taking temperature readings a t frequent the mean value of being (122,000 * 2500) intervals throughout the run. The errors by cal./mole. The heat of vaporization was also (IO) The referee has kindly called our attention to the fact that calculated, being 78,800 cal./mole at 1250'K. experiments to settle the oxide film question could be carried out in Possible sources of experimental error are considan apparatus like that described by Blewett, Liebhafsky and Henered, the slowing down of evaporation by thin nelly in J. Chem. Phys., 7 , 478 (1939), for the determination of the oxide films probably being the most important. vapor presure and rate of evaporation of barium oxide. He points out that if the rates of evaporation in such an apparatus are proporThe accommodation coefficient appears to be tional to the area of the opening, then oxide films are not retarding unity. the evaporation, provided that the vapor pressure equilibrium is
a
a
COLUMBUS, OHIO
maintained withiu
[CONTRIBUTION FROM THE
RECEIVED NOVEMBER 12, 1943
DEPARTMENT O F CHEMISTRY, AGRICULTURAL AND MECHANICAL COLLEGE OF TEXAS],
Temperature Coefficients of Electrical Conductance of Solutions Containing Sodium Chloride, Potassium Chloride or Magnesium Sulfate or Mixtures Thereof BY RAYMOND W. BREWER Introduction Very little accurate information on the variation of electrical conductance with temperature is available in the literature. In this paper equations for very accurately calculating equivalent conductance as a function of centigrade temperature have been worked out. Temperature coefficients of equivalent conductance have been calculated with five-place accuracy. Temperature coefficients of specific conductance of certain standard potassium chloride solutions and of conductivity water have also been calculated. The variations of the coefficients due to temperature changes, concentration changes and mixing of electrolytes have been determined. Calculations Equivalent Conductance as a Function of Temperature.-Equation I was used for representing the equivalent conductances of twenty different solutions as a function of centigrade temperature. Eq.Cond. = A
i=
a
+ bt + cP + dta
(I)
The preparation of solutions and the experimental data have been described previously.lJ The (1) Raymond W. Bremner. Thomas G. Thompson and Clinton L. Utterback, THIS JOU8NAL, 60, 2616 (1938). (2) Raymond W. Bremner, Thomas G . Thompson and C. L. Utterhack, ibid., 61, 1219 (1939).
ratio of the number of millimoles of sodium chloride to the number of millimoles of magnesium sulfate in a given quantityvof each of the four solutions that contain both of these salts is 16.4315. Similarly the ratio of the number of millimoles of sodium chloride to the number of millimoles of potassium chloride in a given quantity of each of the four solutions that contains both of these salts is 47.2916. The most dilute solution of each type is designated as Solution No. 1, while the most concentrated solution is designated as Solution No. 4. Solutions of intermediate concentrations are numbered 2 and 3, respectively. The constants a, b, t and d of Equation I were evaluated from the experimental data for each solution by the method of least squares. By use of the resulting equations the equivalent conductance was calculated for each solution a t 0, 5, 10, 15, 20 and 25'. The average deviation of the calculated from the experimentally determined value was only 0.a0670. In no instance was the deviation greater than 0.0270, which is the approximate maximum error in the original data. In Table I are listed the values of the constants of equation I for each solution. The constant (d), which is the coefficient of the term of highest degree, is in every instance negative. This in&cates a point of inflection a t a higher temperature
TEMPERATURE COEFFICIENTS OF ELECTRICAL CONDUCTANCE
March, 1944
in each conductance vs. temperature curve, which is an essential requirement for an equation that satisfactorily represents electrical conductance as a function of temperature. The second degree equations A 5: a bt ct' and A = AO (1 at bt2) were found to be inadequate for making the calculations. The deviations of the calculated from the experimental values ranged up to 0.1% or more when they were used.
+
+ +
+
TABLE I CONSTANTS FOR THE EQUATION A =
0
f bt f ct2 I- dta
Solu- Grams of wlute in tion 1000 g. of water a X 104 b X lo4 c X 10 d X 104 Sodium Chloride Solutions 5.61836 573268 17669.9 98.081 -0.3481 1 NaCl .3292 11.30020 549441 16719.7 92.316 2 NaCl ,3191 3 NaCl 19.94438 627386 15822.3 88.058 ,2277 4 NaCl 27.26159 513557 15338.6 80.874
-
1 2 3 4
KCI KCl KC1 KC1
1 2 3 4
MgSOd
MgSOc
Potassium Chloride Solutions 0.15069g 796016 23802.8 125.654 0.301442 787640 23472.6 123.695 0.537882 779097 23225.7 118.655 0.716222 774437 23027.0 119.224
-
,7270 ,6903 .Ml3 .6315
Magnesium Sulfate Solutions 0.704166 452660 14624.2 1.41629 401717 12922.4 2.49969 361457 11664.6 3.41678 341053 10906.1
-
,6457 .6321 .4536 .6604
87.688 75.583 60.412 64.458
MISO, MgSO, Mixed Solutions of Sodium Chloride and Potassium Chloride 1 NaCl 5.61836 CKCl 0.151522 575820 17686.1 97.930 ,3787 2 NaCl 11.30020+KCl 0.304756 551653 16695.6 97.240 .4700 3 NaCl 19.84439 +KCl 0.537882 529131 15896.9 85.328 .2788 4 NaCl 27.26158 KCI 0.735220 515739 15320.1 86.140 .3470
-
-
-
+
Mixed Solutions of Sodium Chloride a d Magnesium Sulfate 1 NaCl 5.61836 MgSOc 0.704166 548633 16883.9 97.260 .3986 2 NaCl 11.30020 MgSOc 1.41629 520802 15835.2 95.810 - .5179 3 NaCl 19.94439 +MgSOc 2.49969 495340 14940.6 84.325 - .3418 4 NaCl 27.26159 f MgSOc 3 41678 480024 14331.2 83.209 - .3909
-
+ +
For these reasons Equation I is recommended for use in calculating equivalent conductance as a function of centigrade temperature. Temperature coefficients of equivalent conductance were calculated by use of Equation I1 and the constants are listed in Table I. Temp. coef. of eq. cond.
b Adt
+ 2ct 4- 3dta A
(11)
They were calculated with five-place accuracy for each of the 20 different solutions a t 0, 5, 10, 15,20 and 25O, and are listed in Part 1of Table 11. Specific Conductance as a Function of Temperature.-Equation 111 has been used previously to calculate the specific conductances of 0.01 demal and 0.1 demal potassium chloride solutions in the temperature range 0 to 25O* Sp. cond. L = a 4-bt ct2 dtJ (111)
-
+ +
(3) Raymond W. Bremnu and Thomas G. Thompson, THIS J O V U ~ A L ,6% 2372 (1937).
PART
TABLB I1 I-TEMPERATTJRE aBPFICIENTS CONDUCTANCE Coef. X 101
-
OF
EQUIVALENT
(dA/AdQ X 101
Solution
00
1 2 3 4
30823 30431 30001 29867
10' Sodium Chloride 28048 25713 27732 254~53 26196 27408 27236 25026
1 2 3 4
29902 29801 29811 29734
Potassium Chloride Solutions 27230 24953 22971) 27166 24896 22930 27128 24846 22876 27084 24825 22872
1 2 3 4
32307 32168 32271 31976
Magnesium Sulfate Solutions 29272 26661 24390 29117 26483 24185 29046 26333 24013 28960 26314 23976
60
445
16O Solutions 23716 23490 23292 23140
20'
25O
21986 21802 21634 21608
20470 20318 20172 20080
21236 21208 21154 21163
lgeo0 19688 19634 19652
22394
20624 20359 20234 20026
22160
22001 21894
Mixed Solutions of Sodium Chloride and Potassium Chloride 1 30716 27956 25628 23633 21901 20379 2 30266 27669 25416 23463 21746 20221 3 30044 27393 25160 23247 21588 20138 4 29706 27161 24987 23103 21454 19996 Mixed Solutions of &,lium Chloride and Magnesium Sulfate 1 30780 28059 25746 23758 22015 20484 2 30408 27817 25568 23596 21850 20296 3 30162 27544 25312 23388 21697 20209 4 29855 27332 25153 23251 21574 ZOO86
PART 2-TEMPERATURR
COEFFICIENTS OF SPECIFIC CON-
-
DUCTANCE
OC. KC10.01D KCIO.1D Conductivity water
Coef. X 106 (dL/Ldt) X lo( 0 5 10 16 18 20 25 29782 27036 24704 22701 21627 20967 19421 29185 26539 24272 22304 21241 20575 19041 4 3 m 36200 31800 2
9 2800f~ ~ 2
7 26300 ~
When applied to the conductivity water used the constants obtained for speafic conductance X 106 are a = 0.495, b = O.O2lg, c = -0.000002 and d = 0.0000039. Since the conductance of the water used was only a small correction factor, it was less accurately determined. By use of Equation IV temperature coefficients of specific conductance were calculated; those of 0.01 demal and 0.1 demal standard potassium chloride solutions with five-place accuracy, and those of the conductivity water with three place accuracy. They are listed in Part 2 of Table 11. Temp. coef. dL b 2ct + 3dP (IV) of sp. cond. LX = L
+
Discussion of Results Effects of Concentration.-As illustrated by Part 1of Table I1 the temperature coefficients of equivalent conductance decrease with increasing concentration in every instance. This is probably because the coefficients for water are higher, as shown in Part 2 of Table 11. The data on standard potassium chloride solutions substantiate this observation. The d e c t of temperature on this decrease depends upon the particular salt or mixture of salts
FREDERICK T.WALL
446
involved. The decrease is most rapid at 0' and progressively becomes slower up to 25") for all the solutions containing a high proportion of monovalent ions. Solutions containing only magnesium sulfate and water exhibit the reverse behavior. The decrease is slowest for the most dilute solutions (potassium chloride only) and progressively becomes more rapid to those of higher concentration (sodium chloride). These effects are best observed by plotting coefficients against concentrations. Effects of Temperature.-The temperature coefficients of equivalent conductance considered decrease by about 1.5 to 2.0% of their values for each degree increase in temperature. The fact that they decrease is consistent with measurements showing coefficients to be negative a t much higher temperatures. This decrease is most rapid for water and becomes less rapid the more concentrated the solution, except for solutions containing only magnesium sulfate and water. This difference and also the one mentioned in the preceding paragraph are likely due to the fact that magnesium sulfate is a different type of electrolyte in that it yields divalent ions. Effects of Adding a Second Salt.-The addition of a salt that forms solutions with temperature coefficients higher or lower than those of sodium chloride solutions to the latter, produces solutions with coefficients of intermediate value. The magnitude of the intermediate value depends upon the concentration, and the temperature, even though the mole ratios are kept constant. The effect of adding a salt is either in opposition to or in addition to the effect of increasing the concentration, depending upon whether the coefficients of solutions of the added salt are higher or lower, respectively, than those of solutions containing only sodium chloride and water. For example, the addition of magnesium sulfate to sodium chloride solutions increases the tempera-
[CONTRIBUTION FROM THE
Vol. 66
ture coefficients of the latter. Thus, two opposing factors axe in operation, the effect of adding a salt with a larger temperature coefEcient outweighing the effect of increasing the concentration. When temperature coefficient is considered as a function of concentration, there is a pronounced maximum in the temperature coefficient at concentration no. 3 for magnesium sulfate solutions at 0". Slight maxima occur also a t the same concentration for this salt at 25' and for potassium chloride solutions a t 0". These maxima are reflected in the corresponding sodium chloride solutions to which the salts mentioned have been added. The maxima, particularly for the magnesium sulfate solutions a t O", are larger than could be attributed to experimental errors, and as yet we can offer no explanation for them. I t is a rioteworthy fact that they occur mainly at 0".
Summary An equation is recommended for calculating the equivalent conductances of solutions as a function of centigrade temperature. The maxinium deviation of the calculated from the experimental equivalent conductance was 0.02%, and the average deviation was only 0.006%. 2. By use of the differentiated form of the equation the temperature coefficients of equivalent conductance of twenty different solutions have been calculated with five-place accuracy at 0, 5, 10, 15, 20 and 25'. Also temperature coefficients of specific conductance have been calculated a t 0, 5, 10, 15, 18,20 and 25' for the conductivity water used and for 0.01 demal and 0.1 demal standard potassium chloride solutions. 3. Variations of temperature coefficients of electrical conductance of the salt solutions, due to concentration changes, temperature changes a d the addition of a second salt have been determined. 1.
CVLLFGESTATION, TEXAS
NOYESCHEMICAL
RECEIVED AUGUST31, 1943
LABORATORY, UNIVERSITY OF ILLINOIS]
Osmotic Pressures for Mixed Solvents' BY FREDERICK T. WALL
During recent years osmotic pressure measurements have assumed increased importance as a means of determining molecular weights of high polymeric Although the theory of osmotic pressures for simple systems has been well formulated, little attention has been devoted to the theoretical aspects of osmotic pressures for (1) OriSinal manuscript received July 12, 1943. (2) (a) G. V. Schulz, 2. Dhysik. Chem., 176, 317 (1936); R. M. Fuosr 8nd D. J. Mead, J . Pkrs. Ckcm., 47, 59 (1943); P. J. Flory,
T H I SJOWRNAL, 65,372 (1943). See also H. Mark, "Physical Chemistry of High Polymeric Systems." Interscience Publishers, Xew York, N. Y..1940, p. 228, for a general disctlssion. (b) G . G e e Trans. Porodav ,So(
86. 1171 (1940)
systems with mixed solvents.
Since G. Gee2
has carried out measurements under such condi-
tions, it appears desirable to consider thermodynamically the significance of osmotic pressures for mixed solvents and to find out just what it is that one measures experinlentally. For an ordinary solution consisting of a solvent (A) and a solute (S), the osmotic pressure is a definite thermodynamic property of the solution. It is defined simply as the excess pressure which must be applied to the solution to increase the partial pressure of the solvent up to the vapor pressure of the pure solvent at the same tempera-
