May, 1958
ACTIVITYCOEFFICIENT OF HCL IN KCL SOLUTIONS
627
TABLE I11 CONPARISON O F THE LATTICECONSTANTS O F SEVERAL CALCIUM PHOSPHATES Ca2NH*H?(P04)4.2H20 Ca2KH7(POd)o*2H20 Ca( H2P04)2.Hz0 CaCI(H~PO>).HIO 5 G7 A. 5.76 Asb 5.72 A. 5.79 A. 11.92 17.14 12.13 12.52 6.51 6.41b 6.46 6.50 98' 11' 90" 98" 44' 97" 57' 118" 31' 119O 0' 118" 1' 117' 45' 83" 9' 90 9 5 O 54; 98" 0' 5.89 A. 8.57 A. 5.90 A. 5.99 A.
Lattice constants a b C C Y '
P Y dozo
Density, g./cc. 2.17 2.33 2.19 2.28 Calcd. Pycnometric 2.10 2.35 2.22 2.*29 2.22 2.36 2.23 2 30 From refractive indexes" Formula wt. per unit cell 1 1 2 4 See E. S. Larsen and H. Berman, U. S. Geol. Survey Bull. 848 (2nd ed.) 1934. a Gladstone and Dale equation. ported axes of Walter-LBvy, et uE.,'O are interchanged for this comparison.
The apparent high stability of the Ca-PO4 sheets suggests that other calcium phosphates may contain similar sheets. The unit-cell constants for the calcium chloride phosphate, CaC1HzP04.Hz0,in Table III are given to show that this compound has dimensions a, c and 0,that are close to those of the other salts. The plate-like habit of this compound is characteristic of the others and is in accord with the same Ca-PO4 sheet structure being present in this compound. An alternative selection of unit-cell constants in the a-c plane has a = 5.76 A., c = 6.20 .& and 0 = 115' 20'. This may be the correct set for comparison with the other salts, although the fit is not quite as good. The similarities noted between the unit-cell constants apparently were not recognized by Walter-Levy and co-workers.'O It is reasonable to assume that the monohydrated bromide salt CaBrHzP04.Hz0, reported by WalterLBvy and Vincent,ll also possesses the same layer structure. (11) L. Welter-L&vy and J. P. Vincent, Compt. rend., 241, 1207 (1955).
Re-
Chlorospodiosite, Ca2PO4C1,has lattice $mensions12 u = 6.17, b = 6.89 and c = 10.74 A. Of these, a and c are nearly the same as two dimensions in the Ca-P04 sheet o[ dicalcium phosphate dihydrate, 6.239 and 10.84 A. The latter dimensions are for a nearly orthogonal b-centered cell derived from the cell given by Beevers and R a i ~ t r i c k . ~ A slight distortion of the Ca-PO4 sheet along with the extra calcium ions could easily increase the symmetry in the sheet to satisfy the requirements of the orthorhombic space group of chlorospodiosite. The occurrence of the corrugated sheet in chlorospodiosite would be of considerable interest in that it would extend this feature to a thermally stable anhydrous compound wore basic than dicalcium phosphate. The corrugated sheet, therefore, may ocour in many alkali and alkaline earth salts containing the tetrahedral XOrtype anion. Acknowledgment.-Mrs. Inez J. Murphy made the chemical analyses. (12) A. L. Mackay, Mineralog. Mag., SO, (No. 222) 166 (1953).
THE ACTIVITY COEFFICIENT OF HYDROCHLORIC ACID I N POTASSIUM CHLORIDE SOLUTIONS BY HERBERT S. HARNED AND ALANB. GANCY Conti,ibulion No. 1484 f r o m the Department of Chemistry of Yale University, New Haven, Conn. Receiued Februa7y 9, 1958
The activity coefficient of hydrochloric acid in potassium chloride solutions a t constant total molalities at 25" has been determined from suitable cells without liquid junctions. Anal sis of the results confirms the conclusion of McKay that although the logarithm of activity coefficient of the acid varies fnearly with its concentration, the logarithm of the activity coefficient of potassium chloride varies quadratically with ?ts concentration.
Measurements of cells of the type
relationship is valid, the question arises as to whether a similar equa t'ion
H2/HCl(ml),MCl(m2)IAgC1-Ag
indicate that the activity coefficient, y , of the acid varies linearly in a mbture of constant total molality,m. Thus log
YI
= log Y N O )- mm2
(1)
where log -yl(a) is the activity of the pure acid of concentration ml = rn, and m2 is the coilcentration of the salt. For systems for which this linear
log yz = log
7x0)
- a21m1
(2)
holds for the second electrolyte. For systems for which equation 1 is found valid, McKay' has devised an ingenious method of computing CYZI without the assumption that equation 2 is valid. For systems coiitaiiiing two uni-univalent electrolytes (1) H. A. C. McRay, Trans. Faradag Soc., 51, 003 (1055).
HERBERT S. HARNED AND A. B. GANCY
628 azl may
Vol. 62
be computed by the formula
TABLE I
THE ACTIVITYCOEFFICIENT OF HYDROCHLORIC ACID AT 25" IN POTASSIUM CHLORIDE SOLUTIONS AT VARIOUSCONSTANT TOTAL MOLALITIES.AT1 = Yi(OBS.) - yl(CALCD.)
The limiting values of azl when ml approaches m, 0121(~), and when ml approaches zero, a21(o), are m
~ z I ( ~ )=
log
and az1(0)
=
+
(YZ(O)/Y~(O))
d log ( Y m / m ) ) l d m
d
(4
m
+ m daddm +
a12
(5)
m1 0.50 .36 .23 .10
0.27227 .28165 ,29373 .31619
m = 0.5 yi(obs) 0.7590 .7453 .7343 ,7221
1.00 0.5 .3 .1
0.23321 ,25436 .26881 .29829
m = 1.0 0.8114 .7603 .7411 .7234
E
A.yi
'0.0000 ,0006 .0004 - .0001
-
+
0.0000
As a result of a survey of existing precise data for - ,0009 uni-univalent mixtures, McKay found that the - .0009 system, hydrochloric acid-potassium chloride, + .0002 showed a marked variation of azlwith the concenm = 1.5 tration. Since many of the earlier2 values of a12 were derived from only two measurements a t acid 0.0000 1.5 0.20726 0.8962 1.0 .22094 .8410 + .0010 concentrations of 0.01 and m, we have subjected 0.5 .24218 .7868 - .0006 equat,ion 1 to a more rigorous test by making pre0.1 .28622 .7469 - .0008 cise measurements of the system at total concentrations of 0.5, 1, 1.5, 2 and 3. These new results, m = 2.0 supplemented by the application of McKay's 2.0 0.18642 1.008 0.0000 method should definitely fix the thermodynamic 1.0 .21109 ,8822 ,0000 characteristics of this system a t 25". 0.5 .23240 .8243 - .0009 Experimental Results 0.1 .27635 ,7838 + .0015 Table I contains the observed electromotive m = 3.0 forces in absolute volts of the cells at one atmos3.0 0.15183 1.318 0.000 phere hydrogen pressure and at acid concentra2 . 1 .16777 1.154 .003 tions, ml,and total concentrations, m, as desig1.1 .19178 1.000 - ,001 nated. The third column contains values of the m = 0 . 5 ; log yl = -0,11976 - 0.0540m~ activity coefficient of hydrochloric acid in the mixm = 1.0; log y1 = - .09077 - .0565m~ tures. The fourth contains the difference between m = 1.5; log y1 = - .04760 - .0562m~ values of activity coefficient computed by the linear m = 2.0; log 7,= - .00358 - .0580m~ equations at the bottom of the table and the obm = 3.0; log yl = + .11978 - .0627m2 served activity coefficients. It is apparent that equation 1 expresses the results to a high degree of TABLE I1 accuracy. The values of the coefficients of the CALCULATED VALUES OF cyzl ACCORDINQ TO EQUATIONS 3, 4 linear term agree closely with those obtained from AND 5 the earlier data of Harned and ha me^-,^ namely, m = 4.0 m = 3.0 m = 2.0 m = 1.5 m = 1.0 0.056, 0.055, 0.057, 0.062 at 1, 1.5, 2 and 3 total molality. However, the new value of 0.054 at 0.5 total molality differs considerably from the earlier 0.060 0.063 0.053 0.042 0.0 0.041 result of 0.062. .059 .065 .055 .043 0.5 .043 .062 .068 .058 .048 1.0 ,045 Calculations by the Method of McKay .065 ... .061 .052 1.5 .046 Table I1 contains the values of a21 computed by ... ... .064 .055 2 . 0 ' .048 equations 3, 4 and 5. At each total concentration, ... .059 2.5 .051 and that at ml = the result at ml = 0 equals azl(o) ... .. .062 3.0 .054 m is azl(m).This result confirms the earlier com... ... 3.5 .057 putation of McKay that azl varies with the concen... ... ... 4.0 .060 tration of the components and that this variation can be expressed within narrow limits by the linear TABLE I11 equation 0121
=
~ZI(O)
+ Pzlml =
a2w
- P21mz
(6)
where pzl has the value of -0.005 over the concentration range of one to five molal. McKay obtained -0.0065 for & at three to five molal. Conclusions and Summary The present measurements of the cells leave no (2) H. 6.IIarned, J. Am. Chem. Soc., 5'7, 1865 (1935). (3) H. S. Harned and W. J. Hamer, $bid., 56, 2194 (1933); Bee also
H. S. Harned and B . B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd Ed., Reinhold Publishing Corp., New York, N. Y., 1958.
11E
0.5 1 1.5 2 3 4
QUANTITIES FOR USE IN log YI(0) log Ya(0)
-
-
0.1198 .0908 ,0476 - .0036 - .1198 - .2460
PZL=
-
EQUATIONS 7, 9 AND 10
-12 - aam 0.069 0.054 0.1971 .0555 .063 .2182 .060 .0562 .2328 ,053 .0580 ,2396 .042 .0627 .2418 .0660 .041 .2358 0.005; m = ml mz; t = 25".
+
$(a)
0.899 .897 .902 .912 .937 .965
doubt that the linear equation log
YI
=
log
-
~ ~ ( 0 ) a m 2
(7)
May, 1058 expresses the variation of the activity coefficient of hydrochloric acid a t constant total molality, m = ml m2, with a high degree of accuracy. The parameter, azl, computed by equations 3, 4 and 5 varies with both the total molality m, and the molalities of either of the components according to the linear relationship
+
a21
629
NOTES
=
aZl(0)
+
Bzllnl
=
0121(m)
- Pzlm
any of these mixtures from 0.5 to 4 total molalities a t 25” are compiled. Suitable values a t intermediate molalities can be obtained by interpolation. The osmotic coefficients, q5(x), in any of these mixtures are given by d(x) - b(0) =
-azi(rr)~
(8)
As a result the activity coefficient of potassium chloride is found to vary quadratically with its concentration. Thus log YZ = log Yzto) - a21(G)vl.1- PZlrn12 (9) As pointed out by McKay, thermodynamics requires that pzl does not vary with the total molality. I n Table 111, the quantities necessary for the rapid computation of the activity coefficients in
+ 721
+
(a12
-
O~ZI(O))S~
+2
??apz,xz
n i ~ ~ ~ (10)4 x 3
where +(o) is the osmotic coefficient of a potassium chloride solution a t concentration m, and x = mdm.
This contribution was supported in part by the Atomic Energy Commission under Contract AT(30-1)1375. (4) See Ref. 3, p. 016.
NOTES ELECTROLYSIS OF SODIUM INTO A REACTION VESSEL’ BY WILLIAM L. JOLLY
unless the sodium is first distilled away or dissolved away, and (3) because an ordinary glass reaction vessel is used, the method is not applicable to other alkali metals.
Univeraity of California Radiation Laboratory, Livermore,, California, and Department of Chemistry, Berkeley, Californza Received January l 4 # 1968
Experimental Apparatus.-The apparatus is pictured in Fig. 1. The only unusual item is the reaction vessel, which is constructed of Pyrex glass. Two insulated wires are sealed to tungsten rods which project through glass seals from the bottom of the inner glass tube. The filament from a Sylvania 60-watt light bulb is attached by spot-welding the nickel filament leads to the tungsten rods. The filament is about 1 cm. from the bottom of the reaction vessel. The lower part of the reaction vessel is thin-walled.
I n chemical vacuum-line work, it is often necessary to introduce a small, measured amount of sodium metal into a glass reaction vessel. This is usually accomplished by a tedious process culminating in the breaking of a fragile bulb containing a weighed amount of the metal.2J This note describes a simpler process for accomplishing the same result. It is well known that hot glass is an electrical conductor, the current being carried by the mobile sodium ions.4 Thus, it is a simple matter to electrolyze a molten sodium salt using an evacuated light bulb as a c a t h ~ d e . ~ By . ~ a similar procedure it is possible to electrolyze a measured amount of sodium metal into an evacuated reaction vessel. The advantages of the procedure are (1) the sodium introduced is spectroscopically pure16( 2 ) the amount of sodium introduced is readily determinable with high accuracy, (3) exceedingly small amounts (of the order of micromoles) of sodium may be introduced, and (4) a predetermined amount of sodium may be introduced. The disadvantages are (1) the sodium usually must be introduced before the other reactants, (2) the tungsten filament must be present during the reaction (1) This research was sponsored in part by the U. S. Atomic Energy Commission. (2) R. T. Sanderson, “Vacuum Manipulation of Volatile Compounds,” John Wiley and Sons, Inc., New York, N. Y., 1948. (3) G. W. Watt a n d D. M. Sowards, J . A m . Chem. SOC.,76, 4742 (1954). (4) G.W. Morey, “The Properties of Glass,” 2nd ed., A.C.S. Monograph No. 124, Reinhold Publ. Corp., New York, N. Y., 1954. (5) R. C. Burt, J . Opt. SOC.Am., 11, 87 (1925). ( 6 ) D. K. Alpern, J . Chem. Educ., 34, 289 (1957).
IOU
I VARIAC
IODINE
UE
*
I S T E E L BEAKER
MOLTEN No NO,
-350O
Fig. 1.
