380
W. R. CARPERAND P. A. D.
DE
MAINE
Salts of the Group 11-A Metals Dissolved in Nonaqueous or Mixed Solvents.
111. Precision Conductance Data for Ca(NO,),*PH,O, Mg(N0,),*6H20,or Be(NO3),*3H,ODissolved in Methanol or Methanol-Carbon Tetrachloride’
by W. R. Carper Department of Chemistry, Cdifornia State College, Loa Angeles, California 90052
and P. A. D. de Maine2 Department of Chemistry, University of California, Sania Barbara, California 98017
(Received July 8, 1966)
Precision conductance data between 10 and 40” are reported for Be(N0&.3Hz0, Ca(K03)2.4Hz0, and hfg(NO&.6Hz0 dissolved separately in pure methanol, and for Be(N03)23H2O dissolved in methanol-carbon tetrachloride. Also described are the JanzMcIntyre-type conductance bridge and the thermostated bath used. All data were processed by computer programs containing the self-judgment principle. Compatibility of the data with several equations is discussed.
-
Introduction I n preceding papers, 3,4 the literature was reviewed and Conductance values reliable to better than 2% were given for several salts of the group 11-A metals dissolved separately in nonaqueous solvents. For most systems, plots of the specific conductance us. salt concentrations at a fixed temperature yielded two intersecting straight lines. For each salt at each temperature the concentration at the intersection point was found to be a linear function of the static dielectric constant of the pure solvent. Discussed here are new conductance data, reliable to O.l%, for three nitrates of group 11-A metals dissolved in methanol or in methanol-carbon tetrachloride a t 10, 20, 30, 35, and 40’. Compatibility of these data with various conductance theories was tested by the self-judgment method of curve fitting5-’ in which the preselected limits of reliability for the raw data determine the compatibility of data and the maximum permitted errors associated with each value for each parameter. This curve-fitting method, described in the Data Processing Nethod section, is free of the ambiguity inherent in “graphical” and “statistical” methods. The Journal of Phyeical Chemistry
Experimental Section Fisher Spectroanalyzed methanol and CC14 were saturated with Matheson anhydrous grade nitrogen (dew point less than -40’) immediately before use. Frequent purity checks, made with an Aerograph Model A-90-P chromatograph with firebrick column and helium as the carrier gas showed less than 0.01% impurity in both solvents. Dielectric constant and conductance data for both solvents agreed with published values.s In analyses of the Fisher purified grade Be(NO&. (1) Taken from the Ph.D. Thesis of W. R. Carper, University of Mississippi, 1963. (2) Address correspondence to this author at the Center for Computer Science and Technology, Institute of Technology, National Bureau of Standards, Washington, D. C. 20234. (3) W. R. Carper and P. A. D. de Maine, J. Chem. Eng. Data, 9, 316 (1964). (4) W. R. Carper and P. A. D. de Maine, unpublished data. (5) P. A. D. de Maine, Comm. Assoc. Computing Machinery, 8 , 518 (1965). (6) P. A. D. de Maine and R. D. Seawright, I n d . Eng. Chen., 55, No. 4, 29 (1963). (7) P. A. D . de Maine and R. D. Seawright, “Digital Computer Programs for Physical Chemistry,” The Macmillan Co., New York, N. Y.: (a) Val. I, 1963; (b) Val. 11, 1965.
CONDUCTANCE OF GROUP 11-A METALSALTS
381
3Hz0, Fisher Reagent grade Mg(N03)2.6H20, and Baker Reagent grade Ca(N03)z.4H20the cation content checked to within 0.4% of the theoretical value. The standard solutions used in the calibration of the conductance bridge and cells were prepared from conductance water and calcined Analar grade KC1, both saturated with the dry nitrogen. Preparation of solutions, filling the conductance cell, and sealing the cell were carried out in a dry nitrogen atmosphere. Resistance measurements were made by the four leads method at 10,20,30,35, and 40’ with the precision conductance equipment to be described. For each solution at each temperature the resistances (Ev)measured at 20, 5, 2, and 1 kc (V) were plotted against 1/V and the resultant straight line was extrapolated to infinite frequency. Only extrapolated resistances, E,, have been used in our calculations. Resistance measurements with fresh solutions showed reproducibility within 0.1%. Static dielectric constants for the methanol mixtures were measured at 10, 20, 30, 35, and 40’ with the high precision Wissenschaftlich-Technische Werkstatten multidekameter bridge (Type DK-06) described elsewheree9 Viscosity coefficients for the salt solutions at 20’ were calculated in the usual manner from flow times measured by means of a free-flow electroviscometer. lo Concentration ranges for the solutions studied are given in Table I. Table I: Salt Concentration Range (Scr) and the Per Cent Volume of CCld (near 20’) for the Salt-Methanol-CC4 Solutions (G is the Number of Different Salt Concentrations at Which Conductances Were Obtained) Salt
Ca(NO&. 4H20 Mg(NOd2.6H20 Be(NO& * 3H20
% CClr
Scr X 104, M
(3
0.00 0.00 0.00 0.02 0.06 0.10
3.682-36.82 4.847-48.47 3.989-39.89 3.989-39.89 3.989-39.89 3.989-39.89
9 10 10 10 10 10
Description and Calibration of Equipment. The precision conductance bridge was a copy of one already described” which uses the “four leads method.”I2 The central component is a General Radio Co. 1605-A85 impedance bridge. Bridge resistances were carefully checked’ against resistors obtained from the National Bureau of Standards. Our operational methods have been fully described by Janz and McIntyre.” Conductance cells were mounted with a Plexiglas collar bound by aluminum strips for easy insertion into
the high-precision thermostated 30-gal capacity oil bath. The constants for the two Sargent (Type S29815 and 5-29885) conductance cells were determined at several temperatures by the method of Lind, Zwolenk, and FUOSS’~ through use of KCl-HZO solutions and data in the literature.sb Cell constants were 0.9122 (10.OoO4) and 0.002248 (i0.000002). The constant temperature bath was constructed from a fiber-glass-insulated stainless steel film-developing tank of 35-gd capacity. Heat was supplied by 42 15-w light bulbs mounted on chemically resistant Plexiglas-55 and totally immersed in the 30 gal of Fisher conductance bath oil in the tank. Fifteen switches permitted use of any number of light bulbs. A refrigeration unit, consisting of a compressor (pressure 150-202 psi) containing Freon-12 gas and a 0.25-hp motor, was attached under the tank. The cooling coils lay along two opposite inner sides of the tank and perpendicular to the heating tray of light bulbs. Two high-speed multiple-bladed stirrers, driven by 0.05-hp Dayton Electric Co. 5K002 air-cooled motors and controlled by conventional heavy-duty variacs, were mounted in diagonally opposite corners of the tank in order to maintain temperature uniformity in the bath. A heavy-duty (30-amp) Curtin Model 7600 negative (normally off) mercury relay switch and a mercuryplatinum variable thermostat controlled the refrigeration unit to within O.0lo of the desired bath temperature. A Fisher transistor relay (Model 30) and a sensitive mercury-toluene thermostat, constructed in our laboratory, controlled the heating circuit. The conductance bridge and thermostated oil bath were in an air-conditioned dehumidified room with less than 2’ temperature variation over long periods. The bath temperature, frequently checked with a Beckmann differential thermometer which had been calibrated against a National Bureau of Standards thermometer, varied less than 0.005’ over several days. This cor-
(8) (a) N. A. Lange, “Handbook of Chemistry,” Handbook Publishers Inc., Sandusky, Ohio, 1956; (b) “Handbook of Chemistry and Physics,” 41st ed, Chemical Rubber Publishing Co., New York, N. Y., 1960; (c) B. E. Conway, “Electrochemical Data,” Elsevier Publishing Co., New York, N. Y.,1952; (d) L. Scheflon and M. B. Jacobs, “The Handbook of Solvents,” D. Van Nostrand Co. Inc., New York, N. Y.,1953. (9) P. A. D. de Maine, J. 5. Menendez, and W. C. Herndon, unpublished data. (10) P. A. D. de Maine and E. R. Russell, Can. J. Chem., 39, 1929
(1961). (11) G.J. Janz and J. D. E. McIntyre, J. Electrochem. Soc., 108,272 (1961). (12) F. S. Feates, D. J. G. Ives, and J. H. Pryor, ibid., 103, 580 (1956). (13) J. E. Lind, J. J. Zwolenk, and R. M. Fuoss, J . Am. Chem. Soc., 81, 1557 (1959).
Volume 70,Number 2 February 1966
382
responds to a maximum error in the measured resistance of 0.01% for a temperature coefficient of 2%/OC. The resistances of all solutions were measured initially at 20' and then the solutions were slowly brought to another temperature by slow changes (less than 2O/hr) in the bath temperature in order to avoid Soret'4 eflects. Photochemical effects were eliminated by dying the bath oil with croceine scarlet (National Aniline Corp.).
Data Processing Method In the self-judgment method of curve fitting,' the preselected limits of reliability for the raw data, as defined by the instrument reliability factors, are considered an intrinsic part of the experimental information. Values for the ordinates and their associated maximum permitted errors are computed from this information. The self-judgment principle6 is used to reject those data points farther than the maximum permitted error from the median curve. Median values for the parameters ( P ) and their maximum possible (permitted) errors ( A P ) are computed from the G2 accepted data points and their associated maximum permitted errors. I n the de~cription?~ of the conductance feeder program 32 (call word FBAAA) the 16 equations tested are described fully. All salt concentrations and solution densities were computed from weights and/or volumes of the components (measured near 20') by means of program 5 (call word AAAAE). Ideality of solutions at each temperature was assumed, and density measurements of selected solutions at 40' showed that this assumption was responsibIe, a t most, for an error less than 0.1%. All conductance-viscosity data were processed with the variable dimensioned programs 32 and 326 (call words FBAAA and ZAAAS)'" which contained the newer definition of maximum possible error (Appendix E of ref 7b). In program 32 the instrument reliability factors selected were as follows: WAC11 = WAC21 = 1.0, lowest (WL21) and highest (WUl1, WU21) measured values for specific conductance (WU11) and concentration (WL21, WU21). The two maximum permitted deviations (DEVF1 and DEVF2) were both set equal to 0.5, 0.4, 0.2, and 0.1% in turn. Each of the 16 conductance equations?" was examined for data compatibility. For each equation a t each temperature the reject-reatore commands' for program 326 were selected after examination of autoplots of data prepared with program 501 (call word AEEEE).
Results and Discussion With DEVFl = DEVF2 = 0.005 (ie., with limits of 0.5y0)only three16 of the 16 conductance equations The Journal of Physical Chmistry
W. R. CARPERAND P. A. D. DE MAINE
listed in Chapter IX of ref 7b were compatible with the new data. Included in the 13 equations which the data do not fit are the second ( L = 3) and third ( A = 4) Fuoss-Onsager equations which contain the mean activity coefficient cf) and fraction of salt dissociated (r>.16 For each salt system a t each temperature and for each solvent composition the Walden product, viscosity coefficient (7) times molar conductance ( p ) , increases markedly as the salt concentration ( M ) decreases. Values for 7, p , Walden product, and M are given in Table I1 for methanol systems a t 20'. These results Table 11: Values for Molar Conductance ( p ) , Viscosity Coefficient ( v ) , and Walden Product ( q p ) at 20" for Methanol Solutions of the Salts at the Indicated Concentrations Concn,
?I
Salt
M X 10'
P
CP
Ca(NO&. 4H20
3.68 7.36 11.06 14.73 18.41 25.77 29.45 33.14 36.82
108.66 95.81 88.70 83.91 80.59 75.15 74.13 72.21 70.33
0.576 0.579 0.580 0.581 0.581 0.582 0.582 0.583 0.585
62.58 55.48 51.45 48.72 46.82 43.71 43.14 42.07 41.11
3.99 7.98 11.97 15.96 19.95 23.94 27.93 31.91 35.90 39.89
138.33 118.62 110.22 104.02 99.39 95.28 93.51 91.25 89.20 86.32
0.580 0.581 0.581 0.582 0.582 0.582 0.582 0.582 0.583 0.584
80.26 68.89 64.17 60.49 57.82 55.43 54.42 53.13 51.98 50.38
4.85 9.69 14.45 19.39 24.23 29.08 33.93 38.77 43.62 48.47
176.41 162.58 153.44 147.08 142.95 139.08 135.18 133.75 129.68 126.47
0.579 0.581 0.582 0.583 0.584 0.584 0.585 0.586 0.587 0.587
102.16 94.38 89.26 85.69 83.41 81.28 79.12 78.36 76.07 74.28
1P
(14) R. M. Stokes, J. Phys. Chem., 65, 1277 (1961). (15) The first Fuoss-Onsager (L = 2), the expansion (L = 5), and the specific conductance vs. salt concentration (L = 12) equations. (16) Compatibility with these equations was tested by assuming that roJand j * have the form: +'.6 = a1 alc0*6 . a,+r ~ " 1 2 . With this expansion rnethod,lb actual values for y0e6 and j *
+
are not required.
+..+
383
CONDUCTANCE OF GROUP 11-A METALSALTS
Table 111: Results of Data-Compatibility Tests by the SelfJudgment Method for the Indicated Salt Dissolved in Methanol at 20' with the Expansion (E) ( p = pa SIC''^ SZC S3Calx S4Ca) and Fuoss-Onsager (F-0) ( p = h SIC'/^ S2C In C &C, with $2 = E and Sa = J F h ) Equations. Maximum Permitted Errors Are Given in Parentheses and the Selected Maximum Permitted Deviations for the Molar Conductance (1.1) and Salt Concentrations (C) Are DEVFl and DEVF2, Respectively. The Salt Concentration (C) and Relative Location ( R L ) ,Beginning a t the Lowest C, of Rejected Data Points Are Given in the Last Column. Term. Means That the Calculation Was Terminated Because Less Than Four Data Points Were Accepted
-
DEVFl = DEVFP
Eq
E F-0 E F-0 E F-0
Ca(NOs)z* 4H20' 0.004 0.004 Be(NOa)s* 3HzOb 0.005 0.005 0.004 0.004 0.002 0.002
E F-0 E F-0 E F-0 E
Mg(NOa)a 6Hz0 0.005 0.005 0.004 0.004 0.002 0.002 0.001
E F-0
F-0
+
+
+
+
+
S1/10'
- 3.78 (0.54)
Sr/lOS
+
RL (c x 104)
w
0.613 (0.170) -0.443 (0.159)
-4.29 (1.70) -0.511 (0,242)
0,616 (0,315)
-5.06 (0.98)
161.5 (4.4) 168.5 (6.70)
-8.22 -8.24 -8.74 -8.95
(0.93) (1.53) (0.59) (1.15)
1.92 (0.29) -0.777(0.238) 2.10 (0.17) -0.888 (0.180)
-22.12 (2.98) -0.931 (0.356) -24.61 (1.55) - 1.10 (0.27)
9.77 (0.73)
241.8 (7.9) 234.5 (10.8) 246.8(5.0) 240.3(8.2)
-7.90 (0.75)
-0.733 (0.115)
-0.842 (0.173)
-0.535 (1.243) -4.74 (2.06) -0.535 (0.994) -4.42 (1.82) - 1.10(1.72) -4.42(0.91) -0.773(0.842)
-0.602 (0.343) -0.372(0.291) -0.602(0.274) -0.329 (0.256) -0.398 (0.604) -0.329(0.128) -0.515 (0.296)
13.52 (3.17) -0.417(0.411) 13.52(2.53) -0.357 (0.359) 10.47 (8.63) -0.357(0.180) 12.15 (4.23)
10.90 (0.16)
+
6 (22.1) 6 (22.1)
6(23.9) 6(23.9) Term. 2 (7.95), 6 (23.9), 9 (36.0)
231.5(5.6)
-8.75 (0.67) -8.75 (0.53)
-7.13 (4.35) -7.99 (2.13)
205.0 (12.3) 241.3 (16.9) 205 .O (9.8) 238.2 (15.2) 210.5(16.0) 238.2(7.6) 207.3(7.85)
8 (38.81) 7 (33.9), 8 (38.7) 8(38.7) 5(24.3), 7 (33.81, 8 (38.7) Term.
0.001
For DEVFl = DEVF2 < 0.004 calculations for the expansion and Fuoss-Onsager equations are terminated ( i e . , RL(C) = Term.). = DEVF2 = 0,001 RL(C) = Term.
' For DEVFl
suggest that the order of cation mobilities is Mg2+ > Be2+> Ca2+. Elsewhere, it was reported that addition of up to 1 mole % of water to salt-methanol systems yielded maximum changes of 3.0 and 0.5% in the viscosity coefficient" and molar conductance,lS respectively. Thus the unexpected reversal in cation mobilities cannot be attributed to nonideality or partial reversible solvolysis of the ions or to hydrolysis of the cation with formation of hydrogen ions. Calculations for the dilute solutions show that the equivalent conductance for each salt at each temperature is substantially less than SOT0 of its limiting value extrapolated from the Fuoss-Onsager or the expansion equations (see below). Thus each of the three salts is only partially ionized in dilute solution (10-4 M I . The new method of curve fitting (see data-processing method) with DEVFl = DEVF2 = 0.005, 0.004, 0.002, or 0.001 was used to test compatibility of the
new data with the Fuoss-Onsager equationI9 and with the equation p = po
+ s1co.5 + s2c +
s3c1.5
4-s4c2
Here p and C are the molar conductance and salt concentration, respectively. I n Table 111 are given details of these tests for methanol solutions a t 20'. For the magnesium nitrate the data fit the expansion equation best. For the Ca and Be salts the pattern of rejected data points shows clearly that the poor fits for both the Fuoss-Onsager and expansion equations are not due to uncertainty in the data. Similar results were obtained a t each temperature. The ~~
~~
~
~
(17)D. 0.Johnston and P. A. D. de Maine, J . Chem. Eng. Data, 8 , 586 (1963). (18) M. M.de Maine and P. A. D. de Maine, J . Miss. Acad. Sci., 8, 294 (1962); D.0.Johnston and P. A. D. de Maine, J . Electroc h a . Soc., 112, 530 (1965). (19) R. M.Fuoss and L. Onsager, J . Phys. Chem., 61, 668 (1957).
Volume 70, Number .2 February 1966
W. R. CARPERAND P. A. D. DE MAINE
384
s
dielectric constant of the solvent. Plots of similar form were obtained at each of the five temperatures. Two linear regions in plots of specific conductance os. salt concentration are found for many rare earth, transition metal, and alkaline earth salts dissolved in alcohol or al~ohol-CCl~.~ The conclusion that for
6.7
’ X
6.8
L
.*
$
6.9
.* 13
E 7.0 13 0 CI
7.1 3
I
ii
32.62
I
32.63 Dielectrio constant.
I
11
32.64
Figure 1. Intersection point us. dielectric constant of methanol-carbon tetrachloride mixture for Be( NO& .3Hz0 at 20”.
comparatively large maximum permitted errors in the limiting molar conductance ( P O ) for precision data illustrate another inherent weakness of conventional curve-fitting methods. The Fuoss-Onsager equation incorrectly predicts that the limiting molar conductances are in the order hlg = Be > Ca salts (Table 111). With the expansion equation the expected order (Be > Mg > Ca salts) is obtained. Moreover, the large negative values obtained for SI,E, and J - Fpo with the Fuoss-Onsager equation appear to be of no real significance physically. Mathematical arguments2O and the fact that the Onsager equation (p = p o BC0e6) is an asymptotic form of the empirical “expansion” equation provide additional justification for its use in computing the limiting molar conductance (PO). For the Be(NO& -3H20-CHaOH-CC14 systems, plots of specific conductance vs. salt concentration (at fixed temperature and solvent composition)4 consist of two intersecting straight lines, each defined by at least four data points. The self-judgment method of curve fitting with DEVFl = DEVF2 = 0.002 was used to obtain median values for the parameters for each pair of lines, and Table IV contains results for the Be(N03)2.3H20 systems at 20’. Figure l shows the salt concentration at the point of intersection (C,) of the two lines plotted as a function of the static
+
The Journal of Physical Chemistry
Table IV : Data for Plots of Specific Conductance us. Be(NO&. 3H20 Concentration for CHsOH-CCL Solutions a t 20’. For the Linear Portions in Two Concentration Regions Are Given Values for the Slope (S)and Intercept ( I )on the Ordinate. Cr Denotes the Concentration a t Which the Two Linear Sections of Each Plot Intersect. GI/G = 4/5 Means That Four of the Five Data Points Were Accepted when DEVFl = DEVF2 = 0.002 cancn range, M
-Salt
%
7 3 . 9 9 to 19.95-7
x
lo--
7 2 7 . 9 3 to 39.89--
CClr (vol)
sx
IX
sx
IX
Gl/G
100
10s
Gl/G
100
106
CIX lo*
0.00 0.02 0.06 0.10
4/5 5/5 5/5 5/5
8.13 8.17 8.15 8.11
3.34 3.59 3.58 3.59
414
5.43 5.43 5.40 5.37
21.46 21.94 22.57 22.78
6.70 6.80 6.89 7.01
4/4 4/4 4/4
each salt concentration region a different ionization process predominates is unacceptable in the continuum model of ionization. However, if this view is accepted, the nonlinearity of the plots of “point of intersection” vs. solvent dielectric constant (Figure 1) and similar results for several aliphatic alcohols4 indicate that bulk solution and/or solvent properties are not the primary factors in the ionization of these salts in alcohol-CC14 solutions. These results can be understood if it is supposed that complex formation and the geometry of the solvent lattice are important precursors to ionization.
Acknowledgment. Sincere thanks are due the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. (20) J. B. Scarborough, “Numerical Mathematical Analysis,’’D. Van Nostrand Co. Ino.,New York, N. Y., 1953.
