FLUIDITY OF ELECTROLYTES. I1
511
these strains, to give a thermodynamically more stable structure, produces slow internal changes persisting over a long period of time. Very slow cooling through temperatures only slightly below those at which the glass is fluid favors the production and growth of crystalline regions in the mass, the importance of this tendency being very greatly dependent on the composition, however. Such crystalline regions-especially if the crystal structure is quite anisotropic, with strength and other properties varying greatly with direction-may be very deleterious, producing inhomogeneity and other undesirable properties in the final product. SUMMARY
The equilibrium between crystalline and non-crystalline conditions in a solid or liquid and the rate at which the equilibrium state is approached are considered as functions of ( I ) the net energy changes for small internal structural rearrangements (shifts of position of single atoms or of orientation of groups of atoms), (8) the activation energies for such rearrangements, and (3) the temperature. Annealing and devitrification phenomena and the necessary requirements for the (practically) permanent existence of a vitreous substance are considered from this standpoint. REFERENCE (1) LAMER,V. K.: J. Chem. Phys. 1,289 (1933).
T H E FLUIDITY OF ELECTROLYTES. I1 EUGENE C. BINGHAM AND ROBERT T. FOLEY Department of chemistry, Lafayette College, Eaaton, Pennsylvania Received March 10, 1943
In the former paper (1) the fluidity elevation of the individual ions was calculated and the additivity of the fluidities demonstrated. It is now proposed to study the rheological data of mixtures of electrolytes in order to explain certain anomalies. The viscosities of mixtures of inert liquids were early erroneously assumed to be additive (curve AT in figure 1): 7 = aw
+ bm
(1)
Only slowly has it become clear that the fluidities (PI and (02 must be additive, and that the concentrations of the components a and b used must be volume fractions of the components. Even then (4,6)the equation rp
=
~i
+
b92
(2)
512
E'CGEXE C. BIKGHAN A N D ROBERT T . FOLEY
(the curve Nv (normal mixture)) frequently shows n ell-recognized deviations from the observed data, deviations which are of t n o kinds. In the one case, as in that of aniline and pyridine, the components appcar to unite to form a compound of lower fluidity, curve Cp (combining mixture), in the second, typified by potassium nitrate dissolved in water ( 5 ) and also by certain non-electrolytes, there is apparently a breaking down of the association of the water or other complexes, resulting in an elevation of the fluidity curve Dp (dissociating
A
0.5
B
FIG,1. Diagram showing that the curve of additive fluidities Nq gives a normal viscosity curve ivq, to be distinguished from the curve (A?) which would be obtained were viscosities additive. Substances which on mixing give a negative curvature Dq give & viscosity curve Dq which is readily distinguished from Aq, but when there is positive curvature on mixing, the viscosity curve C? approaches more nearly t o As.
mixture). It appears from figure 1-and it may be proved that the conclusion is general-that (1) the values on the Nq (normal viscosity) curve1 are always lower than expected if viscosities were additive, Aq; ( 2 ) that the Dq curve2 is still lower; but (9)that the Cq curve3 is not so low as the Dq curve. But these 1
Obtained by plotting the reciprocal of the fluidity of the Kq curve. the reciprocal of the fluidity of the Dg curve. Obtained by plotting the reciprocal of the fluidity of the Cq curve.
* Obtained by plotting a
FLUIDITY OF ELECTROLYTES. I1
513
predictions are less and less important as the fluidities of the components approach equality. Thus any pair of liquids which on mixing gives a linear fluidity curve should give a viscosity curve whiah is lower than that calculated by equation 1. Moreover, any pair of liquids which expahds on mixing, absorbing heat and exhibiting a fluidity of the Dp type, will show the same effect to an even greater degree, Le., the curve will be still lower, D?. Only when there is evidence of chemical reaction between the components, indicated by heat evolution and contraction as well as in the Cp curve, will the position of the viscosity curve be uncertain, sometimes lower than the calculated but sometimes higher. These peculiarities of behavior afford good but heretofore unused evidence as to the correct additive function. The authors have tested these predictions, using the data of Ruby and Kawai (14) and of Briickner (7). In both cases the deviations between the observed and calculated values are reduced one-half by using the additive fluidities, and the deviations verify the above predictions. A study of the data enables US to point out a fact which has heretofore escaped notice. When two solutions having a common ion, such as hydrochloric acid and potassium chloride or ammonium chloride and potassium chloride, are mixed, the observed fluidity is appreciably below the calculated value. The clue to the reason is the fact that when two solutions of different concentration of any one of the above salts are mixed in equal volumes, the fluidity of the mixture is above the expected linear mean value. When, therefore, a solution of potassium chloride, for example, is mixed with a solution of some other chloride, the potassium ion is diluted, tending to increase the fluidity. If, as in the case of hydrochloric acid and ammonium chloride, they both show the same behavior, there will also be an increase of fluidity due to the dilution of both ions. This correction is most noticeable in the more concentrated solutions, but it amounts to a maximum of 1 per cent for mixtures of 4 N hydrochloric acid and 4 N potassium chloride, and to 0.8 per cent for mixtures of 4 N hydrochloric acid and 4 N sodium chloride, but it is inappreciable for mixtures of 4 N hydrochloric acid and 4 N sodium chloride. With 4 N ammonium chloride and 4 N sodium chloride, the correction rises to a maximum of nearly 6 per cent. Neither Ruby and Kawai nor Briickner have expressed their results as fluidities. We therefore give table 1 for the most concentrated solutions (4 N ) measured by Ruby and Kawai a t 25°C. with the Ostwald viscometer, with an accuracy claimed of 0.05 per cent. The mixtures are so made up that in every case the total normality is four. It will be noticed that the deviations are regular and probably significant. Most interesting are the changes of sign in the deviations, for which we have offered an explanation. These authors worked with solutions having a common ion (Cl-), and therefore in dilute solutions the conditions are very simple. Still simpler, however, are the cases studied most carefully by Briickner, who employed mixtures of equal volumes of solutions of the same salt at different equivalent concentrations at 15°C. and 20"C., using an excellent instrument of his own design. In tables 2 to 5 we give his data for the viscosities and spehfic
514
EUGENE C. BINGHAM AND ROBERT T. FOLEY
volumes of solutions of sodium chloride, barium chloride, potassium chloride, and ammonium chloride a t the different concentrations with equivalent fluidiTABLE 1 Fluidities of mixtures of electrolytes (Ruby and Kawai) PER CENT
ELECTROLYTES
__ 4.0 3.2 2.4 1.6 0.8 0
NaC - _______
1.0954 1.0932 -0.20 1.0574 1.05701 O.Oo(j 0 0.8 1.6 2.4 3.2 4.0 4.0 3.2 2.4 1.6 0.8 0
0
I
I
0.04) 1.13091 1.14831+1.54/1 1.2118 1.2396+2 29 1.3024 1.33101+2:?111 1.4030 1.4223'+1.38i 1.51361 1.51361 0.001
I
-
General average.. . .. .. . . . . . .
i o.oo/l .I
Pealed.
DEVIA-
TION
__ __
1.23781 1.23781 0.001) 1.2068 1.2016 -0.43
0 0.8 1.6 2.4 3.2 4.0 4.0 3.2 2.4 1.6 0.8 0
Pobiid.
(av')
90.41 92.73 95.54 98.68 02.16 05.88
90.41 93.50 t0.83 O.O0 96.60 99.69 02.79 05.88
98.96 92.35 85.94 79.76 73.94
99.49 93.10 86.72 80.33 73.94
77.26 80.64 83.96 87.20 90.41
77.23 80.53 83.82 87.12 90.41
~
pl
1
I1
-0.04 -0.14 -0.17 -0.09
0.39
0.761
1
I _
TABLE 2 Viscosities of sodium chloride solutions (Bruckner) m
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
(OBSERVED)
1.0008 0.9808 0.9617 0.9441 0.9266 0.9112 0.8621 0.8816 0.8678 0.8544 0.8420
0.011439 0.011826 0.012355 0,012951 0.013651 0.014475 0.015435 0.016618 0.017833 0.019315 0.021 178
87.42 84.56 81.07 77.21 73.26 69.09 64.79 60.54 56.08 51.78 47.23
0.010086 0.010482 0.010962 0.01 1513 0.012147 0.012878 0,013745 0,014682 0.015839 0.017089 0.018673
99.15 95.40 91.22 86.87 82.32 77.64 72.76 68.11 63.13 58.51 53.57
ties. Having these solutions, mixtures of equal volumes were made from them and the viscosities determined. These data are given in tables 6 to 22 inclusive, together with the calculated value?.
615
FLUIDITY OF ELECTROLYTES. I1
Bruckner himself did not question the validity of the additive viscosity formula, but in 97 per dent of the mixtures studied, the viscosities calculated
TABLE 3 Viscosities of barium chloride (+BaCls) solutions (Brwkner) ul
0.0
0.5 1 .o 1.5 2.0 2.5 3.0
(OBS%VED)
1.0008 0.9572 0.9182 0.8823 0.8500
0.8189 0.7902
0.011439 0.012018 0.012687 0.013413 0.014238 0.015203 0.016383
(OdELD)
87.42 83.20 78.81 74.55 70.23 65.77 61.04
0.010086 0.010645 0.011285 0.011967 0.012722 0.013615 0.014688
(OBSERVED) *ma
99.15 93.94 88.61 83.56 78.61 73.45 68.08
TABLE 4 Viscosities of potassium chloride solutions (Brilckner)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
1.0008 0.9780 0.9562 0.9363 0.9175 0.8996 0.8824 0.8666
0.011439 0.011247 0.011140 0.011065 0.011085 0.011105 0.011212 0.011346
87.42 88.91 89.77 90.38 90.21 90.05 89.19 88.13
0.010086 0.009990 0.009952 0.009923 0.009980 0.010045 0.010175 0.010314
99.15 100.10 100.48 100.78 100.30 99.55 98.28 96.95
TABLE 5 Viscosities of ammonium chloride solutions (Briickner) a
0.0 0.5 0.75 1 .o 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
1.0008 0.9927 0.9883 0.9849 0.9774 0.9703 0.9637 0.9574 0.9606 0.9450 0.9391 0.9335
%a
(OBSgVED)
(OBSEPVED)
0.011439 0.01126i 0.011183 0.011129 0.011000 0.010913 0.010862 0.010826 0.010810 0.010861 0.010906
87.42 88.75 89.42 89.86 90.91 91.63 92.06 92.37 92.51 92.07 91.69 90.38
0.011065
0.010086 0.009992 0.009940 0.009924 0.009846 0.009806 0.009789 0.009794 0.009813 0.009879 0.009967 0.010108
99.15 100.08 100.60 100.77 1111.58 101.97 102.15 102.11 101.91 101* 22 100.32 98.93
by his formula are higher than the observed values. This is exactly similar to what has been observed with mixtures of non-electrolytes, as noted by several observers, notably Wijkander, Hatschek (lo), Linebarger (12), Dunstan (S),
516
EUGENE C. BIKGHAY Ah-D ROBERT T. FOLEY
and Kendall ( l l ) , as Tyell as Thorpe and Rodger. These last (15) remark, “The viscosity of a mixture is as a rule uniformly lower than the mixture law TABLE 6 Viscosities of qual volumes of solutions of different concentrations sodium chloride (Briickner)
1
2
3
2
~
0.9441
’
(OBSERVED)
0.012951
77.21
0.011513
86.77 -0.10 81.99 -0.39 77.18 -0.46 72.40 -0.36
3
0.9266
0.013651
73.26
0.012147
4
0.9112
0.014475
69.09
0.012878
5
0.8961
0.015435
64.79
0.013745
3
0.9112
0.014475
69.09
0.012878
77.64
4
0.8961
0.015435
64.79
0.013745
72.76
5
0.8816
0.016518
60.54
0.014682
4
0.8816
0.016518
60.54
0.014682
5
0.8678
0.017833
56.08
0.015839
!
I
63.13
,
I
4
5
0.8346
0.019315
the same salt:
nm’
*is* DESERVED
2
__
(2) of
1
-0.10 56.01 -0.07
1
51.66
1
77.54 -0.10 72.72 -0.04 67.94 -0.17 67.94 -0.17 63.16 +0.03
1
0.017089 I 58.51
51.78
69.02 -0.07 64.67
I
, -0.12
58.35 -0.16
Mean deviation of calculated fluidity from the observed is 0.3 per cent. TABLE 7 Viscosities of equal volumes of different concentrations of the same salt: t(BaC1,) (Bruckner) I
1
**s* (CALCU-
LAIEU)
0.8823
0.013413
74 55 ~
0.011967
83.55
0.8500
0.014238
70.23
0.012722
78.61
0.8189
0.015203
65.77
0.013615
73.46
74.52 -0.03 69.92 -0.31 65.64 -0.13
83.61
+O .06 78.38 -0.23 73.34 -0.12
would indicate.” Briickner noted this too, and he says in almost the same terms, “The viscosity of a mixture of two solutions is always less than the arithmetical mean of the viscosities of the components,” and he made the further significant
517
FLUIDITY OF ELECTROLYTES. I1
remark, “The difference is the greater as the difference between the molecular concentrations of the components is increased.” If the fluidities’are additive, we have a right to expect the calculated viscosities of Bruckner to be greater than his observed values, as is the case, and we may expect the difference to be greatest (3) where the difference in concentrations is greatest, because then the viscosities would be expected to differ most widely. In fact, by using the addiTABLE 8
Viscosities of equal volumes of different concentrations of the same salt: IZCl (Brtickner) 1
I
*a(OBSERVED)
1
1
~
0.9363
0.011065
90.38
0.009923
100.78
0.9177
0.011085
90.21
0.009980
100.20
0.8996
0.011105
89.96
0.010045
99.55
90.30 -0.08 89.78 -0.43 89.70 -0.26
2 3
Viscosities of equal volumes of NaCI ( m =
and NH&l ( m =
2)
ha’ (CALCGLATED)
100.39 -0.39 99.38 -0.82 99.29 -0.26
solutions (Briickner)
:OBSERVED) VIP
1.0
0.9209
0.013608
73.49
0.012152
82.29
2.0
0.9154
0.013609
73.49
0.012197
81.98
3.0
0.9098
0,013642
73.31
0.012246
81.66
77.70 f4.20 78.21 +4.72 78.58
4.0
0.9045
0.013689
73.06
0.012332
81.09
78.43
5.0
0.8991
0.013824
72.34
0.012487
80.08
77.59
86.76 +4.47 87.36 $5.38 87.44 +5.78 86.99 f5.90 85.84 1-5.76
TABLE 10
Viscosities o j equal volumes of NaC1 ( m = 0.6) and NHdCI (m = 0.76) solutions (Briickner) m ~
_
0.75
(os;%im) _
_
_
0.9845
(oB&%vED) _
~
0.011512
(o2&m) ~
_
_
86.88
(0B:KvEo) _
_
0.010213
,
(OB?%ED)
_
_
97.91
( C A 2 L E D ) _
_
_
86.99 +0.11
(c.d%rm) _
_
98.00
+o.w
_
.
_
_
_
_
_
TABLE 11 Viscosities of equal. votumes of solutions of NaCl (m = 1 ) and 4(BaClz) (m = a!)* (Briickner) (CALEULATED) *me
0.0
0.9808
0.6
0,9599
1.0
0.9393
1.5
0.9201
2.0
0.9023
84.70
2.5
0.8846
82.24
0.011826 +71 0.012146 +41 0.012520 +1 0.012863
84.56
95.40
82.33
92.77
79.87
89.89
77.74
87.38
84.27 -0.29 82.14 -0.19 79.94 +0.07 77.81 +0.07 75.65 +0.17 73.42 +0.07
0.8666
3.0
95.19 -0.21 92.58 -0.19 89.92 +O .03 87.44 +O .06 84.92 $0.22 82.34 $0.10 79.65 4-0.40
I
*Mean probable error f 0 . 1 1 per cent. TABLE 12
Viscosities of equal volumes of solutions of NaCl (m = 3) and )(BaCIs) (m = x)* 5
%O
p,lo
(CALCULATED)
-__ 0.0
0.9617
1.0
0.9222
1.5
0.9046
2.0
0.8868
2.5
0.8695
3.0
0.8525
* Mean
0.012355 +I90 0.013110 $59 0.013475 +57
80.93
91.22
76.28
85.72
74.21
83.27
80.34 -0.59 76.04 -0.24 73.91
90.74 -0.48 g5.47 -0.26 82.94 -0.33 80.46 -0.11 77.88 -0.03 75.20 $0.27
probable error f O . l l per cent. TABLE 13
Viscosities of equal volumes of solutions of NaCl (m = 3) and +(BaCln)I z
0.0
aisD
0.9441
1.0
0.9067
2.0
0.8725
3.0
0.8395
i
*me
*!P
(OBSERVED)
(CALCULATED)
77.21
86.87
72.48
81.32
67.77
75.95
62.93
70.42
76.09 -1.12 71.78 -0.70 67.49 -0.28 62.90
*P,*
(OAY~ED)
1-0.012961+486 0.013798 +263 0.014756 +81 0.015891 +18
(OBsEawD)
___-
= I)* (CAL%TED)
85.94 -0.93 80.69 -0.63 75.69 -0.26 70.42 0.00
519
FLUIDITY OF ELECTROLYTES. I1
TABLE 14 Viscosities of equal volumes of NaCl ( m = 1 ) and NH&l ( m = x) solutions (Brilckner) Qlg
X
(oB2%ED)
(OBsEnwD)
(OBsEVED)
(OBSERVED) *no
0.5
0.9768
____________ 0.011761 85.02 0.010444
1.0
0.9731
0.011710
85.40
0.010418
95.98
1.5
0.9691
0.011848
85.85
0.010396
96.I9
2.0
0.9659
0.011593
86.26
0.010364
96.49
3.0
0.9589
0.011519
86.83
0.010329
96.81
4.0
0.9524
0.011456
87.33
0.010313
96.96
5.0
0.9466
0.011430
87.49
0.010327
96.83
95.75
TABLE 15 Viscosities of equal volumes of NaCl (m = ; and NH&l (m = nr
--
QIP QW' 'CALCULATED) (CALCULATED)
~ _ _ 84.91 95.65 +0.09 -0.10 85.83 96.00 +0.02 $0.83 85.99 96.40 $0.21 +0.14 86.35 96.60 +0.09 $0.11 96.66 86.72 -0.11 -0.15 86.57 96.22 -0.74 -0.76 85.72 95.08 -1.77 -1.75
5)
solutions
Qd
(OBS%~VED)
( 0 2 L D )
02&ED)
1.0
0.9545
0.012228
81.77
2.0
0.9483
0.012136
3.0
0.9420
4.0 5.0
(OBS%'ED)
(
*UO
OBSEBVED)
CALCUWLTED
0.010891
91.82
82.40
0.010868
92.10
81.93 $0.16 82.44
0.012094
82.68
0.010858
92.10
0.9367
0.012084
82.85
0.010878
91.93
0.9299
0.012077
82.80
0.010923
91.55
$0.04
82.82 $0.14 82.66 -0.19 81.82 -0.98
%ckner) %la
ALCULATED)
91.54 -0.28 92.14 +0.04 92.22 $0.12 91.77 -0.16 90.62 -0.91
TABLE 16 Viscosities of equal volumes of solutions of NaCl (m = 8 ) and KCI ( m = x) (Bruckner) (O&VXD)
0.0
0.9441
1.0
0.9247
2.0
0.9068
0.012951 +486 0.012943 +345 0.012110
%Q
( o B 2 L D )
(OBsEEvED)
77.21
88.87
77.26
86.58
76.88
85.88
76.28
84.86
75 * 93
84.39
$254
3.0
0.8895
3.5
0.8809
0.012311 +214 0.012317
+zm
~
41.
(CALCULATED)
77.28 +0.02 77.50 $0.62 76.99 f0.71 76.46 +0.53
%O
(CALCULATBD)
86.62 +0.04
86.53 +0.65 85.52 +O.M 84.86 +0.47
_
w
z
1
(OBzVED)
,_- .
___.
0.0
0.9266
1.0
0.9086
~
1.5
0.013651 +985 0.013705 $782 0.013757
1 , ~
1
(0Bs~;lVEo)
(OBSEKVED) %Om
73.26
82.32
72.97
1
~
81.74
j
72.69
1
81.27
(CALCcLATED) Q,.
1
2.5
0.8831
3.0
0.8750
3.5
~
i
0.8672 511: : : :0 ~
~
j
71.91
80.20
71.35
79.58
,
70.85
78.72
i
1475
~
72.93 -0.04 73.23 10.54 73.15 +0.90 73.08 +1.17 72.64 $1.29 72.10 f1.25
, ' ~
1
1
i ~
TABLE 18 Viscosities of equal volumes of solutions of NaCl (m = 2 ) and KC1 ( m = z 2
USE*
0.0
0.9808
0.5
0.9698
1.0
0.9591
1.5
0.9491
96.07
2.0
0.9389
95.87
3.0
0.9198
95.50
Viscositier
0.011826 +71 0.011768 +33 0.011722
84.56
95.40
84.97
95.69
85.31
95.79
TABLE 19 f equal oolumes of solutions of NaCl ( m
= 2)
(CALCULATED)
~
80.63 1617 0.013906 i-563 0.0134016
_*. ____
84.99 $0.02 85.42 so.11 86.72 -0.03 85.64 -0.14 85.13 -0.59
and KC1 ( m =
81.80 +0.06 81.96 f0.69 81.72 f1.09 81.34 +0.71 80.70 4-1.12 80.04 f1.32
Bruckner)
95.66 -0.03 95.85 +0.06
96.00 -0.07 95.76 -0.11 94.75
5)
(Briickner)
*a'
z
(OBSEBIED)
0.0
0.9617
1.0
0.9114
1.5
0.9320
2.0
0.9224
2.5
0.9131
3.0
0.9043
3.5
0.8955
0.012355 +190 0.012289 +lo7 0.012259 +98 0.012275 193 0.012277 +lo1 0.012334 +98 0,012351 +148
(CALCULATED)
80.94
91.22
81.37
91.21
81.57
91.23
81.47
90.99
81.45
90.82
81.07
90.25
80.96
89.96
520
81.51 f0.14 81.82 +O .25 81.78 +0.31 81.66 $0.21 81.23 $0.26 80.70 -0.26
91.40 $0.19 91.55 +0.32 91.31 f0.32 90.94 +0.12 90.30 f0.05 89.64 -0.32
TABLE 20 Viscosities of solutions of equal volume of KCI ( m = 2 ) and NHdCl (m = z) X
*,s*
W
1.0
97.05
1.5
96.64
2.0
96.34
2.5
95* 93
3.0
95.65
4.0
94.99
5.0
94.34
0.011129 +6 0.011072 $2 0.011021 +6 0.0110981 $21 0.0110939 +45 0.011903 $98 0.011889 $214
89.86
0.009930
100.70
90.31
0.009896
101.04
90.73
0.009880
91.06
0.009857
101.44
91.41
0.009836
101.66
91.71
0.009838
101.63
91.83
0.009856
101.45
1
101.21
Iriickner) *PO*
ALCULATED
AICULATED)
90.19 -0.33 90.34 $0.03 90.70 -0.03 90.92 -0.14 91.07 -0.34 90.92 -0.79 90.08 -1.75
100.62 -0.08 101.03 -0.01 101.22 +0.01 101.32 -0.12 101.30 -0.36 100.85 -0.78 99.20 -2.25
TABLE 21 Viscositiea of solutions of equal volumes of KCl (m = 8 ) and NH&I (m = z) (Brzickner) z
*sP
(OBggVED)
1.0
0.9494
2.0
0.9432
3.0
0.9367
4.0
0.9309
5.0
0.9249
0.011042 +65 0.010983 +16 0.010956
UCULATED
90.66
0.009907
100.93
91.04
0.009881
101.20
91.27
0.009889
101.11
91.37
0.009917
100.83
91.12
0.009967
100.32
-1
0.010945 $28 0.010974 $101
TABLE 22 Viscosities of solutions of. equal volumes of KCl ( m = 8 ) and NH,C . 2
*IS'
1.0
0.9300
2.0
0.9241
3.0
0.9183
4.0
0.9127
4.5
0.9097
5.0
0.9073
*a* (oB%LD)
0.011028 +143 0.011m +57 0.011008 +11 0.011039 -2 0.011067 -8 0.011122 +17
90.03 -0.53 90.62 -0.42 91.18 -0.08 90.64 -0.73 90.30 -0.82
100.53 -0.40 101.14
m = x)
rzickner)
-0.08
101.20 -0.09 100.76 -0.07 99.62 -0.70
46.
OBSERVED)
ALCULATED
m%hED)
100.72
89.52 -1.16 90.42 -0.44 90.78 -0.07 90.13 -0.46 90.44 -0.08 89.79 -0.12
99.52 -1.20 100.12 -0.43 100.20 -0.03
90.86
0.009945
100.55
90.85
0.009976
100.23
90.50
0.010033
99.67
90.36
0.010068
99.32
89.91
0.010127
98.74
99.75
+O 08 99.30 -0.02 98.60 -0.14 I
522
EUGENE C. BINGHdRI AND ROBERT T. FOLEY
Nevertheless, the deviations which remain are often outside of the limit of experimental error and are worthy of consideration. Bruckner mixed solutions of different concentrations of the same salt and thereby eliminated the possibility of chemical combination between difierent ions, but even when fluidities are considered, the differences mere not thereby eliminated, the deviation from linear being in cases several per cent, as in solutions of ammonium chloride: c.g., 2.5 N ammonium chloride has a fluidity of 92.06, compared with a calculated value of 88.9 = (87.42 90.38)/2. The explanation of this is identical, as given by Rabinowitsch (13) and Hingham (5) independently, but that need not concern us here. (It is the breaking up of the water complex molecules by the slightly hydrated ions.) It is enough for our present purpose to state that ammonium chloride shows “negative curvature” or it has a curve of the Dp type, as does potassium chloride. Barium chloride, on the other hand, has a fluidity curve of the normal or Np type. We may calculate the fluidities of barium chloride solutions (figure 2) by the use of the formula
+
p
= 87.44 -- 8.64~,at 15OC.
p
= 99.15
-
10.38c, a t 20°C.
where c is the normality of the salt (see also table 23). If, therefore, a 2 N solution of barium chloride is made by mixing together equal volumes of 1 N and‘ 3 N barium chloride, we calculate a fluidity for the resulting 2 N solution of 78.39 instead of the 78.61 observed, which is hardly more than experimental error. It is quite different if we prepare a 2 N solution of potassium chloride by exactly the same technique, viz., by mixing together equal volumes of 1 h’ and 3 N solutions of potassium chloride. It is not true that the calculated additive fluidity of 89.5 would be observed, because it has long been known that potassium chloride solutions show negative curvature with a maximum in fluidity a t about 5 N . In fact, the fluidity of a 2 N solution is 90.2, which is greater than that of either component of the mixture and 0.8 per cent greater than the calculated value. Attention is directed to the fact that the calculated fluidity is here less than the observed, yet had we selected in place of potassium chloride a substance like zinc chloride, which in solution shows positive curvature, the reverse would have been true, i.e., the deviation mould probably have been positive. Bruckner’s data enable us to propose a principle that substances which show neither positive nor negative curvature (figure 3) in their fluidity-concentration (Np) curves should give additive fluidity (Xp) curves on being mixed with each other. If one compound is used which shows negative curvature, Le., of the Dp type, the calculated value will be low, but if of the C 9 type, the calculated fluidity will be high. If two mixtures of the Dp type are mixed, the calculated fluidity may agree with the observed if the curves are congruent. An example of this sort is given in mixtures of 1N potassium chloride solution with an equal volume of 1 N ammonium chloride solution where the fluidity shows a deviation of only 0.08 per cent. But the importance of the congruence of curves is shown by the fact that ( 1 ) when 1 N potassium chloride solution is mixed with an equal volume
523
FLUIDITY O F ELECIROLYTES. 11
FIQ.2. Fluidities of aqueous solutions of barium chloride, sodium chloride, potassium chloride, and ammonium chloride at 15°C. (after Briickner).
TABLE 23 Fluiditu of barium chloride solutions NORMALITY C
0.0 0.5 1.0
1.5 2.0 2.5 3.0
(0S:;L)
87.42 83.20 78.81 74.55 70.23
(CALEILED)
87* 44 83.12 78.80 74.48 70.16
(OBS%VPD)
99.15 93.94 88.61 83.56 78.61 73.45 68.08
(cA2LisD)
99.15 93.96 88.77 83.68 78.39 73.20 68.01
524
E C G C S E C. BISGHAM APiD ROBERT T. FOLEY
of 5 N ammonium chloride there is obtained a rather large deviation of -2 per cent; ( 2 ) when a 3 AT potassium chloride solution is m i d with an equal volume of 1 N ammonium chloride, there is also a rather large deviation of - 1 per cent; (3) yet when a 3 11-solution of potassium chloride is mixed with a 5 N solution of ammonium chloride, the deviation sinks in this concentrated solution to a negligible value of -0.1 per cent. In the last case the curves are nearly congruent,. Since barium chloride show neifher positive nor negative
MOLECULAR CONCENTRATION FIG.3. The fluidities of sodium chloride and barium chloride in equal parls by volume (after Bruckner). Curve 1,1 N solutions a t 15OC.; curve 2 , 2 A'solutions st 15'C.; curve 3, 3 K solutions a t 15°C ; curve 4 , l N solutions a t 20°C.; curve 5 , 2 N solutions a t 20°C.
curvature, and sodium chloride shows only slight negative curvature, \re conclude that, according to the above principle, solutions of these two salts should on mixing give fluidities very close to the calculated values. Bruckner furnishes the data for this comparison in our tables 11, 12, and 13 (shown also in figure 3). The divergence between the observed and calculated values is about 0.2 per cent, nearly what can be expected, the data extending to 3 N .
525
FLUIDITY OF ELECTROLYTES. I1
Having now found examples of these types of fluidity curves, it would seem logical to attempt to measure this factor of polarity, or whatever it may be called, which causes one salt to show positive curvature and another negative. Any paper on the fluidity of liquids is hardly complete unless changes of volume are taken into consideration. We reproduce the curves of specific volumes of the solutions in figure 4 but postpone any discussion for the time being.
1.00
0.95 0.90
0.85 0.80
0.75
0
4
2
3 NORMALITY
I
FIG.4. Specific volumes of solutions of barium chloride, sodium chloride, potassium chloride, and ammonium chloride at 15°C. (after Bruckner). EXPERIMENTAL
Having suspected the value given for the ionic fluidity elevation of lead (2) to be incorrect, we have measured the fluidity of a 0.02 N solution of lead chloride at 25°C. and obtained a new elevation constant, showing that the previous value was seriously in error, owing to a mistake in calculation from the reliable data of Gruneisen (9). Our data now agree in giving to lead a negative value, as expected, of -28.2. That the value is now in agreement is shown as follows: SOLUTION ~~
"C.
1 N Pb(N0a)n. ......................... 0.5 N Pb(N0a)z......................... 0.02 N PbCh............................
25 25 25
89.2 101.3 111.4
89.8 101.2
111.5
526
EUGENE C. BIKGHAM AND ROBERT 1. FOLEY
fluoride (- 27.6) and potassium iodide (7.86) have the disadvantage that lithium fluoride is only r!ightly soluble. Sodium nitrate (- 6.54) and potassium nitrate (3.34) do not differ widely in fluidity but, according to the above discussion, should probably show some divergence between observed and calculated values at high concentrations. A t 0.05 N concentration, lithium fluoride and potassium iodide a t 25OC. obey the Ian of additive fluidities, as shown in the following table: VOLUUE CONCENTPATION K I UXTVBE
Coalcd.
Cabsd.
0 0.25 0.50 0.75 1.0
110.7
Mixtures of 1 N sodium and potassium chlorides give the following table of fluidities a t 25OC.: VOLUME CONCENTRATION KClYlXTURE
I
0 0.25 0.50 0.75 1.0
Cobsd.
Ccalod
102.2 104.4 106.6 109.4 112.3
102.2 104.4 107.4 109.4 112.3
Mixtures of 1 N sodium nitrate and potassium nitrate give the following fluidities: ‘OLQIIE CON XNTBATIOh
TEXPERAIURE
KNOs
Pobd
~
_
Coalod.
_
_
‘C.
10
20
0 0.25 0.50 0.75 1.0
73.5 75.2 77.2 79.0 80.7
0
94.0 96.4 98.4
0.25 0.50
0.75 1 .o 0 0.25 0.50 0.75 1.0
119.4 121.4 124.4 126.3
119.3 121.6 124.0 126.3
In the chlorides and nitrates we might expect the observed fluidity to be slightly higher, in view of the strong negative curvature of these two potassium salts, but it is hardly noticeable a t this concentration. Either higher concentra tions or increased accuracy might bring out these effects.
-
FLUIDITY OF
ELECTROLYTES.
I1
527
CONCLUSIONS
1. The valuable data of Bruckner and also of Ruby and Kawai on mixtures of electrolytes up to a concentration of 5 N have been studied. Since these workers incorrectly assumed that viscosities are additive, we have calculated the differences between observed and calculated values on the assumption that fluidities are normally additive, and we have thereby reduced the differences by 50 per cent. hlthough this is not more than the experimental error in many cases, it is noticeably more in some. We have proved that the differences remaining are a t least partly due to an effect not heretofore considered, i.e., the dilution of each solute dudng the operation of mixing. A suggestion is made as to a method of correcting for this. 2. In the earlier paper on the fluidity of electrolytes (l),a positive value for the "ionic elevation of fluidity" of lead was given with great reservation. That value was obtained from the reliable data of Gruneisen for lead nitrate. Using lead chloride, we have now determined a value which is negative, as expected. On recalculating the value from lead nitrate, it turns out that the data of Gruneisen do yield a result closely in harmony with our own, making the ionic elevation -28.2. 3 . Fluidity data have been obtained for mixtures of normal solutions of sodium chloride and potassium chloride a t 25"C., of normal solutions of sodium nitrate and potassium nitrate at lo", 20°, and 30°C., and of 0.05 N solutions of lithium fluoride and potassium iodide a t 25°C. Higher concentrations should be used for more significant results. REFERENCES (1) BINGHAM, E. C.: J. Phys. Chem. 46, 885 (1941). (2) BINGHAM, E. C.: J. Phys. Chem. 46, 896 (1941). (3) BINGHAM, E. C.: Fluidity and Planticity, p. 90. McGraw-Hill Book Company, Inc., New York (1922). (4) Reference 3, page 160. (5) Reference 3, page 178 et sep. (6) BINGHAM, E. C., AND BROWN, D. F.: J. Rheol. 3, 95 (1932). (7) BRUCKNER, H.:Wied. Ann. a,287 (1891). (8) DUNSTAN, A. E.: J. Chem. SOC.86, 817 (1904). (9) GR~NEISEN, E.:Wiss. Abhandl. physik. Reichsanst. 4, 237 (1905). (10) HATSCHEK, E.: The Viscosityof Liquib, p. 146. 0.Bell and Son, Ltd., London (1928). J., AND WRIGET,A. H.: J. Am. Chem. SOC.42, 1776 (1920). (11) KENDALL, (12) LINEBARGER, C. E.: Am. J. Sci. [4] 2, 331 (1896). (13) RABINOVICH, A. J., J. Am. Chem. SOC.44, 954 (1922). (14) RUBY,C. E., AND KAWAI,J.: J. Am. Chem. Soc. 46,1119 (1926). (15) THORPI,T.E., AND RODGER, J. W.: J. Chem. 800. 71, 360 (1897).
