STUDIES ON ELECTROKISETIC POTEXTIALS. VI Electrical Phenomena a t Interfaces‘ BY HENRY B. BULL .4ND ROSS B I K E S GORTNER
Historical and Theoretical The existence of electrical conductance at a solid-liquid interface which increases the conductance of a system above that normally expected can hardly be doubted since it has been demonstrated by several workers. Thus Stock2showed that quartz powder in such liquids as nitrobenzene and aniline greatly increased the apparent conductivities of these liquids. Briggs3 found that surface conductance must be taken into consideration in determining the specific conductance of a liquid for the purpose of calculating the {-potential from streaming-potential data. McBain, Peaker, and King4 have made accurate quantitative determinations of the surface conductance of KCl solutions at glass and silica interfaces and find it to be appreciable. Stock? at the suggestion of Smoluchowski undertook to investigat,e the question of surface conductance. He employed in this research certain of Smoluchowski’s equations. Smoluchowski considered a system of capillary tubes and proceeded to calculate the ratio of the curremt carried by the surface potential, ie., that due to surface conductance, to that carried by the bulk of the liquid. The infinitesimal amount of current, dI,, carried by an infinitesimal element of the double layer moving with a velocity, u, is given by the following relation. dI, = q u dS dr... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(I) where q is the charge per unit area on the double layer, dS is an infinitesimal section of the circumference, and dr is an infinitesimal normal to the wall. Then
I,
=
q s u dS dr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
But the velocity at any point is given by
u
=
au -r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ar
(3 )
1 From the Division of iigricultural Biochemistry, University of Minnesota. Published with the approval of the Director, as Paper No. 9j1,Journal Series, Minnesota Agricultural Experiment Station. This paper is taken from Part I11 of a thesis presented by Mr. H. B. Bull to the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June 1930. *Anz. Akad. Wiss. Krakau, (A)1912, 63j. 3 J. Phys. Chem., 32, 641 (1928). J. Am. Chem. SOC.,51, 3294 (1929).
HESRY B. BULL AND ROSS AIKEX GORTSER
310
Then substituting (3) in
(2)
I, =q s s r d S dr . .
(4)
ar
Integrating part of this expression
is the potential difference across the double layer and is where o2 equal to the {-potential. D is the dielectric constant. Substituting ( 5 ) in (4)
I.
=
9 { e dS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 ~ . ar
.(6)
Integrating through the entire circumference and assuming a linear relation between u and r, we have
I . = D5 - s - ud . " " " " 4"
...........................
'
' '
(7)
where d is the thickness of the double layer. The movement of the layer of ions with a charge, q, per unit area is produced by an externally applied electrical potential. The resulting force acting on the double layer is
F
av
av
q- ......................................... ax
where - is the potential gradient of the externally applied electrical ax potential. Now a t equilibrium the electrical forces tending to produce motion of the liquid must exactly equal the forces tending t o retard the flow of the liquid. This resisting force is
R
au ar
= - q.....
...................................
'
(9)
where q is the coefficient of viscosity. When equilibrium has been reached (9) must equal (8)
Assuming a linear relation between u and r, we have U
av........
d q = g-
ax
where d is the thickness of the double layer
STCDIES I N ELECTROKIXETIC POTENTIALS
3'1
Substituting the value of u/d in ( 7 ) , we have
DTS aT7 I. = -q -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.(I2)
4 v
Xow the current carried by a cross-section of the liquid is
where A is the area of the cross-section occupied by the liquid and the specific conductance of the liquid. Dividing (12) by (13)
Substituting
(I j)
K
is
in (14)
5 = 1.4
($)2&
............. . . . . .
which is the final equation of Smoluchowski. It is to be noted that in the derivation of this equation the same assumptions are involved which are used in the derivation of the equation for electroosmosis, cataphoresis, and streaming potential. S o additional assumptions have been made. It is possible to modify equation (16) by the appropriate substitution so that two new equations are obtained, one expressing the thickness of the double layer and the other the charge per unit area. Briggs5 pointed out that K 8 - K - 1, _- - ...................................... ('7) K 1.4 where K~ is the specific conductivity of the liquid in the capillary pores and K is the specific conductivity of the liquid in bulk. K~ - K is taken to be the so-called surface conductance. Then substihting in ( 1 6 )
From the streaming potential equation
Colloid Symposium Monograph, 6, 4 1 (1928)
HENRY B. BULL AND ROSS A I K E S GORTNER
312
Substituting
(20) Ks
in (19) we have
-
K
and
=
( H7&7 ' . .) ........................
8
(q)'
s17
d =-
......................
( K * - K ) ~
which is a convenient equation expressing the thickness of the double layer.
TD = d q in (16) we have Now substituting the expression 4T
K~
-
K
=
S
(dq)' . . . . . . . . . . . . . . . . . . . . . .
S
= -
q'd . . . . . . . . . . . . . . . . . . . . . . . . . A7 Substituting the value of d as given by ( z z ) , we have
S
. . . . .(23)
. . . . . . . .(24)
.......... . . . . . . . . . . . . . .
,
. (zj)
. . . . .( 2 6 )
or q =
(Ks
-
,
K)
A
P
- HKa - . . . . . . . . . . . . . . . . . . . . . . . . . .( 2 7 j
which is an equation expressing the charge per unit area at the interface, The dielectric constant does not appear in either equation for the thickness of the double layer ( 2 2 ) or for the charge ( 2 7 j which relieves us of making any assumptions concerning the magnitude of this constant. Now it is not possible in our work with ic cellulose diaphragm to determine the actual numerical ratio of X,#Sin equations ( 2 2 ) and (z7), but we can at least assume that it is n constnni f o r nriy giwn diaphragm throughout a series of determinations. I t should be possible therefore to determine the behavior of the charge on and the thickness of the double layer upon the addition of electrolytes by use of the above equations. This is the object' of the present research. The streaming potential apparatus used in this investigation was a modification of that developed by Rriggs3 and later again modified by Martin and Gortner.6 The technic is described and the apparatus is figured in diagrams I and 2 of the paper by Martin and Gortner.* All volumetric apparatus used in this research was calibrated and the corrections used when necessary. The quadrant electrometer and potentiometer were adjusted in the usual manner. __ 8
J. Phys. Chem., 34, r 5 q (1930).
STUDIES IN ELECTROKINETIC POTESTIALS
313
The diaphragms used in this research were in all cases made from cellulose. .4t the beginning of the research, four packages of Schleicher and Schull filter paper, No. 589, were ground in a ball mill with 95 per cent ethyl alcohol to a pulp. The cellulose was then filtered and dried in uucuo a t 9j0 for 8 hours and stored in sealed glass containers. The cellulose was suspended in the liquid to be studied at least 48 hours before it was used. The cellulose was packed quite tightly in the cell. After the diaphragm was in place in the apparatus, at least 700 cc of the solution to be studied mas streamed through it before any determinations were attempted. The washings were discarded. The two halves of the streaming potential cell were cleaned carefully before each determination with sulfuric acid dichromate solution and rinsed out with distilled water and finally with some of the solution to be used in the experiment. Determination of the Specific Electrical Conductance of the Liquid in the Diaphragm Immediately following the determination of the streaming potential, the streaming potential cell was connected to the conductivity apparatus and the resistance of the diaphragm determined. Later, when the series of experiments on a particular diaphragm was completed, the cell constant of the diaphragm was determined by replacing the liquid in the diaphragm by KI'IO KC1. Knowing the cell constant and the resistance, the specific conductivity is calculated in the usual manner. Calculation of the {-Potential From the observed values of the pressure, the electromotive force, and the specific conductance, the c-potential may be calculated. The pressure must be expressed in dynes per square centimeter and the specific conductivity observed in ohms-' must be multiplied by 9 X 10ll to convert it to C.G.S. electrostatic units. Substituting these conversion factors in the following equations { = -4.lrH ? K y
DP and collecting constants we have
r
tl = 847,649,000 -
D
Hxs T
where H = observed electromotive force in millivolts, q = coefficient of viscosity of the liquid, K~ = specific conductivity of liquid in diaphragm in ohms-', D = dielectric constant of liquid, P = pressure in centimeters of mercury, { is expressed in millivolts. I n order to determine the surface conductance a conductivity measurement of the liquid in bulk was necessary. This was done a t the same temperature as the strenming potential determination and on the liquid which
HEKRY B. BULL A S D ROSS AIKEN GORTNER
314
had actually been used in the streaming potential measurements. A Washburn conductivity cell designed for high precision work was used. The surface conductance was obtained by subtracting the specific conductance of the liquid in bulk from that in the diaphragm. Chemicals The water used throughout this investigation was doubly distilled and had a specific conductance of 4.8 X IO-^ ohms-‘. It was used fresh. The salts were the purest obtainable on the market. S o additional purification was attempted. Criteria of Validity Results It is essential, if we are to attach any meaning to our results, that they must be reproducible. I t is to be emphasized, however, that in order to compare results they must have been obtained from material treated in an identical manner. This is particularly true in respect to the time that the cellulose has been allowed to remain in contact with the liquid, since it is generally agreed that the c-potential decreases with time when the material is allowed to remain in contact with the liquid. That this is true is clearly shown by the work done by Martin and Gortner6 and by Lachs and Kronman.’ The data on three diaphragms with water-cellulose are shown in Table I.
TABLE I Showing Variability in Streaming Potential lleasurements Diaphragm
Pressure
His P X
Pressure
IO”
cm H g I
71 9
-10
75 1 78 9
- 9 90 -10
72 0
02
=
69 .o
- 9.48
75.5
-
79.8
75 9 79 1
23
Average Hhs P 2
65.7 74.5 81.4
72.I
9.48 - 9.45
-12
04
-11.72
-11.67
Average HK,/P = 7
IO)
- 9 85 - 9 io - 9 70
- 9 90 X IO-^
Average HK,:’P = -9.58 3
H K P~ X
cm Hg
-11.50
Bull. acad. Polonaise sei. lettres, (-4) 1925, 286.
78. I 82.7 X IO@ i3.9 78.1 83.4 X IO-^
- 9’53 - 9.68 - 9.82
-11.34 -11.26 - I O .97
315
STTDIES I S ELECTROKIXETIC POTESTIALS
These results were selected purely a t random and may be said to represent, the usual variations encountered. They perhaps leave somet.hing to be desired from the point of view of reproducibility, but when it is remembered that with pure water the observed potential is extremely sensitive to traces of electrolytes and is more erratic than with salt solutions, the disagreement is not serious. Due to the fact that the gold electrodes are not reversible in the usual sense of the word, it was feared that marked polarization might develop. To satisfy ourselves on this point, we determined the streaming potential as a function of the pressure. The results are shown in Fig. I . 90
Q)
75
I vi c ,S v)
0
200
100
1(0
300
E.M.F. in Millivolts FIG.I Showing the relation betFeen the streaming potential and the pressure, as experimentally determined in our apparatus using a cellulose diaphragm and 0.1 X IO-^ XaC1 as the liquid being streamed through the diaphragm.
I t will be noted that the result is a straight line passing through the origin. Had there been polarization of the electrodes, this would not have been the case. That the diaphragm had attained equilibrium with the liquid was tested for in every determination by obtaining at least three values while streaming the liquid in one direction and three more values in the reverse direction. Results The data for the function, HK,/P,are given in Tables I1 through I S and summarized along with data for
(F)',
-
KB
P
( K . - K ) ~
and the {-poten-
tial in Tables X through XS'II and the results graphed in Figs. z through 9 for various concentrations of aqueous solutions of KCl, NaC1, RIgC12,CaC12,
HENRY B. BULL AND ROSS AIKEN GORTNER
3 16
K2C03,K2S04,K3P04,and ThCI, at a cellulose interface. As a convenience the function,
II
- K (%)*which
is proportional, though not equal, to the
KB
thickness of the double layer is designated by d’, and the function, ( K ~ - K)
-,KP~ Hwhich is proportional to the electrostatic charge per unit area is
designated by q‘.
TABLE I1 Data for MgCI? Concentration MgCL 0 00
Pressure
HK~,’PX
em Hg 61 3
-15
78.1
-15
X IO-^
5
57
2
-1j
5
79 6 78 3
-15
5
--Is
3
j
48 X
-1j
66.3 80.9
-1o.j
x
IO-^
73.9
-11, j
- I
13.7
x
- 8.52
58 9
- 8.84
-
80 6
- 9’42 - 9 45
9.95
60.5
i8 9
X
- 8 83 - 8 . j ~
IO+
63 0 81.4
79.3 - 8.60 Average HKJP = - 8 . j o X IO@
50.I
80 6
76 j
- 6.90 - 6 34 - 6.68
Average HKJP = -6 . 6 X IO-^
-10.;
10-6
79.5
I
-11.4 -11.1
51 2
80.9
0.8 X IO-^
j
80 6 78.j
9.76 Average H K ~ ~=I ’- 9 . 3 2
0.4 X IO-^
106
IO-j
74.5 81 . i
-11.1
Average HK/P. = - 1 1 . o j 0.20
H K P~ X
cm Hg
75 5 -15 Average HK.,’P = 0 .I O
Pressure
IO$
61.8 81.3 78.1 jj
X
-
2.69
66.9
80.7
-
2
.oo
81.1
x
8 oj 8.50
- 8.24
-
5.10
6.75 6 . j ~
IO-5
81.9
Average Hu./P = - 2 . 6 2
-
10-5
-
3.10 2.71
31;
STUDIES I N ELECTROKINETIC POTENTIhLS
TABLE 111 Data for CaCL Concentration
Pressure
HK~/X P
Pressure
106
CaCL
cm Hg
--
0.00
cm Hg
i1.2
-13.7
.o
-13.8 -14.0
72
69.5
Average HK,/P = 0 . 1X I O +
X
IO+
72.9
- 1 3 .7 X
j I
71.9
-10.4
73.7 78,4
53.8 76.9 82.3
x
10-3
0 . 8 X IO-^
j2.2
-9.3 -9.2
73.1 80.4
-10.0
-8.9 -8.0
Average HK,/P = I
. 6 X IO-^
-10.8
-8 . 9 0 X
70.5 i9.0
-9 .o -8.8
82.3
-a.
Average HK,/P =
7
- 8.8; x
-9.4 -9.3
IO+
-9.2
59.0 78.2 83.5
-10.5
-10.1
82.8 75.5
x
-10. j
57.9 76.9 82.9
80.3
Average H K J P = - 9 . 5 5
-11.6
IO-^
-9.80 -9.45 -9.20
Average HKJP = 9 . 5 5 X 0.4
.8
-10. j
- IO. 7 X
-13.4 -13.6
IO-^
43.5
Average H K J P = 0.2
68.3
-9.5 -9.2
10-5
66 . o 80.2 82.9
-9.5
-8.5 -8.4
IO-6
67.8 80.3
-9.5 -8.6
76.4
-8.6
10-5
H E S R Y B. BULL AND ROSS AIKEN GORTNER
TABLEIT Concentration NaC1
Pressure
Data for XaC1 Hia ‘P X 1 0 5
cm Hg 0.00
75 9 i9 1
-9.8;
73.1
-10.23 -9 90
is
--Io
72 0
-9.70
71.9
X IO-^
9
02
io 3
-12.80
i8.5 73.9
-12.34 -12.45
Average HKJP = - I 2 0 . IO
X IO-^
72.9 75.7
74.7 78.6 , 6 X IO-^
-13.90
-13.8;
- 1 3 .i o Average HKJP = - 14.I X X IO-^
7 = .3
..13.1 79.0
-14.0
-13.8 -13.7
Average HK,,/P= - 1 3 . 7 5 X 0.4
X IO-^
0 . 8 X IO-^
69.5 74.; 78.3
-13.4
61.j
-12.40
-9.70
-12.81
- 1 2 .j o -12.58
74.1 76.5
-14.30
i3.5
-1j.50
-14.40
IO->
72.6
-13.8
i5.9 79.2
- 13.6 -13.6
IO-&
73.2 76.9 -13.5 80.2 Average HK,/P = - 1 3 . 3 0 X IO-^ -13.4
-13.3 -13 . o -13.1
70.I
-12.45
75.7
-11.6 -11.6
77.7
-12.35
82. I
-11.2
Average Hx,/P 1 . 6 X IO-^
67.8 74.8
IO’
IO-’
69.7
79.7
0.2
HxS P X
cm Hg
Average Hh,/P = - 9 . 9 0 X 0.05
Pressure
=
- I I .95 X IO-^
-10.02
-
71.7
IO.20
80. j -10.2j Average HK./P = -IO .go X
75.2
79.4 82 . 3 IO-’
-11.6 -11.6 -11.8
STUDIES I N ELECTROKISETIC POTENTIALS
319
TABLE V Data for KCl Concentration
Pressure
Hxs/’P x
Pressure
105
HKS’P X 1oS
KCl
cm Hg 51.9
0.00
78.4
cm Hg
- 13 .o - 12.6
Average HKJP = o.oj X
IO&
IO-^
- 12 . 4 X
X IO-^
82.4 76 . o
- 13.8
77.2
-13.8 -13 . 8
-13 .6
-13.8 X
IO-^
48.7
-15.1
59.1
- 12.4
82.2 76.1
-14.3 -14.3
77.4 84.4
-14.1 -14.2
x
IO-^
36.7
-13.7
63.3
-13.1
79.0
-14.3
82.4
-14.2
78.2
-14.4
81.2 66.8 71.4
x
10-6
-12 .i -12.4
50.3 82.9
-I?
72.2
Average HKJP = 0.8 x IO-^
IO-5
80.6
85.5 -13.9 Average HKJP = -13 , 9 0 . 4 X IO-^
-12.4
- 12.6
-13.8
Average HKJP = - 1 4 . 0 1 0.20
-11.5
78.2
77.4
Average HK,/P = 0 . 1 0X
51.6 83 .o
J
- 12 . 9 x
41.6 76.7
-11.75 -12.3
83.3
-12.2
Average HKJP =
-I 2.8
X
-12.50
- 12.95 -13.40
10-5
53.2 76.8
-13.7 -12.6
68.7
-73.4
10-~
HENRY B . BULL AND ROSS A I K E S GORTSER
320
TABLE
VI
Showing Values of H/P for Various Concentrations of K 2 C 0 3at a Cellulose Interface Concentration X
Sormality 0 00
103
Pressure
H/ P
Pressure
HIP
mv/cm
cm Hg
mv/cm
65 7
-4
611
73 9
74 5 81 4
-4 -4
489 471
78 1 83 4
-4.343 -4.314 -4.202
70.6
-3.392
78.4
-3.475 -3.397
cm Hg
Average H/P = -4 405 0.10
72 . 2
-3.518
79.5
0.20
-3.515 84.7 -3.536 Average H / P = -3.472
83.3
67.6 81.9
-1.819 -1.807
6s .9 81.7
85.1
-1.815
Average H / P = 0.40
85.4
-I . 2 3 ~ .
, 8573
66.6
-1.216
82.1
74.6 83.6
- I . 206
84.5 87.6
-1,202
Average H/P = 0.80
-I
- I ,904 - I ,903 - I ,896
75.5 80.9 84.6
-
-I
-I .207 - I .
176
,2061
,7019
76.6
,7169
81.3
,6973 Average H/P = - 0.6969
-
,6984 ,6703
STUDIES I N ELECTROKINETIC POTENTIALS
321
TABLE VI1 Showing Values of H/P for Various Concentrations of
&SO4 a t a Cellulose Interface Concentration X
Kormality 0.00
103
Pressure
H/P
Pressure
H/P
cm Hg
mv/cm
cm Hg
mv/cm
72.1
78.5
-3.557 -3.611
82.7
-3
69.0
-3
75.5 79.8
-3.536 -3.527
*
536
663
Average H/P = -3,5716 0 . IO
68.9
-2.721
82.6
-2.451
82. j
-2.406
85.1
-2.391
85.3
-2,432
70.7
-2,595
80.7
-1.629
83.5 85.7
-1.622
83.0 85.0 86.6
-0.9638
81.5
- 0.4969
83.9 86.3
-0.4946 -0.4866
Average H/P = - 2.499 0.20
80.j
83,I
- I . 623 -1.632
85.5 - I . 674 Average H/’P = - I . 633 0.40
82.7 84.2 85.9
- 0.9068 - 0.9086 -0.8789
-1.621
-0.9764 -0.9815
Average H/P = -0.9360 0.80
76. I
-0.5519
81.1 85. I
-0.
j610 - 0 . 5699 Average H/P = -0,5268
HESRY B. BULL AND ROSS AIKEN GORTSER
322
TABLE TI11 Showing Values of H / P for Various Concentrations of K3P04at a Cellulose Interface Concentration X
h’ormailt y 0.0
103
Pressure
cm Hg
H,/P
Pressure
H/P
mv/cm
cm Hg
mr/cm
78.0 81.4
-2.
84.7
-2.727
-2
jj6 751
ilverage H / P = 0 .I
-2
76
j
-2
T i 9
-2
771 766
80 4
-2
ij4
754
68.3 76.5
-2.554 -2.555
77.9 71.9
-2.734 -2,566
83 ’ 7
-2.526
86. I
-2.601
Average H / P = - 2 . j 9 1 0.2
84. I
-1.688
75.7
- I . 803
74.6 79.3
-1.702
79.2. 82.8
-1.799 -1.793
74.4 77.3
- I . 384
79.3
-1.374
-I.
683
Average H / P = 0.4
83.4 70.6
-I.
77.2
-1.2f5
- I . 744
-1.270
288
Average H/P = -1.3291 0.8
71.1 76.7 83. I
- .6962
- ,6844 - .7099
Average H / P = -0.6968
-1.384
STUDIES I N ELECTROKINETIC POTESTIALS
32:
TABLE IX Data for ThCli Concentration X
Xormality 0 00
0.0;
0.IO
103
Pressure
H/P
Pressure
mv/cm cm Hg cm Hg 63 I -5.594 73 6 73.4 - 5 . j8j 79 2 80.0 -j.606 83 j Average HI'P = - 5 4 j 1 j ;2.8 ii.8
*-
-3.372
15.0
-3.560 -3
54.3
-1,278
-0.9484
65.;
72.3
+1.916
68.3
78.3
$1.948 +1.926
82.3
81.5 Average H/P = 0.40
-5.22:
-3.348 i9.2 81.3 -3.327 83 ' 7 Average H/P = -3.4251
72.0 -0.9097 76.3 82.2 79.8 -0.9273 Average H/P = - I . 0803
0.20
HfP
mv/cm - j ,407 -j, 2 9 0
6j.1 71.8
+I.
981 74,4 i9.6 83.6
0.80
e 56.2 fo.92j2 15.2 +0.912j 80.0 74.5 + o . 9068 84.2 81.6 Average H/P = to.9677
1.60
68.6 78.8
j612 73.3 -I-0.5964 80.0 82.7 $ 0 . j98j 84.2 Average H / P = j ,464
+
- I. 2 3 8 - 1 . I80
11.2
4-1.643 +1.658 Average H / P = + I , 6 2 4
$0.
I
--
+I.590
80.2
-3 491 -453
+1.660 +1.608 + I , 585
HENRY B . BULL AND ROSS A I K E S GORTSER
324
TABLE X Summary of Data for KC1 I
=
Concentration
I
x
103;2 =
3
2
mv 0 .oo
-10.91
0 .os
-1 2 . I4
0 .I O
- 12.37
0.20
-12.23 -11.35 -11.26 -11.96
0.40 0.80 I
.60
-12.4 -13.8 -14.01 -73.9 --I2.9 -12.8 -13.6
p; 3
HK
= --B
P
x
4
5
mhos
poise
26.5 34.8 42.4
0.8 0.8 0.8 0.8 0.8 0.8 0.8
j6.2
67.0 96.0 125
.o
105;
4
=
(Ks
-
x
K)
Io6;
6
7
46.37 43 . 7 2 37.06 19.84 13.63 11 .84
-21.36 -25.23 -30.23 -40.41 -51.92 -74.98 -91.87
6
7
45.44
-20.71
55.02
-21.99 -22.83 -25.81 -31.36 -446.29 -61.44
27.51
TABLE XI Summary of Data for NaCl
5 =
mv. 0.00
-10.00
0.05
-12.83 -14.10 -13.75 -13.14 -12.07 - I O 90
0.10
0.20
0.40
0.80 I
3
2
I
.60
- 9.90 -12.60 --r4.10 -13.75 -13.30 -11.95 - I O 90
4
5
nihoS
poise
10 5 27.7 32.2 35.5 41.7 55.3 67 o
0.950 0.960 0.938 0.938 0.925 0.950 0.938
57.99 j0.01
39.27 24.55 16.61
TABLE XI1 Summary of Data for MgCh Hxa = Concentration x 1 0 3 ; z =
