THETHEORY OF h I E M B R . 4 N E
Nov., 1952
POTENTIAL
1017
near the surface followed by rapid transformation t o the higher melting form.
In contrast, the unstable (low-melting) form of oleic acid tended to transform to the stable form much more readily. On cooling the mixtures rich TABLEI in oleic acid to about 8 to 10' the samples suddenly BINARY FREEZING-POINT DATA" hecame essentially solid; and, on heating in the Acetamide-oleic acid system Acetamide-elaidic acid system constant temperature bath, melted so that relaFreezing point,, Freezing point, 'C Mole MetahIofe Y AIetatively few crystals remained a t the temperatures acetarni8e Stable stable acetamic!e Stable stable indicated by the clotted line. At this stage, or 0.00 16.3 13.5 0.00 43.8 sometimes before, the sample again became essen4.42 15.9 10.31 42.5 tially solid because of the formation of the higher9.37 12.2 19.47 41.5 melting crystalline modification of oleic acid, or of 12.60 15.1 29.87 40.2 the molecular compound when the acetamide coii(15 .O)* (14.8)* (34.2jb (39.6)b centration was between 15 and 22 mole %. The 17.20 16.3 11.4 36.01 39.9 sample then showed a melting point corresponding 21.54 18.4 10.7 (37.8)" (4O.O)c to the upper solid curve. Because of this behavior 21.75 18.3 40.08 45.1 40.3 24.65 19.1 44.96 51.G 40.7 the freezing points involving the unstable modifi30.55 20.5 . 46.08 53.6 40.8 cation of oleic acid could not be obtained with the (30.8)" (20.6)' (47.2)d (40.9)d same assured accuracy. 34.14 31.6 20.7 50.59 59.9 47.1 The acetamide branches of the diagrams for these 36.73 37.7 21.3 60.26 69.7 58.4 two cis-trans isomeric acids almost coincide. It (39.2jd (21.G i0.21 75.1 64.G will be noted, however, that the freezing points for 39.34 42.3 23.8 79.75 78.1 67.9 the elaidic acid system tend to fall above the 44.40 35.6)d 90.06 59.4 69.0 curves as d r a m and those for the oleic acid fall be48.54 5G.0 43.0 100.00 79.7 69,5 low. This is in harmony with the idea that the 70.61 75.2 64.3 molecular compound between acetamide and oleic 82.17 78.0 67.8 acid is less dissociated than that between acetamide 100.00 79.7 G9.5 and elaidic acid, which is indicated by the fact that The values in parentheses were obtained by graphical est.rapolation. b Eutectic. Incongruent inplting point the freezing-point curve for the oleic acid compound is steeper. ((stable). Incongruent melting point (metastable). O C
THE THEORY OF MEMBRANE POTENTIAL BY hIITSURU
YbG.4S.1WA1 AKD Y O N O S U I i E I 1+
1-
In
;( + i)
(34)
In the acidic solution eq. (34) becomes
[
log e R T
E+
- 1 1 = log 6-1 - pH (35) eq. (34) becomes
+l-)-IAE
In the log
- :$?k)
-IAE
- I]
log (p-lKw + p H (36)
MITSURUNAG.AS.A\VA
1022
Vol. 56
AND YONOSUKE KOBATAKE
TABLE IV Calcd. using the data by Sollner and Gregorg: memb., protamine collodion memb. (Hum 20-Shr 20); ratio of concn., 2 : 1; temp., 25.0'; CY and p areobtained from Fig. 3. Electrolyte
B
CI
o.002
0
3
0.01
0
0.001
0.002
0.005
0.01
024 0.02
0.1
Ci/C2
16.4 16.4 16.2 16.2 16.5 16.6
16.2 16.5 16.0 16.2 16.3 16.5
16.0 16.2 15.3 16.1 16.1 16.6
15.7 16.2 14.8 16.0 15.9 16.4
15,2 15.9 13.8 14.9 15.7 16.4
14.4 15.2 11.4 12.4 15.6 16.1
KCI
0.937
0.927
Eoaiod Eobsd
KI
0.927
0.280
Eoaiod
LiCl
0.944
4.60
Eobsd
Ecaird Eobed
TABLE V Calcd. using the data by Masaki'o: menib., collodion; ratio of concn., 1O:l; temp., 25.0'; a and p are obtained from Fig. 4. The reproducibility of these experiments are found to be in the range of the potential below 0.3 niv. Electrolyte
KC1 KBr KI KNO:
0
a
C1/Ce
(N.)
0.919 0.984 Eoaio.(tnv.) Eobs. (mv.) 0.920 1.018 Eo&. (mv.) .Fobs. (mV.) 0.903 1.100 EoaiC.(mv.) .Fobs. (mv.) 0.947 0.148 Eosio. (mv.) Eoba. (mv.)
0.05
0.1
0.005
0.01
53.9 53.82 53.4 52.68 49.3 52.43 46.9 50.07
52.8 52.31 49.4 52.53 48.0 52.21 43.0 45.87
0.5 0.5 46.7 47.61 43.7 46.93 45.6 47.16 28.8 29.82
1.5 0.15 39.6 39.53 36.6 38.18 37.3 39.56 18.1 15.05
where Kw is the dissociation constaiit of the water. Strictly speaking cr is the function of the charge of the membrane (ie., IC/,) and of the ionic mobility in the membrane (Z+, 1-). Therefore a: cannot be constant and is by no means theoretically deter-
2
0.05
0.2
02
0.1
0.2
13.7 14.5 9.0 10.2 15.6 16.2
12.4 13.2
15.3 16.1
mined in general. However, only in the alkaline solution, where the glass electrode is usually used only in the range of lower concentration, CY can be assumed to be nearly constant. Even in the acidic solution it may remain equal to unity for the ideal glass membrane. Then we obtain
Therefore the plot of log log [e&(a - "+*) -lo
F I+ + 1.. ( e m r A E-
1) or
1t + 1- 11 against pH should give a straight line of the sloDe - 1 or 1 in the icidic and dkaliiie solution, respectively.
+
Experimental Verification.-It is desirable to measure the deviation of the membrane potential from the potential of the hydrogen electrode. The essential parts of the apparatus are shown in Fig. 5. The vessel A contains the solution into which are inserted the glass electrode G (Haber type) and the hydrogen electrode €3. The pH of this solution may be changed by the addition of acid or alkali from the buret B. A stream of hydrogen gas, which is purified by Pt-asbest, bubbles through the solution from the t8ubeHa. A junction between the solution in A and the calomel clectrode is made by a satd. KCl bridge. All cells are placed in a thermostat kept a t 25'.
Satd. KCI Calomel electrode (E) Sealed by paraffin
H Z 0
0.1
0.2 'V
fIC1. Fig. 3.-The relation between E- 1C1 (using the data by Sollner and G r e g ~ r HumPO-Shr20{: ,~ protamine collodion memb., C,/C2 = 2: A, LiCI; B, KCI; C, KI.
styro1 Cork Rubber Stopper
I
Glass tsode
Sol. 1 Sol. 2 Caps Fig. 5.-The
measuring apparatus.
The apparatus for measuring the potentials is of a DuBridge type. Glass membranes used in this investigation are those of hard glass and MacInnes glass. 0
0.2
0.8 fIC1.
Fig. 4.-The relation between E-flC1 (using the data of Masakilo); memb. collodion, C I / C ~ = 10. K.Sollner and H. P.Gregor, THIEJOURNAL. 54. 330 (1930). (10) K.Masaki, Mitt. med. Ahad. Xioto ( J a p a n j , 5;35 (1931):
(9)
The deviation of the potential Gf the glass electrode from the potential of the hydrogen electrode is estimated by determining the potential between G and H. Such measurements yield potentials of the cell PtHz I sol. 111 glass11 sol. 2 1 satd. KCl HgCl Hg ( A )
THETHEORY O F MEMERANE POTENTIAL
Nov., 1952
Cell (A) has at all pH of solution 1 the same potentials as long as the glass electrode acts as a perfect hydrogen electrode. This value depends only on the eoncentration of sol. 2 inside the glass electrode, the state of the inside surface of the glass membrane and on the pressure of the hydrogen gas. In real cases, as will be shown by the experiments described below, the potential varies slowly with pH (Figs. 6, 7). It is obvious from eq. (33) that this property is due to the essential feature of the glaas electrode.
A
340 ..
263
/
A
Et-,
p
w2 3 3 5
-----A
a
A
-
$2
+ii
&
Fig. 9. As seen from the curve, observed data fit fairly well with the theoretical results. It may be due to the impossibility of expanding the exponential term of eq. (12) that the experimentd results do not fairly fit the theory
,gd
.d----o-04-
1
vestigators have been obtained by using various buffer solutions. Therefore, they are not adequate for the comparison with the present
e
&-&&&-A-
1
\>O>
O
%W
/
both and I& which vary also with pH. Accordingly, the deviation AE of the potential of cell (A) from the constant value or actually from the extrapolation of eq. (33), which is usually called the
,
k 1%
@ 330 ..
,:LA ’
F;:
O0--O-O
.
255
7 ‘ap,
1023
-70
-
o
E
4 -75
//
do
7
;
k
O
-
1024
31ITSURU
100
Vol. 56
N.4G.4S.i\Vv;1 S N D YONOSUKE KOBATAKE
t {
-
012
(:e) + /In (CI f
Od]
K
(38)
where T< is independent of C and is dependent on Cosl + , I-, al, etc. If a1 = a2 = 1, we obtain RT; 10
AEA =
12
11
PH. Fig. 11.-Error of glass elect,rode in the alkaline solution; meinb., hard glass (memb. l l ) , KOH: straight line, E = 01 pH
+ const.;
+ 1- X x 0.0162,. r;3 ( h 4 0 being assumed) = ki I+ + I 01
= 0.970; p =
l+
10
.
E
10
I ..q. , , ,
b
0
0
p" 0"
SK(39)
The experimental results of the asymmetric potential are given in Figs. 10, 13, 14. It is obvious from eq. (38) or (39) that the asymmetric potential has nearly a constant value and happens to deviate from its coilstant value at the same concentration as the error of the glass electrode, as indicated in Fig. 14.
/
3
'+'
21-
FL- i F F L In ( C d l
11
12
13
PH. Fig. 13.-Asymmetric potential of glass electrode in the alkaline solution; menib., hard glass (memb. 11), ROH: 01
,
11
12
PH.
- :*)
-
Fig. 12.--~1ot of log (e a &,AE 1 against pH; menib., hard glass (menib. Il), KOH.
6 . Asymmetric Potential although asymmetric potential, that is, the potential difference of cell (C) has hitherto been qualitatively attributed to the crystalline state or composition of glass of the inner and outer surface of membrane, it is thermodynamically impossible that cell (C) has any potential difference at the true equilibrium state.
I+ - X k (kn = 0 being assumed) = '-l,+L ki X 0.01627; P1 = -X 0.003057; I< = -13.9.
= 0.970;
Ti
I+
+ 1-
I+
5
'+ +
1-
P
-40 .
c
I
Hg HgCl satd. KCl 1 Sol. I[ Glass 11 Sol. satd. KC1 HgCl Hg (C)
As the ionic diffusion across the glass membrane is supposed to be very much slower owing to its compactness, the stationary state at which ions diffuse into the membrane from both sides of it may reasonably be assumed. This fact will be understood from the experiments that CY in eq. (33) is independent of. the concentration of the solution inside of the glass membrane. Therefore if the distribution function of the pore diameter on one surface of the membrane differs from that 011 the other, the diffusion potential a t one side of the membrane may not be equal to that a t another, so that the asymmetric potential difference is observed. Assuming the concentration in the middle of the membrane to be Co, asymmetric potential AEAis therefore given by
0
5
10
PH. Fig. l.i.-Asymmetric potential of glass electrode; meinb., hard glass (rnemb. lo), HCI and KaOH.
The full line in Fig. 8-13 denotes the calculated values, of 01, Pz, K being assumed. They are seen to be in quite satisfactory agreement with the experimental values of the error of glass electrode and of the asymmetric potential, respectively. Here, it is remarkable that both the asymmetric potential and the error of the glass electrode are fully explained by using the same value of PI. It may probably be due to the freedom of the empirical constant that this agreement is fairly good up to higher ionic concentration than in the DebyeHiickel theory for the dilute solution of electrolyte. The authors wish to thank Prof. K. Kanamaru and Assist. Prof. T. Hata and others at the Laboratory of High Polymers in the Tokyo Institute of Technology for their help and encouragement in carrying out this work.
\ $
A
