Aug., 1939
POTENTIALS OF SIMPLE METALSAT
THE
DROPPINGMERCURY ELECTRODE
2099
[CONTRIBUTION FROM THE SCHOOL OF CHEMISTRY OF THE INSTITUTE OF TECHNOLOGY, UNIVERSITY OF MINNESOTA]
Thermodynamic Significance of Polarographic Half-Wave Potentials of Simple Metal Ions at the Dropping Mercury Electrode BY JAMES J. LINGANE~ ’The electrodeposition of simple (hydrated) metal ions at the dropping electrode is a chemically reversible process when the resulting metal is soluble in mercury, and may be represented by Mn+ + ne + Hg e M(Hg) (1) where M(Hg) represents the amalgam formed on the surface of the mercury drops.* Heyrovsky and Ilkovic3have pointed out that if the foregoing reaction takes place reversibly the dropping electrode should be subject only to concentration polarization, and accordingly its potential a t every point on a discharge wave should be given by
The theoretical significance of K and the factors which influense i t have been discussed in detail by Ilkovic6 and Lingane and K ~ l t h o f f . ~Equation 5 is simply a statement of the fact that the concentration of the amalgam a t every point on the wave must be proportional to the current. By substituting the foregoing relations into eq. 2 we obtain
The half-wave potential is defined3 as the value of Ed,,.a t the midpoint of the wave, and since the last log term becomes zero when i = i d / 2 eq. 6 may be written
where Ca is the concentration of the amalgam formed on the surface of the mercury drops, COis the concentration of the metal ions in the depleted and hence the half-wave potential is given by layer of solution at the surface of the drops, Y, and RT 7,kK E,,2 = E: - -InnFy Yg ys are, respectively, the activity coefficients of the metal in the amalgam and the metal ions in It should be mentioned that the observed value the solution, and E: is the standard potential of the of Ed,,,includes a small iR drop in the solution. amalgam, that is, the e. m. f. of the cell : Reference However, with concentrations of supporting elecelectrode / M”+(a = l)/M(Hg)(a = 1) (I). trolyte greater than about 0.01 M the resistance When an excess of an indifferent electrolyte is of a polarographic cell is generally less than 1000 present so that the migration current is elimi- ohms, and hence the iR drop is usually less than nated, the reducible metal ions reach the surface of 0.001 v. per microampere, which is negligibly the dropping electrode only by d i f f u ~ i o n . ~ small. *~ Representing the concentration of the reducible When the resulting metal is not soluble in mermetal ions in the body of the solution by C, the cury it is simply deposited in the solid state on the current a t any point on the polarographic wave by surface of the dropping electrode, and in such a i, and the diffusion current by i d , we have the case the reduction of the metal ions will be given relation^*^^ by KC K(C - Co)
id =
i
or
id - i co = K
(3)
(4)
and C, = k i
Mn+
+ ne e M(s)
(9)
If this reaction would take place reversibly it readily can be derived that the equation of the polarographic wave should be
(5)
The validity of eq. 3, in which K is the diffusion where E L is the ordinary standard potential of current constant, has been amply demonstrated.2)4 the metal. Quite obviously the curve of this (1) Present address: Department of Chemistry, University of equation is not symmetrical about the half-wave California, Berkeley, California. (2) For a detailed review of the fundamental principles of the point, and therefore in this case the half-wave polarographic method see I. M. Rolthoff and J. J. Lingane, Chem. potential has no particular thermodynamic sigR P X , a4, 1-94 (1939). (3) J Heyrovsky and D . Ilkovic, Coll. Caech. Chem. Commun.,7 , nificance. The difficulty of obtaining reproduci198 (1935). (4) J
(1939).
J Lingane and I . M . Kolthoff, THISJOURNAL, 61, 825
(5) D. Ilkovic, Collection Czech. Chem. Commun., 6, 498 (1934): J . chim. phys., (France) 36, 129 (1938).
2100
JAMES
Vol. 61
J. LINGANE
ble electrode potentials in the classical manner with metals that are insoluble in mercury (e. g., metals of group VI in the periodic classification, the iron group, arsenic, vanadium, etc.) is well known, and chemical polarization and passivity phenomena are common in this group. Hence the reduction of such metals according to eq. 9 is in most cases probably not a reversible process. For these reasons the following discussion will be confined to those metals that are soluble in mercury, and whose ions are reduced a t the dropping electrode according to eq. 1.
0.023 v. for the thallous, lead, and indium ions, in good agreement with the theoretical values which are 0.059, 0.030, and 0.020 v. for the discharge of uni-, di-, and trivalent ions. It is evident that eq. 7, and the fundamental assumption that the dropping electrode is subject only to concentration polarization in the discharge of metal ions according to eq. 1, are essentially correct. By setting the second differential of eq. 7, i. e.
!g=Ey;--
1 -
0') equal to zero, i t is found that the curve of eq. 7 has a point of inflection when i = id/2. The polarographic wave is therefore symmetrical about the half-wave point, and EL12 coincides with the true inflection point of the curve. It has been found experimentally2,3 that the half-wave potential is entirely independent of the geometrical characteristics of the particular capillary that is used, the rate of flow of mercury, and the drop time. Therefore, it is evident from eq. 8 that the product kK is constant and independent of these factors. Although both k -0.35 -0.40 -0.45 -0.50 -0.55 -0.60 and K are individually dependent on &.e., Volts US. S. C. E. the properties of the capillary, the Fig. 1.-Log plots of observed current-voltage curves of thallous and lead rate of mercury flow, and the drop ions in 0.1 N potassium chloride, and of indium ions in 1 N potassium time, the effect of these factors on k chloride. The slopes of the three lines are Tl+ 0.059 v., Pb++ 0.033 v., must be inversely proportional to and In+++0.023 v. their effect on K , so that the product Equation 7 has been verified experimentally by kK remains constant. It is also an experimental Tomess and Kolthoff and Lingane.2 By plotting fact2v3that the half-wave potential is constant and Ed,,. against log i / ( i d - i) a straight line results, independent of the concentration of the reducible whose slope is equal to 2.3RT/nFY,and the value metal ions, provided that the composition of the of Ed,,, corresponding to a value of zero for the solution with respect to foreign salts, i. e . , Y,, is log term is the half-wave potential. This is kept constant. It is evident, therefore, that the demonstrated in Fig. 1, where the plots have been half-wave potential is a characteristic property of constructed from experimental current-voltage the reducible ions, and i t has definite thermocurves obtained by the writer, in the electrolysis of dynamic significance. Influence of the Concentration of Supporting 0.002 M solutions of thallous, lead, and indium Electrolyte on the Half-Wave Potential.-Since ions in the presence of an excess of potassium the activity coefficient, ys,of the reducible metal chloride. The current-voltage curves were obions decreases with increasing ionic strength, i t is tained with the apparatus previously d e s ~ r i b e d . ~ ~ ~ to be expected from eq. 8 that El,zshould be shifted As predicted by eq. 7, the experimental points fall somewhat to more negative values with increasing on straight lines. The observed slopes of the concentration of supporting electrolyte. This is three lines are, respectively, 0.059, 0.033, and actually observable experimentally, as shown by (6) J. Tomes, COX Czech. Chem. Commun., 9, 12, 81, 160 the data in Table I obtained by the writer. (1937). nFY
(id
Aug., 1939
POTENTIALS OF SIMPLE METALS AT THE DROPPING MERCURY ELECTRODE
2101
TABLE I HALF-WAVEPOTENTIALS O F THALLOUS, ZINC, CADMIUM, AND LEAD IONS IN VARIOUSCONCENTRATIONS OF SUPPORT- where E& is the ordinary standard potential of ING ELECTROLYTE the metal, that is, the e. m. f. of the cell : Reference Half-wave potentials in volts referred t o the saturated electrode/M"+(a = l)/M(s) (111). calomel electrode at 25". Supporting electrolyte
0 . 0 2 N KNOs 0 . 1 N KNOs 1 NKNOs 0.02 N KC1 0.1 NKCl 0 . 2 5 N KCl 1 NKCl
TI+
Zn++E1/2
-0.451 .459 .477
-0.988 0.997 1.012 -0.988 0.995
-0.459 ,466 .480
-1.022
Pb++
-0.388 .405 .377 .396 .402 .435
-
Cd++
-0.572 .578 .586 - .578 .599 .642
These data were obtained by the manual method of measurement and with the cells that have already been d e s ~ r i b e d ,and ~ ~ ~E d . , . was measured directly against an external saturated calomel reference electrode during the electrolysis. The concentration of the metal ions was 5 X M o r smaller, the current a t the half-wave point was less than 2 microamp., and hence the correction for the iR drop in the solution was negligibly small. The E,,, values are reproducible to about * 2 mv. The negative shift of the Ell2 values with increasing ionic strength is of the order of magnitude predicted by eq. 8, when potassium nitrate is used as supporting electrolyte. The half-wave potential of thallous ions is the same in potassium nitrate and potassium chloride media a t the same ionic strength, but with the other metal ions the negative shift is considerably greater in potassium chloride than in potassium nitrate solutions, due to complex ion formation between the divalent metal ions and chloride ions. It is well known that the half-wave potentials of metal ions are shifted to more negative values by complex format i ~ n . ~ In J potassium nitrate solutions there is no appreciable complex formation, and only the ionic strength effect is operative. Thermodynamic Interpretation of the HalfWave Potential.-In order to interpret the halfwave potentials thermodynamically, i t is convenient to compare them with the ordinary standard potentials of the metals. Consider the cell M(s)/M"+/M(Hg) two phase (II),in which theleft electrode is the solid metal, and the right electrode is its saturated two-phase amalgam. Let a s s t d . be the activity of the metal in the saturated liquid amalgam in contact with a solid phase which may be either the pure metal, or a solid compound, or solid solution, of the metal and mercury. The e. m. f. of this cell is given by
If we express the composition of the amalgam in terms of mole fraction of the metal, N , and designate the solubility of the metal in mercury by N s a t d . and the corresponding activity coefficient by Ysatd., we obtain from eq. 11 E: = Eo f EII
+ RT - In
Nsatd. ysatd.
FU
(12)
By substituting this expression for E8 into eq. 8 we find that the difference between the half-wave potential of a metal ion and its ordinary standard potential is given by
(13)
The first two terms on the right side of this equation are thermodynamic terms, but the last term involves the kinetics of the electroreduction. fn the case of metals which do not form solid compounds or solid solutions with mercury, e. g., zinc, EII is zero. In general, however, when the metal forms a solid compound or solid solution with mercury, EII is equal to - AF/nFy, where AF is the free energy increase in the formation of the solid M,Hgy, according to the reaction xM(4
+ yHg(1) *K H g , ( s )
(14)
It is evident, therefore, that the difference between E,,, and E L depends on three distinct factors; the affinity of the metal for mercury ( A F of reaction 14)) the solubility of the metal in mercury, and the kinetic term kK. A comparison of the half-wave potentials and the ordinary standard potentials of several metal ions is given in Table 11. The values of El,? given for the first four metal ions are the values obtained with 0.1 N potassium nitrate as the supporting electrolyte (Table I). The E,, values of sodium and potassium ions were taken from the compilation given by Heyrovsky and Ilkovic3; they were obtained by using tetrasubstituted alkylammonium salts as the supporting electrolyte. It will be noted that the difference between E,,, and E& is greatest in the case of the alkali metals, due to their great affinity for mercury. In these cases the difference is due chiefly to the large value of E I I ,and the second and last terms in eq. 13 are of subordinate importance. On the
JAMES J.
2102
LINGANE
Vol. 61
TABLE I1 COMPARISON OF HALF-WAVE POTENTIALS AND STANDARD ELECTRODE POTENTIALS OF SEVERAL METALIONS The values of El/, and E L are in volts with respect t o the saturated calomel electrode at 25'. I on El/% EL - E; EII Nsstd. yistd. kK,oalod. -0.582 +O. 123 $0,003" 0.435' 7.75' 0.025 - .372 - .016 . 006d .0143b 0. 717h .033 - ,647 ,069 .0953' ,051" .216' .0025 Zn++ -1.008 .011 0' .0638" .756"' .011 -2.961 Na+ 4- .84 ,780" .0538' 1.28' .005 -3.170 $1.03 1.O O l h .0 2 S h K+ 5.52* .036 * Heyrovsky and Ilkovic, ref. 3. Richards and Daniels, THISJOURNAL,41, 1732 a I n 0.1 N KNO:,; see Table I. Gerke, ibid., 44,1684 (1922). e Hulett, Trans. Am. Electrochem. SOL,7,333 (1905). Clayton and Vosburgh, (1519). THISJOURNAL, 58, 2093 (1936). ' Bent and Swift, ibid., 58, 2216 (1936). Bent and G i U a n , ibid., 55, 3989 (1933). Hoyt and Stegeman, J . Teeter, ibid., 53, 3917, 3927 (1931). Lewis and Randall, "Thermodynamics," p. 267. Phys. Chem., 38, 753 (1534). Hildebrand, "Solubility of Non-Electrolytes," Reinhold Publishing Corp., New York, 58,2220 (1936). 1936. 'n Pearce and Eversole, J. Phys. Chem., 32,209 (1928). " Bent and Forziati, THISJOURNAL, Tl+ Pb+ + Cd+ +
-0.459" .388" - .5w - .997" -2.12b --2.14*
-
+ +
'
other hand, in the case of thallium EIIis negligibly small, but the solubility of thallium in mercury is large, so that the difference between E,,, and E L is determined practically entirely by the last two terms in eq. 13. The solubilities of the various metals in mercury a t 2.5' are listed in the sixth column of the ta$le, in terms of mole fraction, and the corresponding activity coefficients are given in the seventh column. The values of Ysatd, are based on infinite dilution (7, = 1) as the standard state. The last column contains approximate values of kK for the various metals calculated by means of eq. 13 from the observed differences between E,,, and E$, and the experimental values of Ell, Nsatd,,and ?sat& given in the table. In this calculation i t was assumed that the activity coefficient of the univalent ions is 0.8, and that of the divalent ions 0.5, a t an ionic strength of 0.1 M in potassium nitrate solution^.^ Since we had no exact knowledge, a flriori, regarding the concentration of the amalgams formed on the surface of the mercury drops, i t was assumed that the concentrations of the amalgams were so small, under the usual conditions of a polarographic experiment, that 7, was equal to unity. Because of this uncertainty the calculated values of kK can only be considered as approximations, but they are sufficiently accurate to indicate a t least the order of magnitude of the constant k. Although the observed values of E l / 2 - E L , and EII,vary from a few millivolts up to one volt, and the activities of the saturated solutions of the metals in mercury vary widely from 0.01 in the case of lead up to 3.5 in the case of thallium, the calculated values of kK are all of the same order of (7) J. Kielland, THISJOURNAL, 69, 1675 (1937).
magnitude. Unfortunately, no independent experimental method for determining k has yet been discovered, so that a more direct test of eq. 13 is not possible a t the present time. However, the uniformity of the various calculated values of kK constitutes good indirect evidence of the validity of eq. 13. The diffusion current constant K for the metal ions in Table I1 is of the order of magnitude of 5 microamp. per millimole per liter, with capillaries of the usual dimension^.^^^ Hence the apparent value of k, from the data in Table 11, is of the order of 0.005 mole fraction per microamp. for most of the metals. If we express the composition of the amalgams in volume concentration units, the apparent value of k is of the order of 300 mmol. per liter per microamp. This rather large value of k indicates that the deposited metal atoms remain close to the surface of the drop during its life, and that diffusion into the body of the drop is relatively slow. At the present time our knowledge of the diffusion processes in the mercury drops is so meager and incomplete that any attempt at a more detailed interpretation of these results at this time would be pure conjecture.
summary The equation of the current-voltage curves in the electrodeposition of metal ions a t the dropping mercury electrode has been discussed. When the reduced metal is soluble in mercury the dropping electrode is subject only to concentration polarization. Experimental data have been presented which demonstrate that the half-wave potentials of metal ions are shifted somewhat to more negative values with increasinrv ionic strendh of the solution. "
Aug., 1939
MUTAROTATION OF TETRAMETHYL-a-d-GLUCOPYRANOSEAND -MANNOPYRANOSE2 103
The characteristics of the half-wave potential have been discussed, and an equation was derived relating the half-wave potentials to the ordinary standard potentials of the metals. The difference between the polarographic half-wave potential of a simple metal ion and the ordinary standard PO-
tential of the metal was shown to be a function of three distinct factors : (1) the affinity of the metal for mercury; (2) the solubility of the metal in mercury; and ( 3 ) the kinetics of the diffusion processes in the solution and in the mercury drops. RECEIVED MAY 12, 19.19
MINNBAPOI.IS, ~ I I N N .
(CONTRIBUTION FROM THE AVERYLABORATORY OF CHEMISTRY, UNIVERSITY OF NEBRASKA]
Mutarotation of
Tetramethyl-a-d-glucopyranose pyranose
and Tetramethyl-a-d-manno-
BY B. CLIFFORD HENDRICKS AND ROBERT E. RUNDLE
In a previous paper,' a study of the complexity of the mutarotation of d-galactopyranose was reported. In this communication a study of the analogous glucose and mannose sugars is presented. The mutarotation of tetramethyl-a-d-glucopyranose has been investigated by Purdie and IrvineJ2Lowry and c o - ~ o r k e r s ~and - ~ Boeseken and Couvert6 in water and other solvents. These workers, however, gave direct attention to the reaction order of the sugars' mutarotations a t only one temperature. The mutarotation of tetramethyl-a-d-mannopyranosehas been previously reported, though only incidentally. A systematic study of the unmethylated a-d-
initial rotations: [a]OD +11.5; [a]% +6.3; equilibrium rotations: [ a ] ' ~+2.5 and [ a I 2 ' ~-0.2. TABLE I MUTAROTATION OF TETRAMETHYL-&-GLUCOPYRANOSE 25' 2.4298 g. of sugar in 25 ml. of water Time
Min.
Sec.
7 9 11 13 20 25 34 49 62 88
15 0 15 50 30 0 50 0 25 15 0 0
Rotation obsd.
19.60 19.49 19.32 19.15 18.71 18.46 17.98 17.42 17.02 16.50 16.25 16.07 15.75
(kl
AT
+calcd. kz) X 10s 9.00 8.57 8.84 8.75 8.70 8.75 8.78 8.81 9.17 9.20
glucose8 does not support the reportedg complex 104 mutarotation of a-d-glucose. The authors pro125 posed to learn whether methylation and mutam Av. 8 . 8 6 * 0.34 rotation a t or near 0' would give evidence of TABLE I1 mutarotation complexity. OF TETRAMETHYL-a-d-GLUCOPYRANOSE AT Since there is a paucity of data upon tetra- MUTAROTATION 1.0" methylmannose they prepared and followed the 2.819 g. of sugar in 25 ml. of water mutarotation of tetramethyl-a-d-mannopyranose Time Rotation ( k+ ~ kz) X l o 3 Min. Sec. obsd. calcd. also. 9 15 25.32 The two sugars were prepared as indicated in a 10 45 25.30 previous paper.1° The properties of the tetra18 10 25.24 0.754 methyl-a-d-glucopyranose used were : initial rota25 30 25.18 ,644 32 30 25.12 ,786 tions, [ a ]OD +104.0; [a]2 5 ~ 104.0; equilibrium 40 50 25.03 .864 rotations: [~]OD +80.4; [ a I z 5 ~84.8 and m. p. 58 20 24.90 .829 92.5-93.5'. The constants for the tetramethyl81 45 24.82 .670 a-d-mannopyranose used were m. p. 49-50' ; 166 30 24.26 ,709
+
+
(1) Hendricks and Rundle, THIS JOURNAL, 60, 3007 (1938). (2) Purdie and Irvine, J. Chem. Sac., 86, 1070 (1904). (3) Lowry and Richards, ibid., 127, 138 (1925). (4) Jones and Lowry, ibid., 720 (1926). ( 5 ) Richards, Faulkner and Lowry, ibid., 1733 (1927). (6) Baeseken and Couvert, Rcc. trau. chim., 40, 354 (1921). (7) Drew, Goodyear and Haworth, J . Chem. Soc., 1237 (1927). ( 8 ) Isbell and Pigman, Bur. Slondards J. Research, 18, 141 (1937). (9) Worley and Andrews, J . Phys. Chem., 32, 307 (1928). (10) Hendricks and Rundle, THISJOURNAL, 60, 2563 (1938).
255 293 424 .575 646 748
0 0
0 0 0 0 m
23.78 23.62 23.14 22.64 22.46 22.18 20.68
,707 .693 .661 ,660 ,651 ,662
Av. 0.715 * 0.149
