1290
I. A. AMMAR AND S. A. AWAD
Vol. 60
them using the Schulz distribufion (equation 10). 1 --8 This result reduces to that obtained previously66 for the case of a “Gaussian” chain, i.e., one for has been worked out previoi~sly~~ for a2 = 0 (Gauswhich G / M is constant, by substituting u2 = 0. The analogous correction factor qP to be used in sian case). When an # 0 equation A-4 leads to the calculation of the quantity {E”) equation 33.
HYDROGEN OVERPOTENTIAL ON SILVER IN SODIUM SOLUTIONS
HYDROXIDE
BY I. A. AMMAR AND S. A. AWAD Faculty of Science, Department of Chemistry, Cairo University, Cairo, Egypt Received March 2, IS56
Hydrogen overpotential, 7, has been measured on Ag cathodes in 1.0 t o 0.01 N aqueous NaOH solutions, in the current density range 3 X 10-8 to 10-3 amp./cm.2 Measurements have also been cari,ied out at 30, 40, 50 and G O O , and the heat of activation, AH:, at the reversible potential is calculated. The electron number, A, is calculated from overpotential measurements at low cathodic polarization, and the values obtained are very near t o unity. A slow discharge process from water molecules is established as the rate-determining mechanism for hydrogen evolution on Ag in alkaline solutions. The effect of p H on q is also studied and attempts are made toward the explanation of such an effect.
Introduction Hydrogen overpotential a t Ag cathodes in aqueous HCl so1ut)ionswas studied by Bockris and C0nway.l They observed two slopes in the linear logarithmic section of the Tafel lines. This was attributed to the specific adsorption of H 3 0 + ions. A slow discharge rate-determining mechanism was suggested by the above authors to account for their overpotential results. The aim of the present investigation was t o study the overpotential characteristics for Ag in aqueous NaOH solutions. Previous work in alkaline solutions2 indicated that the discharge from water inolecules \vas rate determining. Experimental ntnl technique was essentially the same as and Potter.2 The electrodes were sealed under an atmosphere of pure dry hydrogen in fragile glass hulbs. Spectroscopically pure silver wire (1 mm. diameter) was used. The silver wire was spot-welded to platinum before sealing it into glass. The glass bulbs were broken directly before the measurements were started. Pure sodium hydroxide solutions were prepared under an atmosphere of pure hydrogen, followed by preelectrolysis at 1.0 X 10-2 amp./cni.* for 20 hours on a silver preelectrolysis electrode. All glass p:Lrts of the apparatus were made of arsenic-free borosilicate glass, technically known as “ H y ~ i l . ” ~Solutionsealed taps and ground glass joints were used for the construction of the cell. Connections between the various parts of the apparatus were made with the help of movable glass hridges. The appitratus was cleaned with a mixture of “Anrtlar” nitric and sulfuric acids. This was followed by washing with equilibrium water ( K = 2.0 X mho cm.-l) and the cell \vas then ivrtahed several times by conductance water ( K = 2.0 X 10-1 mho cm.-l) prepared by reflusing equilibrium water under an atmosphere of pure hydrogen for 6 Iioui,s. Before e w h run, care was taken to free the previously cleaned cell from oxygen. This was done by filling the cell completely with conduct8ancewater, and then i,epl:icing this \vater by pure hydrogen before the NaOH solution H’BS introduced. Cylinder hydrogen was purified from oxygen, carbon monoxide and other impurities by passing it over hot copper (1) J. O’hl. Borkris and B. Conway, Trans. Faraday Soc., 48, 724 (1952). (2) J. 0’11.Bockris and E. C. Potter, J . Chem. P h y s . , 20, 614 (1952). (3) Prepared by Chance Bros., L t d . , Birmingham, England.
(450°),then over a mixture of Rhot and CuO (technically known as “Hopcalite”) to oxidize CO t o Con. COP was then removed by soda lime. A platinized plrttinum electrode in the same solution and a t the same temperature as the test electrode was used as a reference. The direct method of measurements was emand ployed, and Tnfel lines were traced between 3 X amp./cm.2 The potential was measured with a valve p H meter millivoltmeter, and the current with a multirange milli-micro-ammeter. At low currents, the current was checked by measuring the p.d. across a standard resistance. The temperature was kept constant with thi. help of an air thermostat controlled t o &0.5”. The current density was calculated using the apparent surface area.
Results The Tafel line slope, b, the transfer coefficient , a and the exchange current, io, for the cathodic hydrogen evolution a t Ag in 1.0, 0.2, 0.1, 0.05 and 0.01 N aq. KaOH solutions are given in Table I. Figure 1 shows four Tafel lines on Ag in 0.1 N aq. NaOH solution a t 30, 40, 50 and GO”. At GOo the TABLE I Concn. N
1 .o
Temp., O C .
30 40
0.2
0.1
50 60 30 40 50 60 30 40 50 GO
0.05
30 40
0.01
50 GO 30 40 50 60
b (v.)
(I
0.120 ,120 ,120 .120 0.120 ,120 .120 ,120 0.120 ,120 ,120 ,120 0.120 ,120 ,120 ,120 0,122 ,122 ,122 ,122
0,500 ,517 ,533 ,550 0,500 ,517 ,533 ,550 0,500 ,517 ,533 ,550 0.500 ,517 ,533 ,550 0,402 ,508 ,525 .541
io (aiiip./cni.2)
3.2 x 5.0 x 7.1 x 1.1 x 2.2 x 3.6x 5.6 X 8.3 x 2.0 x 3.2 x 5.0 x 8.3x 1.8x 2.8 x 4.5 x i.1 X 1.3x 2.0 x 3.2 x 4.8
x
10-7 10-7 10-7 10-6 10-7 10-7
lo-’
10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7
HYDROGEN OVERPOTENTIAL ON SILVER I N SODIUM HYDROXIDE
Sept., 1956
asymptotic part of the Tafel line is shorter than the corresponding parts at lower temperatures. The transfer coefficient is calculated according to: b = (2.303RT/aF). The electron number, X, defined as the number of electrons necessary to complete one act of the ratedetermining step,4is calculated using
0.4
. 0.3
1291
Hr
t
h
d
v
c 0.2
0.1
0.0
-7
and (2)
exp(X?.F/RT) = 0.05
is the overpotential at which the Tafel line departs from linearity owing t o the appreciable rate of ionization of adsorbed atomic hydrogen. Equation 2 gives approximate values for X (cf. ref. 4). The values of the electron number, i.e., XI (calculated according to equation 1) and A2 (calculated according to equation 2 ) are given in Table I1 for 30,40 and 50". Values of X at GO" could not be calculated owing to the fact that only very few measurements of 7 below 20 mv. can be experimentally obtained (cf. Fig. 1). The relation between 7 and io for small cathodic polarization (below 20 mv.) is shown in Fig. 2 for 0.1 N NaOH solution. 7.
-5 -4 -3 log c.d. Fig. 1.-Tafel lines for Ag in 0.1 N NaOH solution as a function of temperature: I, 30'; 11, 40"; 111, 50"; IV, 60". -6
1
2
4
3
io X 10-7. Fig. 2.-Relat,ionship between 7 (below 20 mv.) a;d the ne! ~ a t h o d i c ~ c u r i ~for e n tAg ill 0.1 N NaOH: I, 30 ; 11, 40 ; 111, 50 .
TABLE I1 a
Values of
Concn. N
1.0
0.2 0.1
0.05 0.01
are given to the nearest first decimnl figure.
Temp., "C.
30 40 50 30 40 50 30 40 50 30 40 50 30 40 50
- (b?/bic)
0
v./amp./cin.
8.0 X 5.0 X 3.5 X 1.2 X 8.3 X 4.3 X 1.2 X 8.0 X a1.7 X 1.5 X 8.0 X 5.0 X 1.7 X 1.1 X 7.0 X
XI
10" lo4 lo4 106 lo4 lo4
1.0 1.1 1.1 1.0 0.9 1.2 1.1 1.1 1.2 1.0 1.2 1.2 1.1 1.2 1.2
lo6 lo4 IO' lo5 10' lo4 106 lo6 lo4
0s
An
0.070 0.070 0,070 0.065 0.065 0.065 0.070 0.065 0.OG5 0.075 0.070 0.070 0,075 0.075 0.070
1.1 1.2 1.2 1.2 1.2 1.3 1.1 1.2 1.3 1.0 1.2 1.2 1.0 1.1 1.2
The effect of pH 011 overpot,ential at three dif3.2 X ferent current densities (3.2 X and 3.2 >( amp./cm.') is given in Table 111. TABLE I11 Temp., ' C .
3.2 x 10-4 anip./cm.z
30 40 50 60
0.025 ,025 ,025 ,025
( b q / b p H ) in v. a t
3.2 x 10-5 amp./cni.2
3.2 x 10-4 amp./cm.2
0.028
0,030
,028
,028
,025 ,030
,030
,025
The heat of activation, AH& at the reversible potential is calculated according t o the equation io = B exp( -AHo*)/RT)
(3)
~ relawhere B is the Eyring entropy f a ~ t o r . The (4) J. O'M. Bockris and
E. C. Potter, J. Electrochem. Sac., 99, 169
(1952).
(5) 9. Glasstone, H. Eyring and K. Laidler, J . Chem. Phys., 1, 1053 (1939).
3.1 3.2 3.3 I / T x 10-3. Fig. 3.-Rel;ttionship between t,he logarithm of the exchange current and ( l / T ) : I, 1.0 N ; 11, 0.2; 111, 0.1;IV, 0.05; V, 0.01. 3.0
tion between log io and 1/T is shown in Fig. 3. Values of A H : , thus calculated, are given in Table IV. TABLE IV
Concn., N
1 .o 0.2 0.1 0.05 0.01
- [d log io/d(l/T) 1.81 x 103 1 . 9 0 x 103 2 . 0 5 x 103 2 . 0 0 x 103 1.81 x 103
A H ( ) * (kcal.)
8 3 8.8 9.4 9.2 8.3
If A H ; is assumed to be independent of concentration, a mean value of 8.8 kcal, is obtained from the results given i n Table IV. Using this mean value for AH5 in equation 3, log B is calculated for the various NaOH solutJions studied. The results a t 30" arc given in Table V. The plot of log B against the 1ogarit)hm of the activit.y of NaOH results in a straight, line wit,h a slope of approximately 0.2. Discussion The act'ivat'ion overpotential associated with the cathodic hydrogen evolution may be attributed t o a slow discharge process, a slow elect,rochemical de-
I. A. AMMAR AND 8. A. AWAD
1292
gested by Glasstone, Eyring and Laidler.5 The value of log B calculated by the above authors for such a rate-determining mechanism amounts to 1.5. This value is independent of the electrolyte concentration. The factor B is expressed by3
TABLE V Concn.. N
-10s io
-log B
1.o 0.2 .1 .05
6.50 6.65 6.70 6.75 6.90
0.20 .35
.01
.40 .45 .60
kT B = AFK h ai exp
sorption or a slow catalytic re~ombination.~A rate-determining slow discharge process is characterized by a Tafel line slope of 0.120 v. a t 30" and by X = 1. For a rate-determining electrochemical desorption, the Tafel line exhibits two slopes of 0.040 and 0.120 v. at 30" in the linear logarithmic section, and A is 2 . A rate-determining catalytic mechanism is distinguished by two Tafel line slopes of 0.030 v. a t 30" (at the low current density range) and v. (manifested by the occurrence of a limiting current a t high current densities). For this mechanism X is also 2. From this and the data given in Tables I and I1 it is evident that the rate of hydrogen evolution at Ag cathodes in NaOH solutions (0.01 to 1.0 AT) is controlled by a slow discharge mechanism. Distinction between the discharge from H30+ ions and the discharge from water molecules can be made with the help of the pH effect on hydrogen overpotential. For the discharge from H30+ ions (cf. ref. 2)
where p is a symmetry factor for the energy barrier of the discharge process, and E is the p.d. between the Helmholtz double layer and the bulk of solution. For the condition when (@/d In UH.) "0 and p"0.5, the pH effect associated with the discharge of H30+ is given by (dv/dpH)ic = -(2.303RT/F) (5 1 thus indicating that q becomes more negative with increase of pH. For the discharge from water molecules (under the same condition as 5 ) , the p H effect is given by (dv/dpH)ic = (2.303RT/F)
Vol. 60
(6)
(F) ,
,
(7)
where K is the transmission coefficient, lc is Boltcmann's constant, h is Planck's constant, ai is the activity of the reactants in the initial state (Helmholtz double layer) and AS: is the standard entropy of activation a t the reversible potential. It is evident from Table V that the values of log I3 calculated for Ag, are different from the value given by Glasstone, Eyring and Laidler. It may thus be concluded that the prototropic transfer is not rate determining, although the discharge takes place from water molecules, for hydrogen evolution on Ag in KaOH solutions. The pH effect associated with the discharge from water molecules is given by (6) when the cathode potential is very near to that of the electrocapillary maximum. I n dilute NaOH solutions, for conditions far from the electrocapillary maximum (d[/d In a") = - (b[/d In a ~ ~=, ) (RT/F) and it follows that 2.303RT (bv/bpH)ic = 2 ( 7 - )
In between the above two conditions the pH effect lies between 60 and 120 mv. per unit increase of pH, a t 30". From Table I11 it is clear that the experimentally observed values of (dq/d pH)io are different from the theoretically deduced values given above. The experimental results cannot also be exdained on the assumDtion that hvdroaen originates- from Na ions and water m d e ~ u l & , ~ since this mechanism requires that ( d q / b pH)i, = 2(2.303RT/F). - I n an attempt to correlate the experimental results, for the p H effect in alkaline solutions with the theory, Bockris and Potter2 have suggested the possibility of an increase in the activity of wat,er molecules in the double layer as compared t o that in the bulk of solution. This is brought about by the orientation of water molecules under the high field strength near the electrode. Under such conditions the effect of pH on q is given by
The condition (@/b In UH.)"O may be applicable when the electrode potential is very near to that of the electrocapillary maximum, whereupon in absence of specific adsorption E 5 0. The direction of change of q with p H is thus a good criterion for the distinction between the discharged entities. It is clear from Table I11 that (dq/d pH)icfor the (9) cathodic hydrogen evolution at Ag in NaOH solutions is positive, thus indicating that the discharge where pv = 1.83 X lo-'* e.s.u. is the dipole motakes place from water molecules. Parsons and ment of water, Cd is the integral capacity of the difBockris6 have shown that in alkaline solutions the fuse double layer, and d = 4 is the dielectric condischarge from water molecules is more probable stant in the Helmholtz double layer. The integral than the discharge from H 3 0 + ions because the capacity, Cd, is calculated according to Grahame.8 supply of H3O+ ions from the bulk of t,he solution The pH effect on q for Ag in alkaline solutions is calto the electrode would be slow. I n such solutions culated according t o (9). Values of ( b [ / blog as.) the concentration of water molecules is approx- are calculated' taking the potential of the electroimately 1014times the concent,ration of H30+ions. capillary maximum on Ag as 0.05 volt referred to The discharge of hydrogen from water molecules the normal hydrogen electrode. For 0.1 N NaOH, may take the form of a prototropic transfer sug- a t 30°, the calculated values of (bq/b pH)i, are: (6) R . Parsons and (1951).
J. O W . Bockris, Trans. Farudau Roc.,
47, 914
(7) (8)
J. O'M. Bockris and R. G.Watson, J . chim. phys.. 49, 1 (1952). D. C. Grahame, Chem. Reus., 41, 441 (1947).
RELATIONSHIP OF FORCE CONSTANT AND BONDLENGTH
Sept., 1956
0 mv. at 3.2 X amp./cm.2, ~2 mv. at 3.2 X amp./cm.2 and -19 mv. at 3.2 X amp./cm.2. Furthermore, the calculated values of (%/a pH)G are dependent on pH. An alternative explanation for the experimental pH effect on q for Ag in alkaline solutions (Table 111) may, thus, be considered. The net cathodic current, i,, is related t o the exchange current, io, by .i = io exp
log B = const.
+ 0.2 log aNa’
1293 (13)
Since the only term in B (cf. equation 7) dependent on concentration is ai, it follows from (7) and (13) that log ai = 0.2 log U N ~ .
(14)
Introducing (14) in (12) one gets
(- a?F m)
Since (bq/b log a ~ * ) i=, - ( b ~ / log d a~s’)ie,equawhere a is approximately 0.5 at 30” (cf. Table I). tion 15, therefore, yields a value of (%/a pH)i, = 0.024 volt a t 30”. The pH effect, thus calFrom equations 3 , 7 and 10 culated, is independent of pH and is very close to the experimental values given in Table 111. i, = XFK kT h ai exp - evp( eap( It must be noted that the validity of the above (11) argument depends on the assumption that A&* Taking ASo* and A H o * as independent of concen- and AHo*are independent of concentration, and tration, equation 11, at constant i, and temperature on the applicability of equations 13 and 14, both of which are based on experiment. reduces to The authors wish to express their thanks to Prof. 7 = const. ( 2 R T / F ) In ai (12) A. R . Tourky for his interest in the work, and to log B is related to log a ~by~the- empirical relation Prof. J. O’M. Bockris for helpful discussions.
F)sF)
(;*’)
+
THE R.ELATIONSHIP OF FORCE CONSTANT AND BOND LENGTH BY RICHARD P. SMITH Deparlmenl of Chemistry, University of Utah, Salt Lake Cily, Utah Received March 19, 1966
It is suggested that the force constant is inversely proportional to the square of the equilibrium internuclear distance for groups of molecules A-B where A and B are in the same column of the periodic table (e.g., 0 2 , SO, SZ,etc.). The relationship also seems to hold for hydrides of elements in the same column. A natural extension would be to suppose that k,R,* is constant for molecules A-B where A is in one particular column and B is in the same or another one, though data are not available to test the more general hypothesis. Our relationship reminds one of a bond length-bond energy correlation of a similar character recently proposed by Pauling.
A number of empirical formulas relating force constant and equilibrium internuclear distance (bond length) have been proposed.’ Such relationships are useful for predicting unknown constants, for indicating probable errors in existing data, and for pointing the way to more complete bond “models1’ or otherwise increasing our understanding of the nature of the chemical bond. It would seem that an empirical relation between molecular constants would be the more likely to be of use in fulfilling any or all of these functions, the simpler it is. Thus the empirical rule that the length of a bond A-R is nearly constant and is usually close to the arithmetic mean of the lengths of A-A and R-B leads a t once to a familiar model in which atoms in molecules are represented by spheres of constant radii (“covalent bond radii”). A more complicated rule, though perhaps more accurate, would not lead to this model. Deviations from the expected lengths may then be discussed in terms of the superposition of other effects on the basic model. Recently Pauling2 has suggested the unusually simple rule that in a series of homopolar bonds in-
volving a particular column of the periodic table (e.g., 0 2 , SP,Sez, Te2) the bond energy is proportional to the reciprocal of the bond length. This relationship is supported by the data for some sequences, but is incompatible with the data for others (e.g., Fz,Clz, Brz,Ip). It has been noted that. kJie2 is nearly constant for the ground states of hydrogen halide^.^ (Here Re is the equilibrium internuclear distance and k, is the force constant for infinitesimal amplitude, terminology and notfation of Herzherg.’) This is illustrated by the plot of ke against R e - ’ for this series, given in F i g . 1. The data used are indicated in Table I . The least-squares straight line through the origin is dr:twn in. It is seen that k&e2 = constant indeed holds very accurately for this series. The above correlation suggests that k e n , ’ may be constant for other groups of this nature. Tests of this hypot,hesisare indicat,edin Figs. 1 , 2 , 3and 4. The data are inostJy taken from f€eraberg4and are collected, with litorature references, in Table I. In each case, the least-squares. lines which pass through the origin are drawn in; the slopes of these lines are given in Table 11. For molecules in
(1) C . Herzberg, “Spectra of Diatomic Molecules,’’ 2nd Ed., D. Van Nostrand Company, Inc., New York, N. Y., 1950, pp. 453-409. (2) L. Pauling. Tars JOUENAL,MI, 662 (1954).
(3) S. Glasstone, “Thooretical Chemistry,” D. Van Nostrand C o . . Inc.. New York. N. Y . , 1944, p. IliO. (4) Ref. 1 , Appendix.
