Oct., 194tj
POLYMERIZATION
AND
[CONTRIBUTION FROM THE
ADS~RPTION AT THE DROPPING MERCURY ELECTRODE
2047
DEPARTMENT OF CHEMISTRY O F THE UNIVERSITY OF OREGON]
Polarographic Reduction of Carbon Dioxide. 11. Polymerization and Adsorption at the Dropping Mercury Cathodel BY PIERRE VAN RYSSELBERGHB I n a recent brief notela we have reported certain ticularly indicated when the variation of the halfobservations made on polarographic reduction wave potential with temperature is small enough waves obtained with solutions of carbon dioxide in to preclude rate complications and therefore real 0.1 molar tetramethylammonium chloride. The irreversibility.‘ As a matter of fact a rather larger slopes of the waves were found to differ appreci- variation with temperature than is usually acably from those obtained in the ordinary reversible cepted is still compatible with reversibility when, reductions involving two hydrogen ions and two as is the case with the following treatment, adelectrons per molecule reduced. This feature of sorption equilibrium constants are incorporated the carbon dioxide waves is shared by many other into the half-wave potentials. Irreversibility polarographic waves on record for which no en- should also manifest itself through a temperature tirely satisfactory interpretation has so far been variation of a in equation (1). The closeness of advanced. I n the present paper we develop, for equation (l),even with a smaller than one or difthose cases (including carbon dioxide) where the ferent from some simple integer, to the ordinary influence of temperature on the half-wave poten- Nernst-type of equation strongly suggests that tial and the slope indicates no irreversibility on similar interpretations apply to all these cases. account of rate complications, an interpretation I n the present paper we show that an equation of based upon consideration of polymerization and type (1), with a smaller than one, corresponds to the reversible reduction of neutral molecules (caradsorption a t the dropping mercury cathode. I n general polarographic reduction waves follow bon dioxide for instance) when several of these molecules, adsorbed a t the surface of the mercury equations of the type2 . drop, share two hydrogen ions and two electrons, RT i E = El/, + - In and when the reduction product is adsorbed a t (YF id - i ( E = absolute value of the cathode potential, El/, the mercury surface but in equilibrium with some = absolute value of the half-wave potential, R = dissolved reduction product in accordance with a molar gas consi;ant, T = absolute temperature, Freundlich adsorption isotherm. By “reversible” a = parameter, F = one faraday, In = symbol of reduction we mean a reduction following a potennatural logarithms, i = reduction current, i d = tial concentration equation of the Nernst type delimiting diffusion current). When a is a small in- rived on the basis of the general condition of electeger i t represents the number of electrons in- trochemical equilibrium. V‘e shall divide our discussion into two parts, volved in the reduction of one ion or one molecule. according to whether the solutions considered are There are, however, many cases on record for which a is smaller than one. Carbon dioxide is buffered or not. We shall introduce the following one more case o.E this type. This situation is par- two notations l/ff= XI2 ticularly frequent with organic reductions and is then often ascribed to one or more of a variety of and factors causing irreversibility. Since in many of ;/id = u these cases the reduction products cannot be iso- Equation (1) is thus transformed into lated i t is impossible to establish whether the xRT u polarographic h:slf-wave potential coincides with E = Et/, 4-In (4) 2F 1 - u a potentiometrically determined reversible oxidation-reduction potential3 or not. In other words, Case I: The Solution is Buffered in such cases, the actual proof of irreversibility is Let us consider the reaction lacking, and it is reasonable to develop interpretations of these waves on the basis of the theory xR 4-2Hf+ 2e- +R,H2 (5) of electrochemical equilibrium which is the foun- in which R represents some reducible substance. dation of the interpretation of the great majority We refer the number x of molecules reduced to of polarographic waves. Such a procedure is par- two electrons rather than to one because, if one elec(1) Presented as part ol a paper entitled “Polarographic Studies on tron were involved, free radicals would be Carbon Dioxide and Chlorophs.11.” by P. Van Rysselberghe and J. hf. formed and there would in general be association McGee a t the Pacific Northwest Regional Meeting of the American of these radicals two by two. If reaction (5) Chemical Society in Scattle, October 2 0 , 1945. (la) P. Van Rysselberghe and 0.J. Alkire, TIIISJOURNAL, 66, occurs reversibly a t the dropping mercury cathode 1801 (1944). Henceforth referred to as Paper I of this series. the reduction potential E would be of the form5 ~
(2) I. If.Kolthoff and J. J. Lingane, “Polarography,” Interscience Publishers, Inc., New York, N. Y.,1941, pp. 194-195. (3) 0. H. hiuller, Cold Sgring Harbor Symposia Quanl. Biol., 7, 59
(1830).
(4) I. M. Kolthoff and J. J. Lingane. reference 2, pp. 163-154, 182-183. (5) I. M. Kolthoffand J. J. Lingane, reference 2, p. 184.
2048
PIERRE VANR~SSELBERGHE
in which c' is the symbol for molar concentration, X designates the reduction product R,Hz, a H + the activity of the hydrogen ion. The activity coefficients of the neutral species are taken equal to unity. The x molecules of R reacting are regarded as 6.dsorbed on the mercury surface in some sort of geometrical pattern: polygons with an R molecule a t each corner, for instance. The hydrogen ions arid electrons react with two of these molecules forming two HR-radicals and forcing in the (x-2) other molecules of R rearrangements of electronic pairs with the resulting formation of a reduced polymer R,H2. The solution being buffered we can write Cx
RT E=E:+-ln2F
cg
(7)
Then, in accordance with well-known steps in polarographic theory, we have i = k (Ck - C ), (8) id
= k Ci
(9)
a formula identical with the empirical formula (4). A wave of this type has a slope dE/du given by -dE - = E ' = - (xRT -+ du 2F
E;/S = 2~
in which Ck designates the bulk concentration of R, CR the concentration in immediate contact with the surface of the mercury drop. Turning now to the reduction product X we shall consider i t as formed and present for the major part in an adsorbed state a t the surface of the mercury drops, the concentration CX in the solution near the drops being in equilibrium with a surface concentration CX,in accordance with a Freundlich adsorption isotherm Cx = KC;,
(11)
in which z is a parameter having some value larger than one. The surface concentration CX, will be proportional to the current i CX,
=
k'i
(12)
Replacing CR and CX, by their values (10) and (12). in (7) . . we get E = E6
+ RT -In 2F
i*
~
(id
- i)"
(13)
with El =: Ea-
In a=+
+ 2RTF In (Kk"R") --
(14)
Introducing the ratio i / i d = u we find RT RT u* (15) E = 12; + - In ii-' + -' nI 2F 2F (1 - U). The half-wave potential corresponds to u = 1/2
1 - u
RT -F
0.051 x
(19)
One should also note that the half-wave is then a point of inflection
E:/, = 0
(21)
Waves for which El/,is not independent of id may be interpreted on the basis of values of x and z different from each other. For such waves the slope E' derived from (15)is
and E:/Z
(10)
1 ZL
which a t the half-wave gives, for 25'
and 1 CR = - (id -'i) k
Vol. 68
(Z
+
X)
RT - = 0.051 + F 2
(23)
The point of inflection is not a t the half-wave, but is such that
or When the point of inflection is located on the experimental wave the corresponding value of u can be introduced in ( 2 5 ) which thus gives the ratio x / z , while the sum x z can be obtained from the slope a t the half-wave according to ( 2 3 ) .
+
Case 11: The Solution is Not Buffered In many cases (that of carbon dioxide for instance) special conditions prevent the use of buffered solutions. This case divides itself into two sub-cases: a. The reducible substance R has no acid properties and the original solution is neutral. b. The reducible substance R is an acid and there is immediate adjustment of the equilibrium between R and H+. Sub-Case a.-Reaction (5) should be rewritten as rR 2H20 + 2e- +K,H2 f 20H- (26j The concentration of OH- is thus (see equatiuri (8))
+
2 COH-
=
-
(C;
-
2i 'R)
=
ki
(27)
and, a t 25' I n case the half-wave potential is independent of hence of the concentration of the reducible substance, we should have z = x, and formula (15) becomes
'id, and
CH+= lO-''kx/Zi (28) This value of CH+can then be introduced into (6) and the resulting formula can be transformed in a manner similar to that of Case I.
OCt. , 1946
POLYMERIZATION AND
ADSORPTION AT
Sub-Case b.--Whether the reducible acid substance R yields one or more protons to the solvent the acidity of the solution will usually depend on the first dissociation constant only. The supporting electrolyte is usually a neutral salt. We have therefore Ci+ = K a C ~
=
E:
+ RT -1n2F
DROPPING MERCURY ELECTRODE 2049
+
carbon dioxide is based. Making z = x 1 in (31) and (32) and multiplying by 2F we get, for u = 1/2 2FE1/, = 2FE: = 2FEo
XR
which can then be transformed into a formula of the same type as (15)
*
(37) (38)
+ HI +R,H2
(39)
xR
Cx
+
+ 2H+ f 2e- +R,H2
or
c;+I
+ RT In K(k'k)z K,
The standard free energy change for the reaction
(29)
and formula (G) becomes E
THE
is (our EO,Ellz,etc., are absolute values of cathodic potentials) AFO = 2FE0
(40)
which can be obtained from 2FEg (with E,* = El/,referred to the standard hydrogen electrode) by the formula
with
AFO = 2FE0 = 2FEz
All the subsequent developments of Case I apply here with the difference that x is now replaced by x 1. In particular, if it is found experimentally that the half-wave potential is independent of id, we have, in place of (19), a t 25'
+
E;/z = 2
(X
+ 1) RT - = 0.051 + 1) F (X
(33)
and, as in (21) E';/%= 0
If, on the other hand, El/, varies with in place of (23)
a:/% =
(2
RT + x + 1) 7
(34) id,
we have, (35)
and, a t the point of inflection, in place of (25)
I t will be shown. in the following paper6 that the reduction waves of carbon dioxide are logically and simply interpreted as belonging to this subcase b of Case 11. Free Energy Changes Involved in the Reduction Process I n this part of the discussion we shall restrict ourselves to Case 11, sub-case b, which is the one upon which the interpretation of our results on
- RT In K(k'k)" K,
+
(41)
Formulas (10) and (12) show that K and 1/K' are of the same order of magnitude. The term ( x 1) ln(k'k) will thus be of a smaller order of magnitude than the term ln(K/K,). The ionization constant Ka will in general be known, E,* is an experimentally determined quantity, while AFO may in many cases be estimated from free energy tables such as that established by Parks and Huffman.' It is then possible to obtain a t least an approximation for the adsorption equilibrium constant K. The method of calculation here outlined will be applied to the case of carbon dioxide in the following paper of this series.6
+
Summary An interpretation of certain polarographic waves is provided by a theory based upon : 1. The sharing of two hydrogen ions and of two electrons by more than one molecule of the reducible substance. 2. The establishment of an adsorption equilibrium of the reduction product between the dropping mercury cathode and the solution. Two main cases are considered: buffered and unbuffered solutions. The latter case is divided into two sub-cases according to whether the reducible substance is an acid or not. EUGENE. OREGON
RECEIVED NOVEMBER 13, 1945
(7) G. S. Parks and H. M. Huffman, "The Free Energy of Some 1932, (6) P. Van Rysselbargbe, G. J. Alkire and J. M. McGee. THIS Organic Compounds," Chemical Catalog Co., New York, N. Y., see Table 40, pp. 210-211. JOURNAL, 68, :!050 (1946).
