cold rooms or otherwise under appropriate low-temperature conditions. Prior estimates of expected recoveries may be made by application of derivations of Rayleigh’s equation (6) presented in this report. ACKNOWLEDGMENT
The method of preparation of the chromatographic column is modified from instructions generously supplied to us via private communications bfClaude Gortatowsky of the Coca-Cola Co. Thanka are due to F. G. I,%, Head
Research Chemist, Spreckels Sugar Co., Woodland, Calif., for advice and counsel, to Gary Underhill, now with Standard Oil, for contributions to the theory, and to Ronald Lathrop for preparing the charts and diagrams. The author also thanks the Spreckels Sugar Co. for the, opportunity to develop the method and for permission to publish this paper.
( 2 ) Emery, E. M., Koerner, W. E.,
c.
( 3 Ax.4~. ) Ge,~rke, CHEM.33, ~ 146 ~ Lamkin, (1961). , , ~~, J. Agr. them, 9 , 85 (1961),
nr,,
(4)Hunter, I. R., Hawkins, S . G., Pence, J. W., 8XAL. CHEW 32, 1757 (1960). ( 5 ) James, 8. T., hlartin, A. J. l’., Biochem. J . 50, 679 (195%). (6) perry, J , H,, ~ d , “, ~ f , ~~ ~ i~ ~ ~~ l n e e d Handbook,” 3rd ed., p. 581, McGraw-Hill, Sew York, 1950. ( 7 ) Phillips, C., “Gas Chromatography,” p. 63, Academic Press, Sew York, 1956.
LITERATURE CITED
(1) Dierssen,
G. A., Holtegaard, K., Jensen, B., Roseii, li.,Intern. Sugar J . 58, 35 (1956).
RECEIVED for review June 4, 1962. Resubmitted Yovember 30, 196%. Accepted -4pril 5 , 1983.
Indirect Polarographic Determination of Acids JAMES C. ABBOT anti JUSTIN W. COLLAT Department of Chemistry, The Ohio State University, Columbus, Ohio
b A polarographic method for the determination of acids has been devised, which depends on the measurement of diffusion currents limited by the acid consumed in the electrode :2e 2H+ = reaction: quinone hydroquinone. Well defined polarographic waves have been found, whose heights are proportional to concentration of hydrogen ion and aluminum ion, alone and in mixtures. General considerations for extending the method to other species which react with hydroxyl ion are given, as well as relations between current and potential for acid-limited waves.
+
+
T
reduction of lJ4-benzoquinone at the dropping meJ-cury electrode, D.M.E., is known to proceed reversibly and to require an equivalent amount HE
of acid for completeness. Alternatively, the process occurring iJi a n originally neutral solution can be interpreted as generating hydroxyl ions. The effects of buffering and of the buffer capacity of the buffer system on the process were first studied by Nueller and Baumberger (14) and Nueller ( I S ) , who showed that a discrete polarographic wave, dependent on the concentration oi a buffer constituent, mas observable when quinonehydroquinone mixtures were electrolyzed a t the D.M.E. in a dilute phosphate buffer solution. hIJeller suggested t h a t a n acid-base titration was taking place at the drop surface in this case and that naves so obtained might be useful in quantitative analysis. Kolthoff and Orlemann ( I O ) , studying the polarography of the quinone-hydroquinone system in unbuffered r,olutions, were able to calculate the pH at the surface
of the D.M.E. in the oxidation of hydroquinone by applying the Ilkovi; equation to the concentrations of species in the system. Later, Collat (4) used the reduction of quinone at the D.M.E. in solutions of zinc and magnesium salts to determine the solubility products of the hydroxides of these elements. In t h a t work the concentration of metal ion was high in comparison to the quinone concentration; the solution, therefore, was equivalent to one which Fvas well buffered, and there was no change in the appearance of the quinone reduction wave from the buffered case. In the present a o r k ~ v econsider the situation where the amount of acid present is insufficient for the reduction of quinone according to Equation 1. Q
+ 2H+ + 2e = H2Q
(1)
Under these conditions the quinone wave splits into two waves, the more positive one representing reduction according to Equation 1, where the acid may be hydrogen ion or any other acidic species, and the more negative wave representing reduction of quinone in a neutral unbuffered solution according t o Equation 2. Q
+ 2H20 + 2e
=
H2Q
+ 20H-
(2)
The first of these two waves has a limiting current proportional to the amount of acid present. It can be made the basis for the analysis of any acid that can be employed in Reaction 1. K e have applied the nieasurement of this wave to the determination of hydrogen ion and aluminum ion, alone and in mixtures. Limiting currents aribing from the acidic species entering into Reaction 1 are distinctly different from those
arising from the electroreduct’ion of these ions, although the laws of diffusion which control the latter process can be applied to them with fair accuracy. Half-wave potentials for the electroreduction of hydrogen and aluminum ions occur at -1.58 and -1.75 volts us. S.C.E., respectively. The quinone reduction waves limited by the diffusion of these two ions and their reaction a t the drop surface as acids have half-wave pot’entials of f0.28 and +0.17 volt us. S.C.E.Khile the diffusion currents defined by t,hese waves are limited by the diffusion of hydrogen or aluniiriurn ions, electrons are not transferred from the D.il1.E. to them, but rather to a molecule of quinone. The potential at kvhich this process takes place depends on the concentration of acid available at the surface of the drop, becoming more positive as the pH decreases. While our work has shown the applicability of this type of polarographic analysis to solutions of hydrogen and aluminum ions, i t could doubtless be extended to other systems. Any substance which reacts completely and rapidly with hydroxyl ion might be determined by its limiting current in the presence of an excess of quinone. EQUATION OF THE WAVE
The current-potential relation for polarographic waves resulting from the reduction of quinone with current limitation by diffusion of acid can be obtained by application of the Kernst and Ilkovic equations. \Ye have examined the individual waves and have employed an extension of the familiar derivation of the “equation of the wave” t o explain the observed shift uf the half-wave potential with concentration VOL. 35, NO. 7, JUNE 1963
859
i
-
I I
I
t 0.3
t 0.1 vs. S.C.E.
V
I
-0.1
Figure 1. Polarograms of acids in presence of quinone 1.00 m M " 0 3 , 0.020M quinone b. 2.01 mM AI(NOa):j, 0.020M quinone c. 1 .OO mM "Os, 2.01 m M AI(NOA, 0.01 OM quinone Supporting electrolyte 0.5M KNOa in all cases a.
site of electron exchange. Since the electroreduction proceeds by the formation of intermediate reduced species, which are later protonated (16), this is not precisely the case. The protonation part of the reaction must take place in a small volume element around the drop. Thus, i, while an exact measure of the extent of quinone reduction, is too large to give an exact measure of the equilibrium H+ concentration in the volume element where the protonation reaction is completed. \Ye expect, therefore, that c i + calculated by this procedure may be somen.hat too small. Introduction of Equation 4 into 3 and substitution of DH+ = 9.34 X 10-j scc.-l ( 7 ) yirltl Ilguation 5 , the "equation of the \vale" for this cahe. E
of the diffusing species. This point \ d l be illustrated by considering the reduction of quinone in a nitric acid solution which cont,ains an amount of acid less than the equivalent amount required by Equation 1. By application of standard procedures (9) i t can be shown that the potential of the D.M.E. a t any point on the polarographic wave is given in volts us. the saturated calomel electrode a t 25" C., and assuming diffrieion coefficients of quinone and hydroquinone equal, by the relation, E = 0.4654
-i + 0.0295 log iQe,_ + 0.059 log c;+
(3)
In Equation 3 c$+ indicates concentration of hydrogen ion at the surface of the D.,\I.E., here assumed equal to its activity, iQ represents the sum of the currents in both parts of the split wavei.e., the current limited by diffusion of quinone to the electrode-and the other symbols have their usual significance. Ordinarily the last term in Equat'ion 3 would be made constant by operating in a buffer solution of adequate buffer capacity, but in the case under discussion i t will be a variable. I t can, however, be estimated in terms of currents by use of the Ilkovi6 equation exactly as surface concentrations of clectroactive species can be evaluated. The result is given in Equation 4.
In this relation iT;" is the diffusion current, measured on the first segment of the split quinone wave and proportional to the bulk hydrogen ion concentration (see Figure 1). Use of the Ilkovi; equation to calculate c$+ for substitution ill Equation 3 iniplies t,hat the hydrogen ion Concentration which satisfies Equation 3 is also that at the surface of t'he drop-Le., at the 860
ANALYTICAL CHEMISTRY
=
0.2327
+ 0.0293 log a-~2 -i i +
+ q OH-
=
RI(OH),
K = [Mt~l[OH-l'2
(s)
+ 0.30 Ed.e, ,
+ 0.20 v fi S.C.E.
Figure 2. Potential-log plots for hydrogen ion
-
c
&l... vs. log (i,,Q ii/:\il/!-~ E , ~ , , , v s . l o lgi , , Q - i / { i c , H + - i / 2 / i Plot of Equation 5, theoretical curve for both sets of data, included ~
controls the pH a t the surface of the Il.X.1;. The quantity c:+, nhich is subrtituted in Equation 3, is given by
This relation differs from the equations which describe the polarographic wave in cases where only concentration gradients of depolarizer and its product must be considered. Here, diffusion of three species makes cancellation of the constant factors and capiJlary characteristics in the lIkovic equation impossible. These quantities must be introduced intoEquation 5 to change the currents, measured in microampere,:, to the concentration unit, moles pcr liter, used in defining the standard potential of the redox system. The situation is analogous to that which obtains when a metal insoluble in mercury is reduced at the D.1l.E. (8). Equation 5 predicts that at a constant quinone concentration thc half-\vale potential of the hydrogrn ion n-ave will depend on concentration of hydrogen ion, which has been found esperimentally to be the case. After the current reaches the value i?+, the reduction of the escess quinone continues with the concurrent generation of hydroxyl ion; (see Equation 2); however, there is an ample potential interval where the current is limited by the concentration of acidthat is, a current plateau suitable for analytical use. We have not considered the case where there is a concentration gradient of hydroxyl ion a t the D.M.E., because of the complications introduced by the acidity of hydroquinone and the polymerization of quinone in alkaline media (6). The argument given above can easily be extended to any acid. For example, a cation which reacts with hydroxyl ion according t o the equation bl+q
equation
(G)
and the relations analogous to 4 a i d 5 arc, respectively, Z>I
-i cfr ([nu]es/ljter) = 607 p,lJ',@tn?/3tl/6 ~
x
10-3
E
=
(8)
i9 - i 0.4254 0.0295 log i + I< 0.050 0.059 log - 1"; - o K.:
+
O.OS9 _ _ log Q
(Zif - 2)
(9)
I n J
