fundamental harmonic faradaic alternating current amplitude due to an applied sinusoidal potential of frequency 2w second harmonic current phase angle applied angular frequency (rad./sec) time (sec) electrode area Faraday's constant absolute temperature ideal gas constant number of electrons transferred in heterogeneous charge transfer step heterogeneous charge transfer rate constant at Eo (cm sec-1) charge transfer coefficient backward first-order rate constant for chemical reaction following charge transfer (sec-l) forward first-order rate constant for chemical reaction following charge transfer (sec-I) equilibrium constant for chemical reaction following charge transfer (= k1/k2). Euler gamma function second harmonic anodic peak current amplitude second harmonic cathodic peak current amplitude second harmonic anodic peak current amplitude with diffusion-controlled process second harmonic cathodic peak current amplitude with diffusion-controlled process
mental harmonic current amplitude for an applied frequency 20. Equation 5 1 shows that an experimental assessment of W(w) is obtained by dividing the experimental fundamental second harmonic current amplitude by the experimental fundamental harmonic current at the second harmonic frequency (at the same Edovalue). Because W(w)is a direct measure of faradaic non-linearity, whereasZ(2w) is unresponsive to this aspect of the faradaic impedance, application of Equation 5 1 serves to isolate for analysis that aspect of the second harmonic current amplitude which represents truly new information not provided by the more conventional dc and fundamental harmonic ac measurements. In addition, data analysis is facilitated significantly because of the simpler theoretical formulation governing W(w),relative to the total amplitude term Z(2w)W(w). NOTATION DEFINITIONS
initial concentration of oxidized form diffusion coefficient of species i activity coefficient of species i dc component of applied potential standard redox potential in European convention amplitude of applied alternating potential reversible dc polarographic half-wave potential (planar diffusion theory) dc polarographic half-wave potential with chemical equilibrium following nernstian charge transfer dc potential at minimum of second harmonic current amplitude polarogram second harmonic faradaic alternating current second harmonic faradaic alternating current amplitude due to an applied sinusoidal potential of frequency w
RECEIVED for review May 22, 1969. Accepted June 23, 1969. Work supported by National Science Foundation Grants G P 5778 and G P 7985.
On the Monobasic or Dibasic Character of Dith iocarbamic Acids Serge J. Joris, Keijo I. Aspila, and Chuni L. Chakrabartil Department of Chemistry, Carleton University, Ottawa I , Ontario Dithiocarbamic acids have been investigated with regards to their monobasic or dibasic characteristics using three methods of analysis. The variation of the summit potentials for oxidation of dithiocarbamic acids at a dropping mercury electrode in ac polarography enables the determination of acid dissociation constants for the sulfur protonation. This factor, and the rate profiles as a function of pH for the decomposition of several dithiocarbamic acids, is used to interpret the unusual acid-base titration curves of dithiocarbamates. It is concluded that dithiocarbamic acids are monobasic. An explanation is given of the difference in the acid-base properties of dithiocarbamates and the analogous amino acids.
IT has recent!y been reported ( I , 2) that uncertainties still exist on the monobasic or dibasic character of the dithiocarbamic acids in acidic solutions-models I and 11shown below are the 1
All correspondence should be addressed to this author.
(1) A. Hulanicki, Tulunta, 14, 1371 (1967). (2) I. M.Bhatt, K. P. Soni, and A. M. Trivedi, J. Znd. Chem. Soc., 45,354(1968).
two possible representations. It is necessary to remove these uncertainties.
R1
\
S N-C
/
\
RZ
R1
S
/ SH
(1)
Also, these acids are known (3, 4 ) to undergo decomposition in aqueous solution. In order to explain the properties of these acids, it is necessary to give definitive statement of their acidic character. This could require an assessment of the acidic character and the kinetics of decomposition, both, preferably, by several independent methods. Some such methods would be to study the acidic character of dithiocarbamates by polarography and potentiometric titrations, and (3) H. Bode, 2. Anal. Chem., 142,414(1954). (4) K. I. Aspila, V. S. Sastri, and C. L. Chakrabarti, Tuluntu, 16, 1099 (1969). VOL. 41,NO. 11, SEPTEMBER 1969
1441
the kinetics of decomposition by spectrophotometry. A comparison of the results of these three experimental studies should elucidate the acidic character of these acids. This paper presents the results of such studies. EXPERIMENTAL
Apparatus. A Metrohm A. C. Polarograph, with Ag/AgCl reference electrode and saturated KC1 bridge, was used in the polarographic studies (amplitude of the modulation wave = 50 mV, frequency = 60 cps). A modified Bausch and Lomb Spectronic 505 recording spectrophotometer was used to study the kinetics of decomposition. Matched silica cells of 10-mm path length were used and maintained at a constant temperature of 25.0 i 1 "C. Reagents. The dithiocarbamic acids used in this study were generated from their corresponding sodium salt. The diethyl derivative (EbDTCNa) was obtained commercially. The others were prepared according to the procedure described in the literature (5). The percentage reagent in the DTC salts were obtained by amperometric titration. Buffers (6) of constant ionic strength (I) were prepared to I = 0.01 for the kinetic studies, and I = 0.1 for the polarographic studies. Dilute hydrochloric acid solutions were used in the kinetic studies for pH values less than 2.2. The pH values were measured, to within i 0 . 0 2 pH unit, with a Fisher Accumet pH meter, Model 210. Procedure. POLAROGRAPHIC STUDIES.In the polarographic investigation, 1ml of air free 2.5 X lo-* M pyrrolidinedithiocarbamate (PyrDTCNa) was added to a deaerated solution containing 23 ml of buffer and 1 ml of gelatin, 0.2%. The pH of the solution was checked after each determination of the summit potential. All experiments were conducted at a constant temperature of 25.0 i 0.1 "C. KINETICSTUDIES.For kinetic studies, solutions of 10-810-4M DTC acids were prepared by adding a measured amount of solutions of unbuffered DTC salt to the various buffers kept in the silica cells at a constant temperature. Mixing of these solutions of buffered DTC salt was done with a Teflon (Du Pont) stirrer or a pipet bubbler and was completed within an average time of six seconds before absorbance measurements were recorded. For longer first order halflives-e.g., over 30 minutes-absorbance measurements were taken on fresh samples withdrawn at various time intervals from the stock of the buffered DTC salt solution, which was kept in an external constant-temperature bath. Because the buffer solutions were dilute, the pH values were determined before and after the addition of DTC salt to check pH constancy. to lO-4M Over the initial concentration ranging from DTC salt, plot of log concentration us. time was found to be linear at all pH values, and gave reproducible rate constants ( i2 %) at any chosen pH value. Absorbance measurements were made at about 280 mp. As the pH was changed from 5 to 1, a small shift (5-10 mp) in the absorption maximum at about 280 mp was found for both the diethyl and pyrrolidine derivatives. RESULTS AND DISCUSSION
Polarographic Studies. At concentrations above 10 -4M, the dialkyldithiocarbamates gave two well-defined anodic polarographic waves. The wave observed at the more negative potential has been characterized as an adsorption prewave arising from the formation of an insoluble mercury
( 5 ) H. L. Klopping and G. J. Van Der Kerk, Rec. Trau. Chim.,
70, 917 (1951). (6) D. D. Perrin, Aust. J. Chem., 16, 572 (1963). 1442
0
ANALYTICAL CHEMISTRY
-0.3-.
-ca 0
>,
-0.4-
W*
-0.5-
. 2.0
0
4.0
.
6.0
10.0 12.0
8.0
PH
Figure 1. Variation of summit potential as a function of pH at 25 OC for a lob3M solution of pyrrolidinedithiocarbamate (sodium salt) Curve n concentration wave Curve b adsorption wave salt on the surface of the mercury drop (7,s). The two waves are seen in both dc and ac polarography and correspond to the following one-electron process (9). R1
S
\ / /
"4.
/
Rz
\
S
R1
\ / / +Hg+
S-
'N-C'
/
R2
\
+ 1 e-
(1)
SHg
It has been observed that the summit potential, E,, in ac polarography (corresponding to the half-wave potential in dc polarography) is essentially constant for both waves at pH values above pH 4.5. When the pH value of the solution is made less than about four, Es shifts toward more positive potentials. Figure 1 illustrates this variation of Eswith pH for PyrDTCNa. This compound was chosen because of its relatively high stability in acidic solutions (4). Equation 1 indicates that the dithiocarbamate molecule reacts with the mercury through one of its sulfur atoms. Thus, it is expected that polarography will be sensitive to the protonation of the sulfur atom regardless of an eventual protonation of the sulfur atom regardless of an eventual protonation of the nitrogen atom in the molecule. The pH dependence of the summit potential can be explained in the following way. The equation for the conventional anodic wave corrcsponding to Equation 1 is:
(7) D. J. Halls, A. Townshend, and P. Zuman, Anal Chim. Acta, 41, 51 (1968). (8) M. J. Brand and B. Fleet, Analyst (London),93,498 (1968). 34, 508 (1962). (9) W. Stricks and S. K. Chakravarti, ANAL.CHEM.,
= activity (RSHg) = (RiRzNCSSHg) (RS-) = (RlRzNCSS-) = Standard potential of the redox couple Eo
()
1.04
0.0-
The ratio between the anionic form of the DTC molecule (RS-) and its sulfur protonated form (RSH) is given by the dissociation constant:
(3) The activity of the polarographically active molecules (RS-)is related to the total activity of the dithiocarbamate (DTCo) by the following expression :
-I
.o-
-;2.03 -3.0-
(4)
-4.0-
Substituting Equation 4 into Equation 2 and introducing the diffusion conditions, one obtains at 25.0 OC:
-5.0I,
I.o
5.0
3.0
7.0
.
SA
PH
Figure 2. Rate profile for decomposition of dithiocarbamic acids at 25 "C where e is a function of the activity and diffusion coefficients of the free DTC and the mercury-complexed DTC molecules, but is essentially a constant for a given applied potential. The half-wave potential (or summit potential in ac polarography) for this wave is described by:
=
constant
+ 0.059 log ("
2"))
(7)
It can be predicted from Equation 7 that at high pH values (where (H+) > Ks), Ell2 should shift toward more positive potentials as (H+) increases; and at low pH values, the slope of a plot of Ell2 6s. log (H+) should be equal to 0.059, for this electrode reaction. The experimental results agree with the above three predictions (AE,/ApH calculated at low pH from Figure 1 equals 0.065). In Figure 1, curve a, the intersection of the two straight lines corresponds to pH = pKs = 3.25 +O.l and is thus the acid dissociation constant for the sulfur protonation of pyrrolidinedithiocarbamic acid. From this agreement between theory and the experimental results, it is concluded that polarography is a suitable method to evaluate the acid dissociation constant of the sulfur atom in protonation of the molecule. However, the above treatment does not provide information about the protonation of the nitrogen atom in pyrrolidinedithiocarbamic acid. Kinetics of Decomposition. The pH dependence of the apparent rate constant ( k ' ) of reaction 8 is shown in Figure 2 for the pyrrolidine and diethyl dithiocarbamates (4).
+
Ri
stant and the pH. Below pH 2 the rate of decomposition is no longer pH dependent. A similar curve has been observed for several other dialkyldithiocarbamates (4). The intersection of the two lines shown in the kinetic profile of pyrrolidinedithiocarbamate is located at the same pH value as the intersection in Figure 1. It thus corresponds to the pKs, as determined polarographically. Such agreement with the results of the electrochemical method is an indirect proof that the electrode reaction is reversible, as has been reported by Halls, Townshend, and Zuman (7). It appears from these results that the limiting rate of decomposition is reached when all the DTC molecules are in the sulfur-protonated form ([H+] >> Ks). The first order relationship between log k' and the pH is best understood by considering that only the sulfur-protonated molecules can undergo the decomposition. The concentration of the DTC molecules in the RSH form is given at all pH values by the equation: (9)
As the overall rate of decomposition (V) is proportional to the concentration of RSH, one obtains the following relationship, where kT is the true rate constant and k' the measured apparent rate constant : = kT
[H+l [DTCo] = k' [ D E o ] ([H+] KB)
+
It follows from Equation 10 that: S
\ / / N--C / \
Rz
k' is apparent rate constant, in min-l Curve a pyrrolidinedithiocarbamic acid Curve b diethyldithiocarbamic acid
S-
Ri -+
2H+
\ NH2 + CS2 /
k'
kr
when [H+] >> Ks
(11)
[H+l Ks
when [H+]
