Literature Cited (1) Niki, H., Daby, E. E., Weinstock, B., Adu. Chem. Ser., 113, 16
(1972). (2) Hecht, T. A., Seinfeld, J . H., Enuiron. Sci. Technol., 6, 47 (1972). (3) Eschenroeder, A. Q., Martinez, J. R., Ado. Chem. Ser., 113,101 (1972). (4) Demerjian, K. L., Kerr, J. A., Calvert, J. G., “Adv. in Environ. Sci. and Technol.”, J . N. Pitts and R. L. Metcalf, Eds., Vol 4, p 1, Wiley-Interscience, New York, N.Y., 1974. (5) Hecht, T. A., Seinfeld, J. H., Dodge, M. C., Enuiron. Sci. Technol., 8,327 (1974). (6) MacCracken, M. C., Sauter, G. D., Eds., “Development of an Air Pollution Model for the San Francisco Bay Area”, Final Rep. to National Science Foundation, University of California, Livermore, Calif., 1975. (7) Graedel, T. E., Farrow, L. A., Weber, T. A,, Atmos. Enuiron., 10, 1095 (1976). (8)Whitten, G. Z., Hogo, H., “Mathematical Modeling of Simulated Photochemical Smog”, Environmental Protection Agency Rep. EPA-600/3-77-011,1977. (9) Gelinas, R. J., Skewes-Cox, P. D., J . Phys. Chem., 81, 2468 (1977). (10) Baldwin, A. C., Barker, J. R., Golden, D. M., Hendry, D. G., ibid., p 2483. (11) Workshop on Chemical Kinetic Data Needs for Modeling the Lower Troposphere, Environmental Protection Agency and National Bureau of Standards, Reston, Va., May 15-17,1978. (12) Pitts, J. N., Jr., Darnall, K. R., Winer, A. M., McAffe, J. M., “Mechanisms of Photochemical Reactions in Urban Air. Volume 11. Chamber Studies”, Environmental Protection Agency Rep. EPA-600/3-77-014b, 1975. (13) Hendry, D. G., “Reactions of Aromatic Compounds in the Atmosphere”, Workshop on Chemical Kinetic Data Needs for Modeling the Lower Troposphere, Environmental Protection Agency and National Bureau of Standards, Reston, Va., May 15-17, 1978. (14) Hampson, R. F., Jr., Garvin, D., “Reaction Rate and Photochemical Data for Atmospheric chemistry-1977”, NBS Special Publ. 513, National Bureau of Standards, Washington, D.C., 1978. (15) Graham, R. A,, Johnston, H. S., J . Phys. Chem., 82, 254 (1978). (16) Graham, R. A., Winer, A. M., Pitts, J. N., Jr., Chem. Phys. Lett., 51,215 (1977).
(17) Graham, R. A,, Winer, A. M., Pitts, J. N., Jr., J . Chem. Phys., 68, (1978). (18) Schere, K. L., Demerjian, K. L., “Calculation of Selected Photolytic Rate Constants Over a Diurnal Range”, Environmental Protection Agency Rep. EPA-600/4-77-015,1977. (19) Darnall. K. R.. Carter. W.P.L., Winer, A. M.. Lloyd, A. C., Pitts, 3. N., Jr., J . Phys. Chem., 80,1948 (1976). (20) Batt, L., McCulloch, R. D., Milne, R. T., Znt. J . Chem. Kinet. Symp., 1,441 (1975). (21) Batt, L., Milne, R. T., Int. J . Chem. Kinet., 8,59 (1976). (22) Batt, L., McCulloch, R. D., ibid., p 911. (23) Mendenhall, G., Golden, D. M., Benson, S. W., ibid., 7, 725 (1975). (24) Barker, J. R., Benson, S. W., Golden, D. M., ibid., 9, 31 (1977). (25) Carter, W.P.L., Darnall, K. R., Lloyd, A. C., Winer, A. M., Pitts, J . N., Jr., Chem Phys. Lett., 42,22 (1976). (26) Weibe, H. A., Villa, A,, Hellman, T. M., Heicklen, J., J . Am. Chem. Soc., 95,7 (1975). (27) Baker, G., Shaw, R., J . Chem. SOC.(London), 1965, p 6965. (28) Cvetanovic, R. J., “Chemical Studies of Free Radicals of Atmosuheric Interest”. Pauer No. 31.12th Int. Svmu. “ . on Free Radica1s:Laguna Beach,’Calif., 1976. ’ (29) O’Neal. H. E.. Blumstein. C.. Int. J . Chem. Kinet.. 5, 397 (1973). (30) Dodge, M. C., Workshop on Chemical Kinetic Data Needs for Modeling the Lower Troposphere, Environmental Protection Agency and National Bureau of Standards, Reston, Va., May 15-17, 1978. (31) Niki, H., “Reactions of Olefins with Hydroxyl Radical and with Ozone”, Workshop on Chemical Kinetic Data Needs for Modeling the Lower Troposphere, Environmental Protection Agency and National Bureau of Standards, Reston, Va., May 15-17,1978. (32) Lloyd, A. C., “Tropospheric Chemistry of Aldehydes”, ibid. (33) Walter, T., Bufalini, J., Gay, B., Jr., Enuiron. Sei. Technol., 11, 382 (1977). (34) Simonaitis, R., Heicklen, J., J . Phys. Chem., 78,2417 (1974). (35) Cox, R. A,, Roffey, M. J.. Enuiron. Sei. Technol., 11, 900 (1977). (36) Chan. W. H.. Nordstrom. R. J.. Calvert. J. G.. Shaw. J. H.. ibid.. 10,674 (1976). ’ (37) Herron. J . T.. Huie. R. E., J . A m . Chem. Soc.. 99,5430 (1977). (38) Niki, H., Maker, P. D., Savage, C. M., Breitenbach, L. P., Chem. Phys. Lett., 46, 327 (1977).
Receiued for reuiew November 28,1977. Accepted July 10,1978. Work supported by the State of California Air Resources Board.
Polarographic Determination of Lead Hydroxide Formation Constants at Low Ionic Strength Carol J. Lind U.S. Geological Survey, Menlo Park, Calif. 94025
Values of f o r m a t i o n c o n s t a n t s for l e a d hydroxide at 25 “C were calculated f r o m normal pulse polarographic m e a s u r e ments of M l e a d i n 0.01 M s o d i u m perchlorate. T h e low concentrations s i m u l a t e t h o s e f o u n d in m a n y freshwaters, p e r m i t t i n g d i r e c t application of the values w h e n considering distributions of lead species. The precise evaluation of species distribution in waters at other ionic strengths requires activity coefficient corrections. As opposed to m u c h of t h e previously p u b l i s h e d work done at high ionic s t r e n g t h , the values reported h e r e were o b t a i n e d at low ionic s t r e n g t h , p e r m i t t i n g use of smaller and b e t t e r d e f i n e d activity coefficient corrections. T h e s e values were f u r t h e r confirmed b y differentialpulse polarography a n d differential-pulse a n o d i c s t r i p p i n g v o l t a m m e t r y data. The logs of the values f o r PI’, &’, and &’ were calculated t o b e 6.59,10.80, and 13.63, respectively. W h e n corrected t o zero ionic s t r e n g t h these values were calculated to be 6.77, 11.07, and 13.89, respectively.
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Environmental Science & Technology
During the p a s t decade t h e scientific world has become well aware of the importance of determining the lead concentration in freshwaters, t h e t y p e s and amounts of its complexes, the f o r m in which i t is adsorbed o n t o p a r t i c u l a t e matter, a n d the toxicity of its free a n d complexed states t o plants and animals. A p r i m a r y s t e p in deciphering t h e s e problems is the determ i n a t i o n of t h e f o r m a t i o n c o n s t a n t s for the lead hydroxide species. T h i s is particularly necessary i n defining t h e d e g r e e of complexing of l e a d b y o t h e r ligands in aqueous solutions at n e u t r a l p H s . T h e s e formation constants need t o be reliably defined. The r e p o r t e d values in the l i t e r a t u r e for t h e f o r m a t i o n c o n s t a n t of t h e 1:1lead hydroxide complex, including values calculated f r o m compilations of free-energy d a t a , h a v e a r a n g e of m o r e than t w o o r d e r s of m a g n i t u d e (1-9). A t neutral pHs, the prim a r y inorganic species a r e Pb2+ and P b O H + , m a k i n g the a c c u r a t e definition of the c o n s t a n t , 61,especially i m p o r t a n t . p 2 is of i n t e r e s t in heavily d i s t u r b e d s y s t e m s of p H s greater t h a n 9. T h e p r i m e i m p o r t a n c e of evaluating p3 in t h i s r e p o r t
This article not subject to U S . Copyright. Published 1978 American Chemical Society
is to serve as a means of comparing the present results with that derived by other means. Most freshwaters have an ionic strength in the order of 0.01 M and lead concentrations rarely as high as 10-6 M. In the past most of the values of the formation constants have been measured in media of 0.1 M ionic strength and higher, primarily of 1M and above, and with lead concentrations greater than M. The values reported here make possible more accurate evaluation of the distribution of lead species because in many cases they can be used directly and, where the ionic strength differs and precision is required, much smaller, more accurate activity coefficient corrections are required than previously. In addition, the low lead concentration used reduces the concentration of polynuclear hydroxide complexes, along with the complications due to their presence, to a negligible amount. The constants reported here were determined by normalpulse polarography ( N P P ) a t 25 “C using solutions 0.01 M in sodium perchlorate and 1.1 X to 4.8 X 10-6 M in lead and having pHs of 8.72 to 11.47. Evaluations of 01’and p2’ were further verified by differential-pulse anodic stripping voltammetry (DPASV) and differential-pulse polarography (DPP), using solutions 4 X lo-‘ to 3 X M in lead and having pHs 7.74 to 9.91. The apparent formation constant, (Iq’,is expressed in terms of concentration and is based on the reaction: Pb2+
+ q0H-
-
Pb(OH),(*-q)’
(1)
The values of pq’ ( q = 1, 2, and 3) were calculated and the values for pq were found through extrapolation to zero ionic strength by the application of activity coefficient corrections. The values of *pq may be calculated a t zero ionic strength for the reaction: Pb2+
+ qHPO
-
+
Pb(OH),(2-q)+ qH+
(2)
Experimental Solutions. The stock solutions consisted of 3 M sodium perchlorate, 0.1 M sodium hydroxide, and 1 M sodium nitrate (all purified by controlled potential electrolysis), 0.1 M lead perchlorate (Orion 94-82-06), and perchloric acid (J.T. Baker Ultrex). All dilutions were made with laboratory-distilled water that had been further distilled in glass and then flushed free of carbon dioxide. The adsorption of lead was minimized by using a relatively inert surface and a large volume-to-cell-surface ratio. This was accomplished by working with 200 mL of test solution in a 250-mL Teflon beaker (10). Establishing a n I n e r t Atmosphere. The solution and the space above it were flushed with purged high purity nitrogen (Union Carbide Corp., Linde Division). The nitrogen was purged by passing it through a Princeton Applied Research (PAR) nitrogen purification kit to remove the last traces of oxygen, a tube of Mallcosorb (20-50 mesh) from Mallinckrodt, Inc. to remove any carbon dioxide, and a wad of glass wool and a 0.01 M sodium perchlorate scrubbing solution to remove particles of Mallcosorb. The latter also equilibrated the gas to the humidity of the test solution, minimizing evaporation. The purging units were joined by lengths of glass tubing and very short pieces of Tygon, minimizing the opportunity for permeation of plastic tubing by gases ( 1 0 ) . Several additional precautions were taken to prevent atmospheric carbon dioxide contamination of the solution and to maintain a low level of oxygen. All cell parts were designed so that they joined flush with each other and where a joint was in suspect of leakage it was sealed with Parafilm. Thus, for example, increments of lead perchlorate or sodium hydroxide could be added via a microburet, inserted through the cell top with a tight seal, without exposing the flushed solution. The
whole unit, including a temperature-control bath, was encased in a plastic bag and nitrogen was bubbled into the temperature-control bath and allowed to escape through the wall of the bag. Instrumentation. All work was done on a PAR 174A polarographic analyzer, using a conventional three-electrode system with a hanging-mercury-drop electrode (HMDE) as a working electrode. For NPP, the scan rate was 1 mV/s and the clock time (the interval between the beginning of consecutive pulses) was 1s. For the D P P and DPASV, the scan rate was 2 mV/s, the clock time 1s, and the modulation amplitudes 5 and 25 mV. Prior to stripping, the metal was plated on a t -0.7 V vs. SCE (saturated calomel electrode) for 1.00 min with stirring and then for 0.50 min with no stirring. The low lead concentrations required amplification of the diffusion currents. This was accomplished by the large electrode surface allowed by the use of the HMDE as a working electrode. For NPP, except for when testing for diffusion control, the surface area was about 2.1 mm2 and for DPP and DPASV about 1.3 mm2. The reference electrode, consisting of the internal part of a double-junction reference electrode (Orion 90-02), was connected by a low-leak bridge to the test solution. A 1 M NaN0:j filling solution in the bridge eliminated the possibility of precipitation of KC104 due to lengthy contact of the reference electrode KCl with the test solution NaC104. This precipitate could alter the data. To minimize surface area, the bridge consisted of 1.0 mm i.d. Teflon tubing and a tapered glass tip. The filling solution made contact with the test solution via a minute hole in the tip. Bridge leakage was low enough that even after 24 h (greater than experimental conditions) the ionic strength of the test solution remained 0.01 M. An attempt to optimize conditions during the measurements was made by using a cleaned platinum-wire counter electrode (the auxiliary electrode) positioned so as to retard the diffusion of oxygen from it to the HMDE working electrode. The electrode was cleaned of the oxide film and the adsorbed hydrogen by storing in an air-saturated 0.1 M perchloric acid containing ferric and ferrous sulfate (11 ). In NPP, potential pulses of 57 ms of successively increasing amplitude are applied from a fixed potential to the working electrode. At 40 ms after pulse application, the current is measured for 17 ms. During the remaining time between the initiation of pulses, 943 ms, the potential stays fixed a t the initial value so that for reversible systems it causes the electrode surface to undergo a form of “pretreatment” approximately reestablishing the initial concentration in the vicinity of the electrode. Often any adsorbed product is removed and the electrode is left clean and a t the same state for each successive pulse (12). The pH was measured with a radiometer G202C glass electrode and the previously described reference electrode. These electrodes were standardized against the appropriate buffers before each set of scans, and their drift was checked a t the conclusion. The drift ranged from 0.00 to 0.04 pH unit. Additional check of the high-pH solutions was made by titrating with acid. When necessary, corrections were made to the pH readings. Theory Electrochemical determination of formation constants is based on data derived from the measurement of the reaction a t the electrode surface. Accurate application of the mathematical relationships described later on implies that this reaction is both diffusion controlled and reversible. (The measurement of the free ligand via pH measurement waives the requirement that the ratio of the ligand-to-metal concentration be very large.) Complicated calculations may be avoided Volume 12, Number 13, December 1978
1407
Table 1. Data Measured by NPP and Used in Calculating Apparent Formation Constant PI’ v
PH
E1/2cr
8.72 8.76
-0.420 -0.421 -0.421 -0.424 -0.427 -0.424 -0.424
8.80 8.93 8.96 8.97 9.02
v
k/Ic
PH
E1/2cr
1.52 1.24 1.16 1.27 1.13 1.41 1.14
9.06 9.07 9.19 9.27 9.31 9.41
-0.427 -0.431 -0.433 -0.437 -0.436 -0.441
Table 11. Data Measured by NPP and Used in Calculating Apparent Formation Constant P i 1.42 1.31 1.30 1.34 1.38 av 1.30
SD 0.13 a
measured as -.0.382 V
if the dissociation constant, Kd, is small enough or the concentration of the ligand large enough that the ratio Kd/[OH] 4 is much less than one (11). Diffusion Control. Diffusion control is shown by a linear plot of diffusion current vs. drop area. This definition is based on the same principle as that applied to the dropping mercury electrode. (In that case the expression id/h1/2 = k is used, where h is the height of the mercury column and k is a constant ( I I ). Reversibility. Reversibility may be identified by the application of Equation 3 ( 2 3 ) a t 25 O C :
v
PH
EIl2Cl
9.56 9.58 9.59 9.60 9.61 9.62 9.63 9.64 9.80
-0.452 -0.453 -0.454 -0.454 -0.453 -0.454 -0.456 -0.456 -0.460
I J I C
v
IS/ I C
PH
E1/2cr
0.89 0.99 1.oo 1.02 1.04 0.95
9.86 9.95 10.05 10.09 10.18 10.20 10.30 10.40 10.50
-0.467 -0.469 -0.474 -0.476 -0.483 -0.483 -0.490 -0.495
1.10 1.30
a
-0.500
IS/ I C
1.09 1.39 1.25 1.19 0.95 1.04 1.06 1.01 1.11 av 1.08 SD 0.13
measured as -0.382 V
a
Table 111. Data Measured by NPP and Used in Calculating Apparent Formation Constant P3’ a PH
10.54 10.73
12.03 12.11
E112cr
v
-0.504 -0.517 not averaged
k/lc
PH
0.909 0.868
10.93 11.12 11.31 11.47 11.64 11.83
...
-0.616 -0.622
Et12cr V
-0.533 -0.549 -0.561 -0.574
-0.588 -0.602
IJIc
0.796 0.796 0.825 0.812 0.796 0.839 av 0.81 1 SD 0.018
In this equation, EHMDE is the potential a t the hangingmercury-drop electrode (HMDE), E112 is the half-wave poa measured as -0.382 V . tential (the potential a t which the value of the diffusion current is one-half the total diffusion-current value for the reduction reaction in question), n is the number of electrons involved in the reduction reaction (for lead, it is 2), id (the diffusion current) is the difference between the current value on the plateau and that for the residual current a t the same E H M D Eand , i is the difference between the current a t the EHMDE and that for the residual current at the same EHMDE. The residual CI rent is the current present when there is no metal available to be reduced. The system is considered reversible when a plot of E H M D against E the log value is linear and has a slope of -0.05915/n k 0.003 V (7). The value of Ell2 = (I3’ . . . CX(q--3)pq’ (5d) F3(X)= equals the E H M D of E the reaction when the log term is zero. Evaluation of t h e Complex. Equation 4 describes the (The right-hand side of Equation 5a is an expansion of the derivation of the formation constants (Iq (14): summation term in Equation 4.)
”’)
The definition and determination of El/* have already been described. The term y represents activity coefficient; I , diffusion-current constants; C, the concentration of the ligand; and the subscripts are: x, ligand; mx, complex; s, when only the free metal ion is present; and c, when complexed metal is present. The ratio of the diffusion-current constants (Zs/Zc) can be determined experimentally from the ratio of the observed diffusion currents of the simple and complexed metal ions when they are a t the same concentration and when all other conditions are constant. The terms R , T , and F have the usual connotations. Ignoring activity coefficients, apparent formation constants (Is’ can be calculated by application of the measured data to Equation 4 to get F o ( X ) , and then by utilizing Equations 5a-5d:
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Environmental Science & Technology
+
Results Tables I, 11, and I11 list the NPP data used in the calculation of &’s. Table IV lists the results of these calculations along with the values of pq for zero ionic strength and similar values of supportive results from DPP and DPASV work. Only NPP E112 values that were shown to be reversible and to be diffusion controlled were used in the calculations. For the DPP and DPASV data, reversibility and diffusion control may exist but were not proven. Thus, results from this part of the work were used only for added confirmation of the NPP results. In making these confirmatory calculations, the difference in peak potentials, E,,, was assumed equal to the difference in half-wave potentials. In the evaluation of the ratios of the constants Zs/Zc by NPP, no trend with respect to pH was indicated for the diffusion currents, either for data relating t o 61’ or for data relating to p2‘. Since there was scatter, averages were taken and applied in the calculations. In the case of the first two data sets relating to pa’, application of the averaged ratio of diffusion currents for p3’ resulted in a far smaller value of P3’ and application of the averaged ratio for p2’ a much larger value of p3’, compared
Table IV. Formation Constants from This and Previous Works method
medium
temp, ‘C
0.01M NaC104 0.01M NaC104
25 25
PH
lead concn, M
log 81’
log 82’
log
831
ref.
Calculated at 0.01 M Ionic Strength NPP DPP and DPASV
1.1 X 10-6-4.8X 4.0 X 10-7-5.0 X
8.7-11.5 6.59 7.7-9.9 6.55
10.80 10.81
13.63
this work this work
...
Extrapolated to Zero Ionic Strength log
NPP a DPP and DPASV a EMF EMF EMF EMF EMF
ASV a
0.01 M NaC104 0.01 M NaC104
25 25
1.1 X 10-6-4.8X 4.0X 10-7-5.0 X
0.3M NaC104
25
1 X 10-3-8 X
and higher 0.3M NaC104 0.3M NaCIO4 and higher 0.3M NaC104 0.015-1.0M (PbNO;! -I-BaN03) 0.1 M KNOB
>5
25 18
>5 x 10-4 5 X 10-3-4 X
25 25
1
x
lo-’
log 83 13.89
log 8 2
11.07 11.08
...
this work this work
5-8
6.29
...
...
3
5-8 >12
6.86
...
...
...
10.88
13.94
6 3
lov2
1 X 10T3-8 X x 10-4
25 25
81
8.7-11.5 6.77 7.7-9.9 6.73
>12 ... 3.8-6.1 6.2
10-6-1 x 10-5
7-11
7.44
...
11.04
14.01
...
...
11.72 10.84e
...
7 8
5 4
13.928
a log bq calculated using activity coefficients determined from the extended Debye-Huckel equation ( 75) and the results from the reference listed. Log Bs reported in ref. 3 and apparently calculated by using activity coefficients determined from the Guggenheim equation ( 75) and by using the results from other works, including ref. 6 and 7. (Presumingthe latter, the conditions listed are for ref. 6and 7.) Log 0,calculated using activity coefficients determined from the Davies equation ( 15) and using the results from the reference listed. Log ps an extrapolationto zero ionic strength reported in ref. 8. *Log pq calculatedfrom free-energy values.
with the values computed from the remaining sets of data found a t higher pHs. This quite likely was due to the fact that more than one complex was making a significant contribution to the value of the ratio of the diffusion currents. Application of the ratios directly related to these data sets resulted in log B3’ equals 13.49 and 13.53. These two log values no doubt are less reliable than those listed in Table IV because there is no way to average out the error in the ratios of their diffusion currents. The standard deviation of the diffusion currents applied to the formation constants causes log (31’ to vary by 0.05, log pz‘ by 0.03, and log p3’ by 0.01. The sets of data a t the four highest pHs also were not included in the averaging of the value of p3’ because the accuracy of their pH values is not as dependable and because the ionic strength of the solutions has been slightly increased by the high ligand concentration. Regardless, they are supportive and their logs range from 13.45 to 13.53. Since the diffusion current constant for an ionic species is the same regardless of the polarographic method, the I s / I c values found by N P P were applied in the calculation of the results from data derived by D P P and DPASV. These results agree well with the N P P results for PI’ and /32’ but vary by too wide a range to be specific about &’. The activity coefficients for the hydroxide ion (0.899) and the lead ion (0.670) were taken from Butler (15),and those for Pb(OH)+ and for Pb(OH)3- (0.904) were estimated from data in Butler ( 1 5 ) , assuming an a parameter of 5. The activity coefficient for Pb(OH)2 was considered to be 1.000. The hydroxide concentration was calculated from hydrogen ion measurements in activity units by applying the K , of water as 10-14.00 and the activity coefficient of the hydroxide ion. Discussion The criterion that the ratio Kdl[OH]
