ULTRACENTRIFUGATIOK OF HYDROLYZED LEAD(II)PERCHLORATE SOLUTIOXS
the extended lengths of the molecules. At higher molecular weights this ratio will become severely reduced with the concomitant re-entry of chains into the crystallite from which they emerge. However, spherulites are formed over this complete niolecular weight range irrespective of the relative size of the crystallites.1o Obviously, therefore, chain re-entry or folding is not a requirement for spherulite forniation in long-chain molecules. Aforeover, from the analysis of the data in Figure 1 the products of interfacial
959
energies are independent of molecular weight over the range studied (irrespective of the value of oe that is chosen). Hence, we niust, conclude that it is highly unlikely that the values of the interfacial energy or the nature of the nucleation acts theniselves deterniine whether many sequences from the same niolecule participate in the developnient of a given crystallite.18
(18) P.J. Flory. J . A m . Chem. SOC.,84, 2857 (1962)
Equilibrium Ultracentrifugation of Hydrolyzed Lead(11) Perchlorate Solutions'a'b
by 0. E. Esval'' and James S. Johnson, Jr. Oak Ridge *VatWnal Laboratory, Oak Ridge, Tennessee
(Received October 6 , 1964)
The degrees of polymerization ( N , ) of 0.025-0.1 M lead(I1) perchlorate solutes were investigated by equilibrium ultracentrifugation from 0 to 1.33 hydroxyls bound per lead. The distribution of hydrolyzed species was polydisperse in all cases studied. Average values of N , were ca. 4 at hydroxyl number 1 and increased further in more basic solutions. The results are in agreement with light-scattering nieasurenients carried out elsewhere and are consistent with a scheme in the literature based on e.1ii.f. studies. Apparent molal volumes and refractive index increments for hydrolyzed Pb(I1) solutes are reported.
Some years ago, a study by equilibrium ultracentrifugation of the hydrolysis of Pb(I1) arid Sn(1V) in basic solution, carried out in this laboratory, indicated We report that niononieric' species were here an'extension of the study of Pb(I1) hydrolysis to solutions on the acidic side of the precipitation point. There have been fewer studies made of the hydrolysis of divalent lead than of many other elements, and perhaps, as a result, there is less controversy over the species formed though agreement between various investigators is not altogether complete. Since others3 have reviewed the literature recently, we shall restrict our attention to a few authors who have covered a wide
enough range of conditions (or have examined their results closely enough) t'o require species higher t,han dimeric for interpretation. I'ederson, from acidity nieasurenients of lead nit rate (1) (a) Research sponsored by t h e U. S.Atomic Energv Commission under contract with the Union Carbide Carp.; (b) from a thesis submitted by 0. E. Esval t o the Graduate School of the University of North Carolina in partial fulfillment of the requirements for t h e Ph.D. degree, 1962; (c) Oak Ridge Institute of Nuclear Studies Graduate Fellow. (2) J. S. Johnson and K. A. Kraus, J . Am. C'hem. SOC.,81, 1569 (1959). (3) F. C. Hents and s. T.Tyree, Inorg. Chem., 3 , 844 (1964). (4) K. J. Pederson, Kgl. Danske Videnskab. Selskab Mat. Fys. J l e d d . , 2 2 , No. 10 (1945).
Volume 60, 2Vumber S
March 1966
960
0. E. ESVAL AND JAMES S.JOHNSON, JR.
as a function of concentration and added acid and base, concluded that the hydrolyzed species Pbz(0H) +, PbOH+, and Pb4(OH)44+were formed. F a ~ c h e r r e , ~ from a variety of measurements, listed Pb4(OH)44+ and suggested that a higher species, perhaps Pb,(OH)d+, was formed under some conditions. Olin,6 in an extensive electromotive force study with both acid-sensitive and lead amalgam cells, listed PbOH +, Pb3(OH)42+. Pb4(OH)44+,and Pbs(OH)84+. Later, from studies in concentrated solutions,’ he added Pbz(OH)3 + and, from calorimetric measurements of acidbase titrations,8 estimated enthalpies for the reactions forming Ph4(OH)44+,Pb3(OH)42+,and Pb6(OH)86+. Huge19 measured the acidities of hydrolyzed lead perchlorate solutions as a function of dilution and listed formation quotients for the species PbOH+ and Pb4(OH)d4+which agree well with those of O h . The more hydrolyzed species listed by Olin would not have been important in the range of Hugel’s measurements, and he did not exclude them. The agreement between these laboratories on the presence and the importance of the Pb4(0H)44+ species is remarkable for the hydrolysis field. From experience with other solutes, however, it seemed that confirinat ion of the main conclusions by methods sensitive primarily to the weights of the species would be useful. The present paper describes a study by equilibrium ultracentrifugation. Hentz and Tyree carried out a light-scattering study of the same system concurrently.3 The conclusions from these weight-average studies are in general agreement with each other and with those made on the basis of the other techniques.
Experimental 1 . Ultracentrifugation. Procedures are similar to those outlined in earlier Centrifugations were carried out with a Spinco Model E ultracentrifuge. Solutions were contained in 12-mm. cells, which were placed in a five-cell Analytical G rotor. Sedimentation was followed by interference optics. The temperature of centrifugation was 25”. Speeds of rotation were between 11,250 and 24,630 r.p.in. ; the speed was selected to give an adequate interference pattern for the fdegree of polymerization and Pb(I1) concentration involved. Computations were carried out on an IBM 7090 computer with a program12somewhat revised from that used previously.10 The equation used for COlW)Utation of degree of polymerization, N , , is N,v=
d In c2’/d(xZ) (I) Az’ - (z’/2)d In [(I ~ ) / ( 1 ~)l/d(~~) ~
+
where subscript 2 indicates the Pb(I1) cOlllpOne~1t; The JniLrnal of Physical Chemi8try
3, the supporting electrolyte ; primes, quantities expressed in terms of monomer units; c, concentration 5 , radius; z’, charge per mononier unit of in moles the lead polymer (which, because of perchlorate complexing, may not be the niaxiinuin possible); 9 = zfcZ’/2c3; Az‘ = AlZ’(1 - s z p ) w Z / 2 R T ; M , molecular weight; 3, partial specific volume ; p, solution density ; w , angular velocity; R, gas constant; and T , absolute temperature. The definition of the (primed) polymeric component 2, Pb(OH)n(C104)z-n - (z’/2)NaC104, is that proposed by Scatchard13and reflects the charge. The symbol n indicates hydroxyl number, the average number of moles of hydroxide bound per mole of lead(I1). The reported values of N , were evaluated for the radius at which the initial concentration of Pb(I1) occurs at centrifugation equilibrium. The procedure for obtaining CZ’ from interference patterns is coinplicated by the effect of charge and the consequent use of the Scatchard definition of components; it is described in detail elsewhere.l b , I 0 2 . Materials. Stock solutions, prepared froin reagent grade PbO and perchloric acid, are listed in Table I along with their hydroxyl numbers. For hydrolyzed
Table I : Stock Pb(I1) Solutions Soln. no.
mmoles of Pb(II)/g. of soln.
Dev.,
mmoles of perchlorate/g. of
Dev.,
p.p.t.
80lIl.
p.p.t.
n
1 2 3
1,297 2.032 0.8243
0.5 1.5 4.7
2.776 2.169 0.5560
3.6 2.3 2.5
0” 0.933 1.326
a
Excess HCIOl present.
solutions 2 and 3, n is given by the stoichiometry (2 times moles of Pb(I1) minus moles of perchlorate) since the free acid is negligible.6 A brownish colora(5) J . Faucherre, Bull. soc. chim. France, 21, 128 (1954) (6) A. Olin, Acta Chem. Scand., 14, 126 (1960); Svensk K e m . Tidskr., 73, 482 (1961). (7) A. O h , Acta Chem. Scond., 14, 814 (1960). (8) B. Carell and A. Olin, ibid., 16, 2350 (1962). (9) R . Hugel, B u l l . SOC. chim. France, 1462 (1964). (10) J. S. Johnson, G . Scatchard, and K . A . Kraus, J . P h y s . Chem., 63, 787 (1959). (11) R. M.Rush, J. S. Johnson, and K . A. Kraus, Inorg. Chem., 1, 378 (1962). (12) The urogram is described more fully in ref. l b . A few modifications and corrections, which (except for centrifugations with short columns in the radial direction) affect results trivially in most cases, have since been incorporated; the revised program and a source deck (Fortran) are available from ORNL. (13) G. Scatchard, J. Am. Chem. SOC.,6 8 , 2315 (1946).
ULTRACENTRIFUGATION OF HYDROLYZED LEAD(11) PERCHLORATE SOLUTIONS
tion of the solutions appeared which, on the basis of a benzidene spot test, l4 apparently stemnied from Pb(IV). The coloration was eliminated by filtration through an ultrafine filter under nitrogen. Solution 2 was prepared at 100’. Solution 3 was prepared froni a basic salt of the appropriate hydroxyl number, which in turn was prepared by the method of Willard and Kassner.15 Solutions prepared froni the solid were slightly turbid, presumably owing to lead carbonate contamination, but filtration gave clear solutions. The stock solutions were analyzed in triplicate for lead by precipitation of Pb,lfo0416; perchlorate was determined as ammonium perchlorate by evaporation of the filtrate froni an amnioniuni carbonate precipitation of lead, followed by heating at 110’ to deconipose excess aninioniuni carbonate. The analyses and iiiean deviations are given in Table I. A concentrated NaClO, stock, prepared by neutralization of HC10, with S a O H prllets to pH 4 while bubbling S2 through, was analyzed by evaporation a t 120’. Fifteen solutions were used in the centrifugations with Pb(I1) concentrations being ca. 0.025, 0.05, and 0.1 M at hydroxyl numbers of ca. 0, 0.16, 0.73, 0.93, and 1.33. They were prepared by weight froiii the appropriate stock solutions of Pb(I1) and XaClOa. The solutions of n = 0.16 were prepared froni stock 1 by addition of XaOH; the solutions of n = 0.73 were prepared by addition of HClO, to stock 2 . The unhydrolyzed solutions, n = 0, had at least 0.003 M HC104 present in excess of Pb(C104)2. All solutions except for the unhydrolyzed became slightly cloudy on standing. Since a solution filtered under nitrogen and sealed against the atmosphere remained clear for months, we presume the turbidity arose froni lead carbonate. IP the most turbid solution, the amount of precipitate was found to be negligible for present purposes (0.004%) and was, therefore, ignored. Densities were measured with a 4i!4-m1. pycnometer, and refractive indices were measured with a BricePhoenix differential refractometer.
Results and Discussion 1. Volumes and Refractive Index Increments. Partial specific volunies of the solutes are needed in the equations for degree of polymerization, N,, and refractive index increments are required for interpretation of equilibrium interference fringe patterns in terms of concentration distributions. The apparent niolal volumes of hydrolyzed lead perchlorate solutes
961
I I I I Apparent Molal Volumes of Pb(OH)n(C104)i2-n)
I
-
I n W
E
3
9
i
a J 0
H
k
z W
LL
h 0. a
0.040
I I I I I I Refractive Index Increment of Pb(OH), (C104)c2-n,
I
I
I
I
0.5 1.0 HYDROXYL NUMBER
I
I 4.5
I
I
(E)
Figure 1 . Apparent volumes and refractive index increments (546 m r ) of hydrolyzed lead perchlorate solutions.
solution containing 1 kg. of water, V , is the volume of “solvent” ( i e . , the volume of a solution of the same iiiolality of supporting electrolyte as the solution of interest) containing 1 kg. of water, and m2’ is the molality of Pb(I1). The precision of the nieasurenierits in supporting electrolyte was not sufficient to justify estiiiiation of the dependence of volume on Pb(I1) concentration; therefore, apparent niolal volunies were used for partial volumes in coniputation of N , . Sonie measureinents were also made in absence of supporting electrolyte; the precision of these is better since slight percentage errors in supporting electrolyte concentration have a large effect on apparent volunies of the lead component computed from solution densities. The values, as expected, are lower in absence of excess ?;aC104. For interpretation of centrifugation results, we have used the line drawn through the values i n (14) F. Feigl, “Spot Tests,” 1‘01. 1, Elsevier Publishing Co.. New York, N. Y . , 1954, p. G8. (15) H., H. Willard and J. L. Kassner, J . Am. (’hem. Soc., 5 2 , 2391 (1930).
are summarized in Figure la. Here V is the volume of
(16) H. B. Weiser, J . Phys. Chem., 2 0 , 640 (1916).
Volume 69, Sumber 9
M a r c h 1966
962
1 JI SaC104 media parallel to the line for solutions without supporting electrolyte (Figure la). Supporting electrolyte partial volumes for computer input and for use in eq. 2 were obtained from literature data. In coniputation of +z for n = 0 (in which case HCIO, was present in appreciable quantities), volumes for the "solvent" were computed by the mixing rule of Young and the data of Wirth arid Collierla were used for supporting electrolyte volumes. Refractive index iricrenierits An646/c are given in Figure l b . The symbol Anb4e denotes the difference in refractive index at ,546 nip between solution and background both having the same niolarity of supporting electrolyte and c, the Pb(I1) concentration in niolesA. Again, thew mas no significant dependence on Pb(I1) concentration. Values for coniputational inputs were taken froin the line drawn through the values obtained in the presence of supporting electrolyte parallel to the points without supporting electrolyte. Literature values were used for SaC1041grefractive index increnients, arid nieasurenients were made in this laboratoryz0for perchloric acid. The effect of changes of input 42 and An/c 011 coniputed N," are indicated in Figure 1. It can be seen that uncertainties in these quantities are not 'important in coniparison with those stemming from assumptions made in analysis of data. 2 . I'ltracenti$ugation. Fifteen solutions, which were ea. 1 31 iri SaC1O4 supporting electrolyte, were centrifuged. Hydroxyl numbers investigated were n 0, 0.16, 0.73, 0.93, and 1.33, and at each hydroxyl nuniber l'b(I1 j concentrations were ca. 0.026, 0.05, and 0.1 31. All were ea. 1 M in SaC104 supporting electrolyte. Comparison of the equilibrium interference patterns for the hydrolyzed solutions with those of the unhydrolyzed :ndicates immediately that polymers are formed. The next question of interest is whether the Pb(I1) solute is found in species all having the same inolecular weight or in a polydisperse distribution. In E'igure 2 , we have plotted the deviation for each centrifugation of In n* from a linear variation with x 2 , obtained by a least-squares fit to a straight line of In n* values at all fringe positions. The syiiibol n* indicates difference between refractive index of the solution a t radius z and the background solution. ideal (constant activity coefficients) uncharged nionodispers~~ solute should give a straight line; an ideal charged nionodisperse solute in supporting electrolyte should produce a curve which is concave downward, and a polydisperse solute, a curve which is concave upward. Figure 2 indicates that all solutions, except the unhydrolyzed, are polydisperse.
The ,Journal of Physical Chemastry
0. E. EWAL A N D JAMES S. JOHXSON, JR.
I"
-O0lu 34
I
33
I
I
44
49
11.252
I1
34
1
39
I
44
1 49
I1
34
. -
0 16
I
l*iiliiii.
39
I1 252
44
49
1
54
19.119
"2
Figure 2. Deviations of In n* from linearity in z2. Points are at fringe positions. Arrows indicate points off scale. Numbers under boxes are speed of rotation in r.p.m.
Polydispersity makes determination of the degrees of polymerization by present methods of data analysis somewhat approximate. With ionic polymers, even in the presence of relatively high concentrations of slightly sedimenting supporting electrolyte, sedinientation is a function of charge, as well as of molecular weight. With nionodisperse solutes or with a fixed polydisperse distribution, an estimate of charge can be made from the concentration dependence of sedimentation, ie., by selecting that charge and niolecular weight best satisfying all results. In this study, different Pb(I1) concentrations are compared at the same value of n. If no two species present have the same hydroxyl nuniber, the reaction to form one from another will involve hydrogen or hydroxyl ions and will, therefore, be dependent on acidity, as well as on total lead concentration. The various species will in such a case be present in approximately (though not exactly) the same concentration ratios, and, consequently, the average degree of polymerization will be relatively (17) T. F. Toung and M. B. Smith, J . P h y s . Cham., 58, 716 (1954). (18) H. E. Wirth and F. N. Collier, J . Am. Chem. Soc., 7 2 , 5292 (1950). (19) H. Kohner, 2. p h g s i k . Chem., B1, 427 (1928). (20) R. M .Rush, unpublished results,
ULTRACENTRIFUGATION OF HYDROLYZED LEAD(II)PERCHLORATE SOLUTIONS
2.0,
I
I
I
I 0.5
I
I
1
I
HYDROXYL NUMBER (nl=0.46
4.0 \.-
963
I
O?
I
I
I
I
..>\
'%.., \ \ '... ' %., \
I
I
I
\
-
I
\
0.2,
\ I I
I I
I I I
I
I'
-
,
I
-- O.IM Pb(Ir)
- 0.05M Pb(n) *.***.,
0.025M P b ( E ) I'
Figure 3. Degrees of polymerization of Pb(OH),(ClO&-,, solutions, computed as a function of assumed charge. All solutions ca. 1 M in NsClO,. 4 indicates maximum feasible charge ( 2 - n).
independent of Pb(I1) concentration. It will be seen are encountered, and benefits are realized, with light that, of the solutions containing hydrolyzed solute, scattering. The values of degree of polymerization computed only at n = 1.33 do species having the same hydroxyl as a function of assunied charge per niononier unit (eq. number appear to be present in important quantities. 1) are given for the various degrees of hydrolysis studied Estimate of charge niay therefore have some significance. A serious handicap in interpretation of results (21) J. Aveston, E. W. Anacker, and J . S. Johnson, Inorg. Chem., 3, here, however, is the fact that one deals with a mixture 735 (1964). of species having different charges, z', and different (22) I t is possible t h a t a more detailed analysis, involving comparivalues of refractive index increments and voluines son of experimental interference patterns with those computed for postulated hydrolysis schemes, may yield more definitive information. (Figure 1). Experimental accuracy is frequently sufficient for such a procedure. Although the values of N , obtained must, therefore, We have achieved some success with this approach in a test case (Bi(II1) hydrolysis: D. F. Keeley, J. S. Johnson, J r . , and K . A. be viewed with some reservation, similarly handicapped Kraus, Abstracts, 141st Meeting of the American Chemical Society, studies in the past, e.g., of U(V1)" and R.~O(VI)~*Washington, D. C., March 1962, p . %I), but whether assumptions concerning activity coefficients of species can be made with sufficient hydrolysis, have indicated that information gained confidence to make the complex analysis which is necessary worthby the technique can be valuable.22 Similar difficulties while is a t present uncertain. Volume 69,n'umber d
March 2966
0. E. ESVALAXD JAMES S. JOHXSOS, JR.
964
in Figure 3. The values for iiiaximuni charge and for zero charge (0.1 J1 Pb(I1) only) are summarized in Figure 4. It is clear that the average degree of polymerization increases with hydroxyl number, whatever assuiiiption is made concerning perchlorate coniplexing. For all hydroxyl numbers except 1.33, N , computed for z’ assumed 0 decreases with increasing concentration, a trend indicating that the Pb(I1) species are charged. The curves for the various concentrations at each hydroxyl number in Figure 3 are so closely spaced that crossovers should be viewed with caution (especially 111 view of the assuiiiptions and approxiinations involved), but the intersections for n = 0.16, 0.73, and 0.93 all occur at values of x’ less than the maxiiiiuni charge, 2 - n. The polymeric species thus appear to toinplex with perchlorates to some extent; consequently, the correct value of N , should be somewhere betn een that computed on the assumption of zero and niaxiniuni charge. There art no data on which i o base estimates of the activity coefficient variations in the hydrolyzed solutions. The values of X, obtained for unhydrolyzed solutions for x ‘ = 2 , which may be taken as a rough guide to departures froni constaIicy, are 0.91 for 0.1 X I’b(I1). 0 9.-) for 0.05 dl Pb(II), and 0.96 for 0.025 dl Pb(I1). The degree of polymerization obtained from light scattering3 for n = 0 deviates froin unity (ca. 0.9) by a comparable amount in the saine direction. 3. Discusszon. In Figure 4, we have plotted the degrees of polynierization obtained from light scattering3 by Hentz and Tyree. Their values fall between those coniput ed froin ultracentrifugation for z’ = 0 and for 1n:ixiniuiii charge. Since the charges inferred by theni froni turbidities are also less than niaxiniuni, the conclus ons drawn from the two weight-sensitive methods are in good agreement. The curw for N , consisterit with Olin’s scheme6 is also shown in Figure 4. Again, there is agreement within uncw-tainty between the different methods. Olin postulates two species, Pb3(0H)42+ and Pb6(OH)84+,having hydroxyl number 1.33, and, consequently, the equilibrium relating them does riot depend on acidity. This is consistent with the observation by ultraceIitrifugatiori that N , for n = 1.33 coinputed for zero charge increased with increasing Pb(I1) concentration (Figure 3). The changes in O h ’ s foriiiation quotients between 0.3 and 3 2L.I total perchlorate are i n a direction indicating perchlorate conipleuing by the polynieric Pb(I1) species, again in agreement with our ultracentrifuge results. A t the time Olin published his results, coiiiputers were appaiently not available to him. We have checnked his con(n1usions by a least-squares fit of his The Jotirnd of Physical Chemistry
1
I
I
Computed for Maximum Charge I ’= 2 - 2 x
7 -.
-
0.1M P b ( E )
Computed for I ’ = 0
--- Computed
f r o m Olin’s Scheme Using Constants for 3 M
2 6-
z
0 ia 5N LL
w
2
3
8
4-
LL
0
w 3W
LL
a
W
0
2-
I 0
0.2
0.4 0.6 0.8 1.0 HYDROXYL N U M B E R ( E )
ts2
I 4$4
Figure 4. Degree of polymerization of Pb(OH),( Clod)?by equilibrium ultracentrifugation; light scattering, ref. 3.
+,
data carried out with programs described elsewhere.23 With the species he postulated for low Pb(I1) concentration (ie., Pb2(OH)3+not included) a very satisfactory fit to his data was obtained (
