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Calculation of molecular weights of humic substances from colligative data: Application to aquatic humus and its molecular size fractions
Calculation of molecular weights of humic substances from colligative data: Application to aquatic humus and its molecular size fractions J. H. REUTER School
of Geophysical
Sciences,
Georgia
Institute
of Technology,
Atlanta,
GA 30332. U.S.A
E. M. PERDUE Environmental
Science/Chemistry
Department,
Portland
State University,
Portland,
OR 97207. U.S.A.
(Received 2 September 1980; accepted in revised form 20 May 1981) Abstract-A rigorous mathematical expression for the dependence of colligative properties on acid dissociation of water soluble humic substances is presented. New data for number average molecular weights of a river derived humic material and its gel permeation chromatographic fractions are compared with an values obtained by a reevaluation of previously published experimental observations on so11 and water fulvic acids. The results reveal a remarkable similarity of fulvic acids from widely different sources with respect to number-average molecular weight.
INTRODUCTION IT HAS been generally recognized that humic substances in soils originate as heteropoly-condensates of such chemically diverse starting materials as phenols, amino acids, carbohydrates, even ammonia (see e.g. FLAIG et (II., 1975). The water-mobilizable fraction of soil humic substances contributes significantly to the chemistry of surface waters through interaction with metals, adsorption of hydrophobic substances, etc. and forms an important fraction of the riverine organic carbon flux to the oceans. One of the major analytical difficulties in the characterization of aqueous humic substances is the lack of any fractionation procedure which will yield pure components which can be subsequently characterized by standard techniques. Consequently, efforts have frequently been devoted to the determination of those bulk physical properties which can be unambiguously defined and determined on complex mixtures. One such parameter is the number-average molecular weight (a,,), which can be readily determined from colligative properties such as vapor pressure and freezing point depression. Recently, both vapor pressure osmometry (HANSEN and SCHNITZER, 1969) and cryoscopy (DE BORCERand DE BACKER, 1968) have been applied for the determination of I@~ values for acid soluble fractions of soil humic substances. In both cases, colligative properties were determined on aqueous solutions of fulvic acids, so that the experimental measurements required corrections for acid dissociation. Lacking a rigorous mathematical expression for the dependence of colligative properties on acid dissociation, different ‘correction’ procedures were proposed in the two studies. This has led to some confusion about the validity of the approaches chosen (see e.g. WILSON and WEBER, 1977).
In this paper, we wish to present new analytical data for an values of water-derived humic substances and their molecular size fractions obtained by gel permeation chromatography. We have developed a rigorous mathematical treatment of the dissociation correction applied to the determination of numberaverage molecular weights for weak polyelectrolytes. This method has been used to re-evaluate analytical data from the above mentioned references. We hope that our discussion will help to remove some misunderstandings and will provide encouragement to generate much needed data on number-average molecular weights of aquatic humic substances.
EXPERIMENTAL To obtain sufficient organic matter for this study, 200 I. of unfiltered water from a small tributary in the Satilla River flood plain (southeast Georgia) were collected in 20 I. polyethylene carboys and immediately transported to the laboratory. The sample was centrifuged at 10,000 rpm (Sorvall Centrifuge Type SS-3, flow-through mode) and concentrated approximately tenfold under reduced pressure (25 mmHg). The concentrate was freeze-dried, yielding a brown, fluffy powder which contains all but the volatile constituents (e.g. HCI) of the original water. This residue was redissolved in distilled water to a concentration of _ 20 g of organic matter per liter. An undissolved residue consisting largely of silica, hydrous oxides of Fe and Al and some high molecular weight organic matter (- 3”/;, of total) was removed from the solution. The solute was desalted by shaking with two batches of cation exchange resin (25 ml of BioRad AGXI, 50-100 mesh, Ht form, per gram of organic matter) and freeze-dried. The ash content was decreased from an initial 7.77” to a final 2.3”/;. Aliquots of the purified river water organic matter were fractionated progressively by exhaustive gel permeation chromatography (GPC) on columns of Sephadex G-50, G-25, G-15, and G-10 using distilled water as eluant. The goal of this fractionation was to obtain chromatographitally well defined excluded fractions. Experiments by REUTER (1977) have shown that the ratio of excluded to
2017
J. H. REUTERand E. M. PERDUE
2018
retarded fractions is to a high degree also determined by reversible conformational changes of the humic molecules. At low solute concentratjons (below 1050 mg/l) conformational changes from extended (or uncoiled) to contracted (or coiled) configurations are affected by the ionic strength and the pH of the solution. Thus, at SHRS concentrations of 100 mg/l, zero ionic strength and pH 7 all of the organic solute was found in the excluded fraction of Sephadex G50. With increasing solute (SRHS) concentrations, the ratio of excluded to retarded fractions decreased until at concentrations above 2ooOmg/l a constant ratio was observed. At and above this concentration the distribution between excluded and retarded fractions was found to be stable against changes of pH (& 1 pH unit) and ionic strength. Therefore, no strict control of either parameter was found necessary to obtain reproducible excluded fractions, as long as humic solute concentrations were held above 2000 mgjl. In order to minimize interactions between the gels and the organic matter, the acidic organic matter solutions were neutralized to pH 7 with NaOH before gel filtration (SCHNITZERand SKINNER,1968). The effluent from each column was separated into an excluded (E) and a retarded (R) fraction. The excluded fraction was rechromatographed on the same gel type to yield a final excluded fraction for further analyses. The retarded fractions from the first and the second run were combined to be chromatographed on the next lower Sephadex grade. Thus, four excluded fractions (G50E. G25E, GISE. GIOE) and one retarded fraction (GlOR) were produced. The final Sephadex fractions were desalted to remove added Na+ using the above named cation exchange resin. A Me~hrolab Model 3OlA vapor pressure osmometer was used to determine vapor pressures of aqueous solutions of SRHS. These data, together with precise pH measurements on the same solutions were used to calculate number average molecular weights as described in the following section of this paper. The accuracy of the method was tested by determining the M. of a known compound (~nzene~ntacarboxylic acid). Infrared spectra were recorded on a Beckman Model 12 Spectrophotometer using KBr pellets. Care was taken to eliminate water from the samples and the potassium bromide (THENGet al., 1966). MATHEMATICAL TREATMENT OF COLUGATIVE PROPERTIES OF WEAK POLYELE~TROLYTES
gative property methods (cryoscopy, ebulhometry, vapor pressure osmometry, etc.) for polymeric nonelectrolytes. The instrument response (e) is related to the total molality of dissolved solute species (m,) by the equation : 0 = Am, + Bm:
+
.
(3)
In the case of nonelectrolytes, mr and C, arc equal, so 0 can be directly related to the total weight concentration(W) of organic solutes by combining eqns (2) and (3).
All the methods described by CLOVER(19751 were based on eqn (4), which was truncated after either the linear or quadratic term. it was pointed out that the statistical significance of derived results is dependent on the order of the equation used to fit experimental data. The constant A, the apparatus constant, is obtained by instrument calibration using a solute of known molecular weight. The &i, value of an unknown sample is determined by a least-bquares method which yields (A/a”) as one of the regression coefficients. None of the equations or regression methods described by GLOVER(1975) are directly applicable to solutions which contain weak polyelectrolytes such as humic substances. Suppose the ith organic solute is a weak acid of the general formula AiH,i, which can dissociate in solution to produce a variety of anions AiH,i_j (j = 1 to ni). Despite the complexity of the multiple equilibria, the mass balance constraint requires that:
The concentration by:
of Ht derived from Ai H,i IS given
i6)
(H”)i = ~ j(/liH"i_i). j-0
The number-average molecular weight (z”) of a mixture of z organic solutes is defined as follows:
The total molality of ions and molecules (mi) arising from AiH,i is: m; = Ci + (H’)i
(7)
and in a mixture of z organic acids, i-l
where ci is the molal concentration of the ith organic solute, whose molecular weight is Ml. The weight concentration of the ith component is ci Mi, so the sum of ail ciMi values equals the total weight concentration ( W) of the mixture of organic solutes. The total molal concentration (C,) of organic solutes equals the sum of all ci values. Thus.
mT=
i mi=C, i:1
+(H*).
IX)
Combining eqns (2), (3) and (8). 0 = ;
[W -I-
n
il;i(H+)]
+
&IW +ii;i,(Hirj2
+
(9,
”
GLOVER (1975) has reviewed the mathematical
of molecular
weight determination
details by absolute colli-
Equation (9) is the fundamentaf equation which must be used to obtain @,, for weak ~olyelectro~ytes. This equation,
which stems sokly
from the constraints
of
2019
Aquatic humus and its molecular size fractions Table 1. CHEMICAL PARAMETERS OF AQUATIC HUMUS FROM THE SATILLA RIVER (SRHS) ANO ITS MOLECULAR SIZE FRACTIONS.
oa
SamDie SRHS G50E G25E G15E GlOE GlOR
1.000 0.036 0.470 0.143 0.145 0.206
C
H N 0 Wt.:; (ash-free)
52.1 54.3 51.4 50.3 50.4 51.8
3.6 4.7 3.6 3.7 3.7 4.2
0.8 1.4 0.7 0.8 1.1 0.8
Ash wt.:
Meq/g
2.3 10.8 0.9 0.9 1.1 0.8
10.4 7.3 10.6 10.1 12.0 9.9
43.5 39.6 44.3 45.2 44.8 43.2
TAb
aweigkt fraction of molecular size fraction btotal acidity--barium hydroxide method
mass and charge balance, can be solved for &in, and does not require information regarding pK, values, regardless of the complexity of the system. There are rigorous linear and non-linear regression methods which can be used to determine %?” from the linear and quadratic forms of eqn (9), respectively. However, it is conceptually more straightforward to use an iterative process to determine @” from eqn (9). Initially, the M, term in parentheses is set equal to zero (analogous to treating the solute as a nonelectrolyte mixture). Least squares analysis yields an ii?,, value from the first order regression coefficient which is subsequently used in the parenthetical term to generate a refined estimate of H”. The process can be continued until successive M,, values agree to the desired extent.
RESULTS AND DISCUSSION
weight fraction (c() of each molecular size fraction is given in Table 1. While recovery of the sodium salts was quantitative (lOOS”~), approximately 187; of the solute was lost during the final desalting step, making it impossible to directly determine the weight fractions of the desalted molecular size fractions. Since total acidity of the molecular size fractions averages 10.0 + 1.7m-equivlg (see Table l), a maximum of 179< variability in Na+ content is expected. Assuming an even distribution of Na+ in the molecular size fractions, the values in Table 1 can be used to represent the weight fraction (z) of each desalted molecular size fraction. The rather broad character of the absorption bands in the infrared spectra of humic substances are generally seen as an indication of a high degree of complexity. It was hoped that the exhaustive gel permeation fractionation to which the aquatic humus was subjected, would reduce the complexity of the mixture and lead to infrared spectra with more distinct features. However, judging from the infrared spectra of SRHS and its molecular size fractions (Fig. 1) very little change occurred. The complex ‘humic’ character of the infrared spectra is maintained down to the lowest molecular weight fraction. This situation is also reflected in the small changes in total acidity and elemental composition among the molecular size fractions (Table 1). Both the linear and quadratic forms of eqn (9) have been used to calculate &?” values for benzenepentacarboxylic acid (ii?” = 298 gimol), SRHS, and the molecular size fractions derived from SRHS by exhaustive
The molecular size fractions obtained by GPC were freeze-dried and weighed as their sodium salts. The
MrcRoNs 3.0 I
3.5 I
11.0 I
6.0 I
5.0
7.0 I
8.0 I
10 I
12 I
GlOR
3500
3000
2500
2000 FREQUENCY
big.
1. Infrared spectra of aquatic humus from the (for explanation
1800
1600
I
I
1
I
1400
1200
1000
800
cram1
Satilla
of fraction
River (SRHS) and its molecular sire fractions
notations
see text).
2020
J. H. REUTERand E. M. PERDUE
Table 2. EXPERIMENTAL BEN~ENPENTACARBOXYL~C FROM THE SATILLA RIVER
SET OF W, pH ANO e VALUES FOR AND AQuATIc HUMUS (SRHS).
ACID(BPCA)
BPCA kd
SRHS ob
PH
2.706 3.331 3.956 4.893 5.518 6.455
1.766
8.0 10.0
1.699
12.0 15.0 17.13 20.0
1.643 1.577 1.54i 1.491
concentration instrument response
Wd
PH
8.0 10.0 12.0 15.0 20.0
2.104 2.030 1.967 1.894 1.796
eb 0.914 1.213 1.511 1.959 2.705
where N is the number of molecular size fractions and xi is the weight fraction of the ith molecular size fraction, whose number-average molecular weight is
1" g/kg in ohm
$,9ht
GPC on Sephadex gels. A sample set of experimental data for benzenepentacarboxylic acid and SRHS is given in Table 2. Weight concentrations (W) of humic substances were not corrected for ash content, introducing a corresponding uncertainty in calculated a” values. The results are summarized in Table 3, which includes the number of observations in a data set, the number of iterations required for convergence (0.015,, variation in a,, for successive iterations), the calculated H” and its 95% confidence interval. Because the 9Soi, confidence interval is dependent on the number of observations and the order of fit (linear or quadratic), those data sets containing only four observations do not yield statistically meaningful a” values, particularly in the quadratic fits. The quadratic fit yields obviously better results for benzenepentacarboxylic acid and is probably the more appropriate form of eqn (9) for analysis of the SRHS data. Therefore, only results calculated from quadratic fits of experimental data will be used in the subsequent discussion. The molecular size fractions yield an values which are much lower than the molecular weight exclusion limits of the corresponding Sephadex gels (e.g. G-50: exclusion limit = 30,000 for globular proteins, $i” = 1231). The measured values do, however, decrease in the expected qualitative manner. The largest molecular size fraction (G-25E, 47%) has an I@” value Table 3. NUMBER AVERAGE MOLECULAR WEIGHTS (l? TIC HUMUS FROM THE SATILLA RIVER (SRHS) AND 1% LAR SIZE FRACTIONS. Linear
_-
Quadratic
SRHS G50E G25E G15E
5 4* 6 4
8 14 11 9
556 1952 1306 725
8 746 75 46
8 12 6 5
614 1231 878 555
4i 4894 11 120
GlOE GlOR
6
10 8
429 577
27 16
5
427 340
;
8
255 _____
inumber of observations number of iterations :+95 percent confidence benzenepentacarboxylic
4
8
R CIC -!!-____.-
293
(M,)i. The (M,)i values derived from the quadratic fit yield a composite an value of 566, which is only about 9T; smaller than the corresponding experimental &?” of SRHS (614). (If the results of the linear fit are used in these calculations, a composite ti,, value of 754 is obtained, which is 38 percent larger than the corresponding experimental tin of SRHS. This comparison again indicates that the experimental data are more appropriately fit to a quadratic equation.) Colligative methods have been previously used to determine @” values for humic substances (DE BORGER and DE BACKER, 1968; HANSEN and SCHNITZER, 1969; WILFXIN and WEBER, 1977). A variety of procedures were used to try to correct the experimental data for acid dissociation. These procedures, which were often ambiguously described, are expressed in this paper in a form analogous to eqn (91, in order to facilitate direct comparisons. The re-calculated results are given in Table 4. The molecular weight calculations of DF, BURGER and DE BACKER (1968) are based on the equation: 0 = $
”
[W +- EW(H+)]
(ill
where EW is the equivalent weigh of their fulvic acid. This equation is roughly equivalent to the linear form of eqn (9), but the use of EW rather than M” IS clearly incorrect. The reported value of De Borger and De Backer of 923 + 22.5 is the average of the iL?,, values obtained by re-arranging eqn (11) and solving for &?, at each value of M! An iterative regression fit of their data to the quadratic form of eqn (9) yields an M, value of 929 k 218. Thus, despite the error in eqn
Fit
lb
n
lb
OF AQUAMOLECU-
Na
6
Cl‘ -_______
)
Sample __-._
6PCAd -___
R
Fit
of 878. The (a”), values and weight fractions of the molecular size fractions (see Table 1) can be combined to calculate the number-average (M,) molecular weight of the unfractionated parent material.
15
___..
Table 4. RECALCULATED (ii,) OF SOIL AND WATER
'3 experimental points, simulated zero point (0 = 0.0, W = 0.0, pH = 5.5) added for statistical evaluation of quadratic fit.
AVERAGE ACIDS.
Linear Ref.*
Sample
Na
lb
MOLFCULA*
Fir
--._. R_
Cl‘
1'
aa
I
S-FAe
12
5
II Ill III BPCAd
6
I
WEiGHTi
Quadratic
--~---.
II interval acid, f$, = 298
NUMBER FULVIC
Fl:
__.~_ q-,
LI ’
I.
1014 816 871 978
43
1:
929
218
970
112
14 18
15 13
938 -i72
5'; 44
262
3
9
,:,:
-'
13
*References: I - De Borger and De Backer Hansen and Schnitzer (1969); Ill - Wilson (1977). a, b, c, d - see footnotes to Table 2 ?soil fulvic acid 'water fulvic acid
(19661; II and Weber
110:! 1
Aquatic humus and its molecular size fractions (Ii), the results reported by DE BORGER and DE BACKER (1968) are essentially correct. The reason for this chance coincidence seems to stem from the fact that their fulvic acid is of such unusually low total acidity (3.0 m-equiv/g) that the correction term for acid dissociation becomes very small. The molecular weight calculations of HANSEN and SCHNITZER(1969), though somewhat cumbersome and difficult to follow, are ultimately based on the linear form of eqn (9) (I = & [W + _,(H’~)]. ”
(12)
The authors used a rearranged form of eqn (12) and solved for a,, at each value of M! The resulting concentration-dependent &?” values were plotted versus W and extrapolated to W = 0 to obtain the ‘correct’ .G” value of 951. An iterative regression fit of their data to the quadratic form of eqn (9) yields an @” value of 970 4 112. Not surprisingly, the results reported by HANSENand S~HNITZER (1969) are essentially correct. They also reported data for benzenepentacarboxylic acid (mol. wt = 298). The regression fit of these data to the quadratic form of eqn (9) yields an I@~ value of 301 $- 7. [A linear fit of the data of HANSENand SCHNITZER(1969) to eqn (9) yields an h7” value of 260. The error resulting from the linear fit is approximately equal to that obtained from our BPCA data.] More recently, WIEON and WEBER (1977) criticized the works of DE BORGER and DE BACKER (1968) and HANSEN and SCHNITZER (1969) for presumably using incorrect equations to describe the acid dissociation equilibria of humic substances, As we have shown, however, the iterative least squares method we have used to correct for dissociation (eqn 9) and the closely related methods of DE BORGERand DE BACKER (1968) and H,ANSENand SCHNITZER (1969) are completely independent of pK, values and the mathematical description of the acid dissociation process. Thus, the criticism raised by WILSON and WEBER(1977) is unjustified. WILSON and WEBER (1977) used the quadratic frrstpoint zero method of BONNARet ul. (1958), applying a dissociation correction procedure which explicitly incorporates pK, values into the calculation method. In essence, their method involves solving the electroneutrality equation for C, at each set of W and pH values. Since a calculated C, can be combined with W to calculate molecular weight (&, = 5+$/C’,)without introducing colligative (0) data at all, their overall correction procedure appears to be based on a circular argument. Furthermore, while the calculation of C, is feasible for a pure solute with known acid dissociation constants, the accurate calculation of C, for fulvic acid solutions from pH data is probably impossible, due to the inherent complexity of such systems (GAMBLE, 1970). Wilson and Weber were thus forced to grossly oversimplify the system, treating fulvic acid as a mix-
ture of two monoprotic acids whose rclutit~~ conccntrations and respective pk’, values were known. Nevertheless, they ‘corrected’ values for acid dissociation by:
If an equivalent correction factor (i4~W’ + &f,(H ’ )) is applied to eqn (9), it can be shown from the resulting equation that (0 - Or), is not a simple polynomial function of (W - WI). as was assumed by WILSON and WEBER (1977). The conceptual and mathenlatic~l errors introduced in this correction procedure ultimately led to incorrect results for their soil and water fulvic acids (644 and 626 g/mol, respectively). Iterative regression fits of their data to the quadratic form of eqn (9) yield M, values of 988 & 55 for soil fulvic acid and 872 & 44 for water fulvic acid. The .%?,,value:< of their fulvic acids are thus quite similar to those prcviously discussed (see Table 4). Since it is highly unlikely that standard soil extraction techniques yield dissolved humic substances which are representative of that fraction of soil humus which is mobilized by meteoric waters, direct cnmparisons of M, values (and other properties) of soil extracts and aquatic humus, should be made with caution. It has been documented that the relative abundance of the high molecular weight fraction of aquatic numus is quite variable (SHOLK~IVITZ. 1976: PERDUE,1979). Concomitant variations of G, of river water organic matter from different river sources are therefore expected. For example, the unusually low acidity (pH 2 4) and low ionic strength (log I = -3.3) of waters in the Satilla River basm (BECK et al., 1974) strongly favor the mobilization of the more water-soluble, low molecuiar weight components of soil humus. Accordingly, the ;M, value of SRHS (614) is significantly lower than other reported values for soil and water fulvic acids (see Table II.
SUMMARY Colligative data for complex polyelectrolytc mixtures can be corrected for acid dissociation using an iterative least squares method which does not requrrc knowledge of either the acid dissociation constants or the concentrations of the individual acid components of the system. This correction procedure allows the unambiguous determination of number average molecular weights of water soluble humic substances._I. Reevaluation of previously published data jiolds &f, values of 872 to 988 for soil- and water-derrved fulvic acids. Humic substances from the unusually acidic Satil’ta River system have an @” value of 614. iG” values of the molecular size fractions of this material range from 340 to 1231, with the largest single fraction (47”/,) having an I%,, value of 878.
J. H. REUTERand E. M. PERDUE
2022
Acknowledgement-We wish to thank S. J. MARTINfor his careful experimental work.
REFERENCES BECK K. C., REUTERJ. H. and PERDUEE. M. (1974) Organic and inorganic geochemistry of some coastal plain rivers of the southeastern United States. Geochim. Cosmochim. Acta 38, 341-364. DE BORGERR. and DE BACKERH. (1968) D&termination du poids moltculaire moyen des acides fulviques par cryoscopie en milieu aqueux. C.R. ,4cud. Sci. Ser. D 266, 2052-2055. FLAIGW., BEUTELSPACHER H. and RIETZ E. (1975) Chemical composition and physical properties of humic substances. In Soil Components, Vol. 1, Organ. Compounds (ed. J. Giesking), pp. l- 21 I. Springer. GLOVER C. A. (1975) Absolute colligative property methods. In Polymer Molecular Weights (ed. P. E. Slade). Part I, Chap. 4. Dekker. HANSENE. H. and SCHNI~ZERM. (1969) Molecular weight
measurements of polycarboxylic acids in water by vapor pressure osmometry. Anal. Chim. Acta 46, 247 254. PERDUEE. M. (1979) Solution thermochemistry of humic substances. Acid base equilibria of the river water humic substances. Chemical Modeling in Aqueous S~wems (ed. E. A. Jenne), pp. 99-114. Am. Chem. Sot. Symp. Ser. No. 93.
REUIXR J. H. (1977) Inferred configuration changes ,>E aquatic humic substances. Geol. Sot. Am. ,4nn. Meet Abstracts with Programs, Vol. 9, p. 1140. SCHNITZERM. and SKINNERS. I. M. (19681 Gelfiitratlon of fulvic acid, a soil humic compound. In I.\vto[~r.\ L& Radiation
in
Soil
Organic
Morfcr
Studies.
pp
41 55
IAEA. SHOLKOVITZ E. R. (1976) Flocculation of dissolved orgamc and inorganic matter during the mixing of river water and seawater. Geochim. Cost&him. Act; 40, 831-845. THENGB. K. G., WAKE J. R. H. and POSNERA. M. (1966) The infrared spectrum of humic acid. Soii Sci. 102, 70-72.
WILSONS. A. and WEBERJ. H. (1977) A comparatlvc stud) of number-average dlssoclatlon-corrected molecular weights of fulvic acids isolated from water and soil Chem. Geol. 19, 285-293.
of Geophysical
Sciences,
Georgia
Institute
of Technology,
Atlanta,
GA 30332. U.S.A
E. M. PERDUE Environmental
Science/Chemistry
Department,
Portland
State University,
Portland,
OR 97207. U.S.A.
(Received 2 September 1980; accepted in revised form 20 May 1981) Abstract-A rigorous mathematical expression for the dependence of colligative properties on acid dissociation of water soluble humic substances is presented. New data for number average molecular weights of a river derived humic material and its gel permeation chromatographic fractions are compared with an values obtained by a reevaluation of previously published experimental observations on so11 and water fulvic acids. The results reveal a remarkable similarity of fulvic acids from widely different sources with respect to number-average molecular weight.
INTRODUCTION IT HAS been generally recognized that humic substances in soils originate as heteropoly-condensates of such chemically diverse starting materials as phenols, amino acids, carbohydrates, even ammonia (see e.g. FLAIG et (II., 1975). The water-mobilizable fraction of soil humic substances contributes significantly to the chemistry of surface waters through interaction with metals, adsorption of hydrophobic substances, etc. and forms an important fraction of the riverine organic carbon flux to the oceans. One of the major analytical difficulties in the characterization of aqueous humic substances is the lack of any fractionation procedure which will yield pure components which can be subsequently characterized by standard techniques. Consequently, efforts have frequently been devoted to the determination of those bulk physical properties which can be unambiguously defined and determined on complex mixtures. One such parameter is the number-average molecular weight (a,,), which can be readily determined from colligative properties such as vapor pressure and freezing point depression. Recently, both vapor pressure osmometry (HANSEN and SCHNITZER, 1969) and cryoscopy (DE BORCERand DE BACKER, 1968) have been applied for the determination of I@~ values for acid soluble fractions of soil humic substances. In both cases, colligative properties were determined on aqueous solutions of fulvic acids, so that the experimental measurements required corrections for acid dissociation. Lacking a rigorous mathematical expression for the dependence of colligative properties on acid dissociation, different ‘correction’ procedures were proposed in the two studies. This has led to some confusion about the validity of the approaches chosen (see e.g. WILSON and WEBER, 1977).
In this paper, we wish to present new analytical data for an values of water-derived humic substances and their molecular size fractions obtained by gel permeation chromatography. We have developed a rigorous mathematical treatment of the dissociation correction applied to the determination of numberaverage molecular weights for weak polyelectrolytes. This method has been used to re-evaluate analytical data from the above mentioned references. We hope that our discussion will help to remove some misunderstandings and will provide encouragement to generate much needed data on number-average molecular weights of aquatic humic substances.
EXPERIMENTAL To obtain sufficient organic matter for this study, 200 I. of unfiltered water from a small tributary in the Satilla River flood plain (southeast Georgia) were collected in 20 I. polyethylene carboys and immediately transported to the laboratory. The sample was centrifuged at 10,000 rpm (Sorvall Centrifuge Type SS-3, flow-through mode) and concentrated approximately tenfold under reduced pressure (25 mmHg). The concentrate was freeze-dried, yielding a brown, fluffy powder which contains all but the volatile constituents (e.g. HCI) of the original water. This residue was redissolved in distilled water to a concentration of _ 20 g of organic matter per liter. An undissolved residue consisting largely of silica, hydrous oxides of Fe and Al and some high molecular weight organic matter (- 3”/;, of total) was removed from the solution. The solute was desalted by shaking with two batches of cation exchange resin (25 ml of BioRad AGXI, 50-100 mesh, Ht form, per gram of organic matter) and freeze-dried. The ash content was decreased from an initial 7.77” to a final 2.3”/;. Aliquots of the purified river water organic matter were fractionated progressively by exhaustive gel permeation chromatography (GPC) on columns of Sephadex G-50, G-25, G-15, and G-10 using distilled water as eluant. The goal of this fractionation was to obtain chromatographitally well defined excluded fractions. Experiments by REUTER (1977) have shown that the ratio of excluded to
2017
J. H. REUTERand E. M. PERDUE
2018
retarded fractions is to a high degree also determined by reversible conformational changes of the humic molecules. At low solute concentratjons (below 1050 mg/l) conformational changes from extended (or uncoiled) to contracted (or coiled) configurations are affected by the ionic strength and the pH of the solution. Thus, at SHRS concentrations of 100 mg/l, zero ionic strength and pH 7 all of the organic solute was found in the excluded fraction of Sephadex G50. With increasing solute (SRHS) concentrations, the ratio of excluded to retarded fractions decreased until at concentrations above 2ooOmg/l a constant ratio was observed. At and above this concentration the distribution between excluded and retarded fractions was found to be stable against changes of pH (& 1 pH unit) and ionic strength. Therefore, no strict control of either parameter was found necessary to obtain reproducible excluded fractions, as long as humic solute concentrations were held above 2000 mgjl. In order to minimize interactions between the gels and the organic matter, the acidic organic matter solutions were neutralized to pH 7 with NaOH before gel filtration (SCHNITZERand SKINNER,1968). The effluent from each column was separated into an excluded (E) and a retarded (R) fraction. The excluded fraction was rechromatographed on the same gel type to yield a final excluded fraction for further analyses. The retarded fractions from the first and the second run were combined to be chromatographed on the next lower Sephadex grade. Thus, four excluded fractions (G50E. G25E, GISE. GIOE) and one retarded fraction (GlOR) were produced. The final Sephadex fractions were desalted to remove added Na+ using the above named cation exchange resin. A Me~hrolab Model 3OlA vapor pressure osmometer was used to determine vapor pressures of aqueous solutions of SRHS. These data, together with precise pH measurements on the same solutions were used to calculate number average molecular weights as described in the following section of this paper. The accuracy of the method was tested by determining the M. of a known compound (~nzene~ntacarboxylic acid). Infrared spectra were recorded on a Beckman Model 12 Spectrophotometer using KBr pellets. Care was taken to eliminate water from the samples and the potassium bromide (THENGet al., 1966). MATHEMATICAL TREATMENT OF COLUGATIVE PROPERTIES OF WEAK POLYELE~TROLYTES
gative property methods (cryoscopy, ebulhometry, vapor pressure osmometry, etc.) for polymeric nonelectrolytes. The instrument response (e) is related to the total molality of dissolved solute species (m,) by the equation : 0 = Am, + Bm:
+
.
(3)
In the case of nonelectrolytes, mr and C, arc equal, so 0 can be directly related to the total weight concentration(W) of organic solutes by combining eqns (2) and (3).
All the methods described by CLOVER(19751 were based on eqn (4), which was truncated after either the linear or quadratic term. it was pointed out that the statistical significance of derived results is dependent on the order of the equation used to fit experimental data. The constant A, the apparatus constant, is obtained by instrument calibration using a solute of known molecular weight. The &i, value of an unknown sample is determined by a least-bquares method which yields (A/a”) as one of the regression coefficients. None of the equations or regression methods described by GLOVER(1975) are directly applicable to solutions which contain weak polyelectrolytes such as humic substances. Suppose the ith organic solute is a weak acid of the general formula AiH,i, which can dissociate in solution to produce a variety of anions AiH,i_j (j = 1 to ni). Despite the complexity of the multiple equilibria, the mass balance constraint requires that:
The concentration by:
of Ht derived from Ai H,i IS given
i6)
(H”)i = ~ j(/liH"i_i). j-0
The number-average molecular weight (z”) of a mixture of z organic solutes is defined as follows:
The total molality of ions and molecules (mi) arising from AiH,i is: m; = Ci + (H’)i
(7)
and in a mixture of z organic acids, i-l
where ci is the molal concentration of the ith organic solute, whose molecular weight is Ml. The weight concentration of the ith component is ci Mi, so the sum of ail ciMi values equals the total weight concentration ( W) of the mixture of organic solutes. The total molal concentration (C,) of organic solutes equals the sum of all ci values. Thus.
mT=
i mi=C, i:1
+(H*).
IX)
Combining eqns (2), (3) and (8). 0 = ;
[W -I-
n
il;i(H+)]
+
&IW +ii;i,(Hirj2
+
(9,
”
GLOVER (1975) has reviewed the mathematical
of molecular
weight determination
details by absolute colli-
Equation (9) is the fundamentaf equation which must be used to obtain @,, for weak ~olyelectro~ytes. This equation,
which stems sokly
from the constraints
of
2019
Aquatic humus and its molecular size fractions Table 1. CHEMICAL PARAMETERS OF AQUATIC HUMUS FROM THE SATILLA RIVER (SRHS) ANO ITS MOLECULAR SIZE FRACTIONS.
oa
SamDie SRHS G50E G25E G15E GlOE GlOR
1.000 0.036 0.470 0.143 0.145 0.206
C
H N 0 Wt.:; (ash-free)
52.1 54.3 51.4 50.3 50.4 51.8
3.6 4.7 3.6 3.7 3.7 4.2
0.8 1.4 0.7 0.8 1.1 0.8
Ash wt.:
Meq/g
2.3 10.8 0.9 0.9 1.1 0.8
10.4 7.3 10.6 10.1 12.0 9.9
43.5 39.6 44.3 45.2 44.8 43.2
TAb
aweigkt fraction of molecular size fraction btotal acidity--barium hydroxide method
mass and charge balance, can be solved for &in, and does not require information regarding pK, values, regardless of the complexity of the system. There are rigorous linear and non-linear regression methods which can be used to determine %?” from the linear and quadratic forms of eqn (9), respectively. However, it is conceptually more straightforward to use an iterative process to determine @” from eqn (9). Initially, the M, term in parentheses is set equal to zero (analogous to treating the solute as a nonelectrolyte mixture). Least squares analysis yields an ii?,, value from the first order regression coefficient which is subsequently used in the parenthetical term to generate a refined estimate of H”. The process can be continued until successive M,, values agree to the desired extent.
RESULTS AND DISCUSSION
weight fraction (c() of each molecular size fraction is given in Table 1. While recovery of the sodium salts was quantitative (lOOS”~), approximately 187; of the solute was lost during the final desalting step, making it impossible to directly determine the weight fractions of the desalted molecular size fractions. Since total acidity of the molecular size fractions averages 10.0 + 1.7m-equivlg (see Table l), a maximum of 179< variability in Na+ content is expected. Assuming an even distribution of Na+ in the molecular size fractions, the values in Table 1 can be used to represent the weight fraction (z) of each desalted molecular size fraction. The rather broad character of the absorption bands in the infrared spectra of humic substances are generally seen as an indication of a high degree of complexity. It was hoped that the exhaustive gel permeation fractionation to which the aquatic humus was subjected, would reduce the complexity of the mixture and lead to infrared spectra with more distinct features. However, judging from the infrared spectra of SRHS and its molecular size fractions (Fig. 1) very little change occurred. The complex ‘humic’ character of the infrared spectra is maintained down to the lowest molecular weight fraction. This situation is also reflected in the small changes in total acidity and elemental composition among the molecular size fractions (Table 1). Both the linear and quadratic forms of eqn (9) have been used to calculate &?” values for benzenepentacarboxylic acid (ii?” = 298 gimol), SRHS, and the molecular size fractions derived from SRHS by exhaustive
The molecular size fractions obtained by GPC were freeze-dried and weighed as their sodium salts. The
MrcRoNs 3.0 I
3.5 I
11.0 I
6.0 I
5.0
7.0 I
8.0 I
10 I
12 I
GlOR
3500
3000
2500
2000 FREQUENCY
big.
1. Infrared spectra of aquatic humus from the (for explanation
1800
1600
I
I
1
I
1400
1200
1000
800
cram1
Satilla
of fraction
River (SRHS) and its molecular sire fractions
notations
see text).
2020
J. H. REUTERand E. M. PERDUE
Table 2. EXPERIMENTAL BEN~ENPENTACARBOXYL~C FROM THE SATILLA RIVER
SET OF W, pH ANO e VALUES FOR AND AQuATIc HUMUS (SRHS).
ACID(BPCA)
BPCA kd
SRHS ob
PH
2.706 3.331 3.956 4.893 5.518 6.455
1.766
8.0 10.0
1.699
12.0 15.0 17.13 20.0
1.643 1.577 1.54i 1.491
concentration instrument response
Wd
PH
8.0 10.0 12.0 15.0 20.0
2.104 2.030 1.967 1.894 1.796
eb 0.914 1.213 1.511 1.959 2.705
where N is the number of molecular size fractions and xi is the weight fraction of the ith molecular size fraction, whose number-average molecular weight is
1" g/kg in ohm
$,9ht
GPC on Sephadex gels. A sample set of experimental data for benzenepentacarboxylic acid and SRHS is given in Table 2. Weight concentrations (W) of humic substances were not corrected for ash content, introducing a corresponding uncertainty in calculated a” values. The results are summarized in Table 3, which includes the number of observations in a data set, the number of iterations required for convergence (0.015,, variation in a,, for successive iterations), the calculated H” and its 95% confidence interval. Because the 9Soi, confidence interval is dependent on the number of observations and the order of fit (linear or quadratic), those data sets containing only four observations do not yield statistically meaningful a” values, particularly in the quadratic fits. The quadratic fit yields obviously better results for benzenepentacarboxylic acid and is probably the more appropriate form of eqn (9) for analysis of the SRHS data. Therefore, only results calculated from quadratic fits of experimental data will be used in the subsequent discussion. The molecular size fractions yield an values which are much lower than the molecular weight exclusion limits of the corresponding Sephadex gels (e.g. G-50: exclusion limit = 30,000 for globular proteins, $i” = 1231). The measured values do, however, decrease in the expected qualitative manner. The largest molecular size fraction (G-25E, 47%) has an I@” value Table 3. NUMBER AVERAGE MOLECULAR WEIGHTS (l? TIC HUMUS FROM THE SATILLA RIVER (SRHS) AND 1% LAR SIZE FRACTIONS. Linear
_-
Quadratic
SRHS G50E G25E G15E
5 4* 6 4
8 14 11 9
556 1952 1306 725
8 746 75 46
8 12 6 5
614 1231 878 555
4i 4894 11 120
GlOE GlOR
6
10 8
429 577
27 16
5
427 340
;
8
255 _____
inumber of observations number of iterations :+95 percent confidence benzenepentacarboxylic
4
8
R CIC -!!-____.-
293
(M,)i. The (M,)i values derived from the quadratic fit yield a composite an value of 566, which is only about 9T; smaller than the corresponding experimental &?” of SRHS (614). (If the results of the linear fit are used in these calculations, a composite ti,, value of 754 is obtained, which is 38 percent larger than the corresponding experimental tin of SRHS. This comparison again indicates that the experimental data are more appropriately fit to a quadratic equation.) Colligative methods have been previously used to determine @” values for humic substances (DE BORGER and DE BACKER, 1968; HANSEN and SCHNITZER, 1969; WILFXIN and WEBER, 1977). A variety of procedures were used to try to correct the experimental data for acid dissociation. These procedures, which were often ambiguously described, are expressed in this paper in a form analogous to eqn (91, in order to facilitate direct comparisons. The re-calculated results are given in Table 4. The molecular weight calculations of DF, BURGER and DE BACKER (1968) are based on the equation: 0 = $
”
[W +- EW(H+)]
(ill
where EW is the equivalent weigh of their fulvic acid. This equation is roughly equivalent to the linear form of eqn (9), but the use of EW rather than M” IS clearly incorrect. The reported value of De Borger and De Backer of 923 + 22.5 is the average of the iL?,, values obtained by re-arranging eqn (11) and solving for &?, at each value of M! An iterative regression fit of their data to the quadratic form of eqn (9) yields an M, value of 929 k 218. Thus, despite the error in eqn
Fit
lb
n
lb
OF AQUAMOLECU-
Na
6
Cl‘ -_______
)
Sample __-._
6PCAd -___
R
Fit
of 878. The (a”), values and weight fractions of the molecular size fractions (see Table 1) can be combined to calculate the number-average (M,) molecular weight of the unfractionated parent material.
15
___..
Table 4. RECALCULATED (ii,) OF SOIL AND WATER
'3 experimental points, simulated zero point (0 = 0.0, W = 0.0, pH = 5.5) added for statistical evaluation of quadratic fit.
AVERAGE ACIDS.
Linear Ref.*
Sample
Na
lb
MOLFCULA*
Fir
--._. R_
Cl‘
1'
aa
I
S-FAe
12
5
II Ill III BPCAd
6
I
WEiGHTi
Quadratic
--~---.
II interval acid, f$, = 298
NUMBER FULVIC
Fl:
__.~_ q-,
LI ’
I.
1014 816 871 978
43
1:
929
218
970
112
14 18
15 13
938 -i72
5'; 44
262
3
9
,:,:
-'
13
*References: I - De Borger and De Backer Hansen and Schnitzer (1969); Ill - Wilson (1977). a, b, c, d - see footnotes to Table 2 ?soil fulvic acid 'water fulvic acid
(19661; II and Weber
110:! 1
Aquatic humus and its molecular size fractions (Ii), the results reported by DE BORGER and DE BACKER (1968) are essentially correct. The reason for this chance coincidence seems to stem from the fact that their fulvic acid is of such unusually low total acidity (3.0 m-equiv/g) that the correction term for acid dissociation becomes very small. The molecular weight calculations of HANSEN and SCHNITZER(1969), though somewhat cumbersome and difficult to follow, are ultimately based on the linear form of eqn (9) (I = & [W + _,(H’~)]. ”
(12)
The authors used a rearranged form of eqn (12) and solved for a,, at each value of M! The resulting concentration-dependent &?” values were plotted versus W and extrapolated to W = 0 to obtain the ‘correct’ .G” value of 951. An iterative regression fit of their data to the quadratic form of eqn (9) yields an @” value of 970 4 112. Not surprisingly, the results reported by HANSENand S~HNITZER (1969) are essentially correct. They also reported data for benzenepentacarboxylic acid (mol. wt = 298). The regression fit of these data to the quadratic form of eqn (9) yields an I@~ value of 301 $- 7. [A linear fit of the data of HANSENand SCHNITZER(1969) to eqn (9) yields an h7” value of 260. The error resulting from the linear fit is approximately equal to that obtained from our BPCA data.] More recently, WIEON and WEBER (1977) criticized the works of DE BORGER and DE BACKER (1968) and HANSEN and SCHNITZER (1969) for presumably using incorrect equations to describe the acid dissociation equilibria of humic substances, As we have shown, however, the iterative least squares method we have used to correct for dissociation (eqn 9) and the closely related methods of DE BORGERand DE BACKER (1968) and H,ANSENand SCHNITZER (1969) are completely independent of pK, values and the mathematical description of the acid dissociation process. Thus, the criticism raised by WILSON and WEBER(1977) is unjustified. WILSON and WEBER (1977) used the quadratic frrstpoint zero method of BONNARet ul. (1958), applying a dissociation correction procedure which explicitly incorporates pK, values into the calculation method. In essence, their method involves solving the electroneutrality equation for C, at each set of W and pH values. Since a calculated C, can be combined with W to calculate molecular weight (&, = 5+$/C’,)without introducing colligative (0) data at all, their overall correction procedure appears to be based on a circular argument. Furthermore, while the calculation of C, is feasible for a pure solute with known acid dissociation constants, the accurate calculation of C, for fulvic acid solutions from pH data is probably impossible, due to the inherent complexity of such systems (GAMBLE, 1970). Wilson and Weber were thus forced to grossly oversimplify the system, treating fulvic acid as a mix-
ture of two monoprotic acids whose rclutit~~ conccntrations and respective pk’, values were known. Nevertheless, they ‘corrected’ values for acid dissociation by:
If an equivalent correction factor (i4~W’ + &f,(H ’ )) is applied to eqn (9), it can be shown from the resulting equation that (0 - Or), is not a simple polynomial function of (W - WI). as was assumed by WILSON and WEBER (1977). The conceptual and mathenlatic~l errors introduced in this correction procedure ultimately led to incorrect results for their soil and water fulvic acids (644 and 626 g/mol, respectively). Iterative regression fits of their data to the quadratic form of eqn (9) yield M, values of 988 & 55 for soil fulvic acid and 872 & 44 for water fulvic acid. The .%?,,value:< of their fulvic acids are thus quite similar to those prcviously discussed (see Table 4). Since it is highly unlikely that standard soil extraction techniques yield dissolved humic substances which are representative of that fraction of soil humus which is mobilized by meteoric waters, direct cnmparisons of M, values (and other properties) of soil extracts and aquatic humus, should be made with caution. It has been documented that the relative abundance of the high molecular weight fraction of aquatic numus is quite variable (SHOLK~IVITZ. 1976: PERDUE,1979). Concomitant variations of G, of river water organic matter from different river sources are therefore expected. For example, the unusually low acidity (pH 2 4) and low ionic strength (log I = -3.3) of waters in the Satilla River basm (BECK et al., 1974) strongly favor the mobilization of the more water-soluble, low molecuiar weight components of soil humus. Accordingly, the ;M, value of SRHS (614) is significantly lower than other reported values for soil and water fulvic acids (see Table II.
SUMMARY Colligative data for complex polyelectrolytc mixtures can be corrected for acid dissociation using an iterative least squares method which does not requrrc knowledge of either the acid dissociation constants or the concentrations of the individual acid components of the system. This correction procedure allows the unambiguous determination of number average molecular weights of water soluble humic substances._I. Reevaluation of previously published data jiolds &f, values of 872 to 988 for soil- and water-derrved fulvic acids. Humic substances from the unusually acidic Satil’ta River system have an @” value of 614. iG” values of the molecular size fractions of this material range from 340 to 1231, with the largest single fraction (47”/,) having an I%,, value of 878.
J. H. REUTERand E. M. PERDUE
2022
Acknowledgement-We wish to thank S. J. MARTINfor his careful experimental work.
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measurements of polycarboxylic acids in water by vapor pressure osmometry. Anal. Chim. Acta 46, 247 254. PERDUEE. M. (1979) Solution thermochemistry of humic substances. Acid base equilibria of the river water humic substances. Chemical Modeling in Aqueous S~wems (ed. E. A. Jenne), pp. 99-114. Am. Chem. Sot. Symp. Ser. No. 93.
REUIXR J. H. (1977) Inferred configuration changes ,>E aquatic humic substances. Geol. Sot. Am. ,4nn. Meet Abstracts with Programs, Vol. 9, p. 1140. SCHNITZERM. and SKINNERS. I. M. (19681 Gelfiitratlon of fulvic acid, a soil humic compound. In I.\vto[~r.\ L& Radiation
in
Soil
Organic
Morfcr
Studies.
pp
41 55
IAEA. SHOLKOVITZ E. R. (1976) Flocculation of dissolved orgamc and inorganic matter during the mixing of river water and seawater. Geochim. Cost&him. Act; 40, 831-845. THENGB. K. G., WAKE J. R. H. and POSNERA. M. (1966) The infrared spectrum of humic acid. Soii Sci. 102, 70-72.
WILSONS. A. and WEBERJ. H. (1977) A comparatlvc stud) of number-average dlssoclatlon-corrected molecular weights of fulvic acids isolated from water and soil Chem. Geol. 19, 285-293.