Kinetics of FeS precipitation: Part 1. Competing reaction mechanisms

Geochimica et Cosmochimica Acta, Vol. 59, No. 21. pp. 4367-4379, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 00 16.7037/95 $9..50 + 00

Pergamon

0016-7037(95)00251-O

Kinetics of FeS precipitation:

Part 1. Competing reaction mechanisms DAVID

Department

of Earth Sciences,

RICKARD

University

of Wales, Cardiff CFl 3YE, Wales

(Received December 22, 1994; accepted in revised form July 10, 1995 ) Abstract-The kinetics of the fast precipitation reaction between aqueous iron( II) and dissolved at 25°C can be interpreted in terms of two competing reactions. The first may be represented by Fe’+ + H,S + FeS(s) This can be described

by an observed

sulfide

+ 2H’.

rate law -d[aH,S]!dt

= k;[aH,S],

where k I is the observed first order rate constant with a value of 90 % 10 s ~’, [ cH$] is the concentration of dissolved H$ in moles per liter, and t is time in seconds. The rate law is consistent with an EigenWilkins model of the process in which the rate is described by d[FeS]ldt

= -d[aH,S]ldt

= k,[aFe’+][aH,S],

where aH$ and aFe*+ are the formally dimensionless hydrogen sulfide and Fe( II) activities which are represented on a moles. liter-’ scale for experimental and practical convenience. The logarithm of k, , the theoretical Eigen-Wilkins reaction rate constant, has a value of 7 + 1 liters.mole-’ . s-’ . The second reaction may be represented by Fe*+ + 2HSThe rate of this reaction may be described

-Fe(HS),(s).

by an observed

-d[uHS-]ldt

rate law of the form

= k;[uHS-I’,

where [uHS- ] is the formally dimensionless bisulfide activity which is represented on a moles ‘liter-’ scale for experimental convenience. The observed second order rate constant, k;, has a value of 1.3 x 1O7 liters.mole~‘.s~’ at 25°C. The result is consistent with an Eigen-Wilkins model of the process in which

2,

k; = k,[uFe2’][uHS-]

where aFez’ is the dissolved Fe( II) activity and the logarithm of k2, the Eigen-Wilkins reaction rate constant, has a value of 12.5 ? 1 liters2.mo1e~2.s~‘. The theoretical interpretation of both reactions suggests that the rates are direct functions of the ion activity products of the iron sulfide precipitates. The second stage of the reaction involves the condensation of Fe( SH)* to FeS with the release of dissolved sulfide back to solution: Fe(SH)*(s)

-+ FeS(s)

+ H2S.

This reaction is relatively slow and results in a sinusoidal form superimposed on the Stage 1 concentrationtime curve. Overall, the rate of removal of total dissolved sulfide from solution by these processes can be empirically modeled by -d[CS]ldt

= ko[B]

and [XS] - [ES],

= e-‘“‘,

where [ ZS] is the concentration of total dissolved sulfide at any time, [ XS]” is the concentration of total dissolved sulfide at t = 0, and k. is a pseudo first order rate constant of 15 s-’ where [ZFe*‘] , the total dissolved iron( II) concentration, is between lo-’ and 10m4 M. Theoretically, the rates of both reactions are directly proportional to [aFez’]. A good approximation for the rate of removal of total dissolved sulfide by the iron(I1) (bi) sulfide precipitation processes in most environments can, therefore, be obtained by using a value for k, of 15 X 10m4/[CFe2+]. Application of the rate laws to natural systems suggests that the relative dominance of the two competing pathways is pH and ZS dependent and independent of CFe*‘. In environments with ppm or greater CS concentrations ( 2 lo-’ M), the rate of sulfide removal is two magnitudes greater in neutral to alkaline systems than in systems with pH < 7. The bisulfide pathway resulting in the formation of Fe( SH)* dominates and the H2S pathway only dominates in acidic environments. The results suggest that, in these 4367

D. Rickard

4368

relatively sulfide-rich environments, a standing concentration of Fe( SH), will he present and may constitute an important component in further reactions, such as pyrite formation. In contrast, in sulfide-poor systems with ZS concentrations at the sub-ppm (
of a black precipitate when sulfide is added to an aqueous iron salt is familiar to all geochemists. It is a most important reaction in natural systems, especially in sedimentary environments, and an acid volatile iron sulfide phase is a familiar constituent of many sediments. Berner (1970) and Rickard ( 1969) originally brought the process into the forefront of the geochemical literature with experimental data suggesting that iron (II) monosulfide was a precursor to pyrite. Berner ( 1967) recognized that the precipitated iron( II) monosulfide had different properties to mackinawite (tetragonal Fe (, +.i ,S), and measured a different solubility product. Rickard ( 1969) and Sweeney and Kaplan ( 1973) extended Bemer’s work and showed that the initial product had an excess of sulfide in the formula that could not be accounted for by simple nonstoichiometry. The initial precipitate was amorphous and developed long-range ordering after around two days at 25°C with the development of a broad ca 5 A peak equivalent to the strong basal reflection of mackinawite. Well crystalline mackinawite, that is with most X-ray peaks well developed, may take up to two years to develop in aqueous solution at 25°C. Baas Becking and Moore ( 1961) originally implicated Fe( SH)2 as a component of this initial precipitate. Voltammetric studies of the aqueous iron( II) sulfide system have led to a variety of proposed complexes. Luther and Ferdelman ( 1993) found evidence for both Fe( SH) + and Fe*SH’+ and Luther ( 1991) noted complexes of the type Fe( SH)S; . Davison et al. ( 1988) interpreted the voltagrams in terms of Fe& complexes. Although all or any of these complexes may exist, the only method to test the nature of their involvement in iron (II) sulfide formation is by kinetic studies. Any or all suggested stoichiometrically and electronically balanced reactions may occur in these systems; however, the actual pathways taken can only be determined kinetically. Rickard ( 1989a) devised a system for the study of the fast precipitation reaction between aqueous iron (II) and sulfide based on a flow through, T-tube system. He showed that this system could give reproducible results down to 100 ms. The initial results of this study (Rickard, 1989b) suggested a twostage reaction. Concentration-time curves indicated that the second stage, which occurred after ca. 400 ms., appeared to reflect a condensation reaction with the release of S (II) species into solution, e.g., Fe(SH)2 + FeS + H$.

well as their theoretical action mechanisms.

implications

for fast precipitation

re-

2. METHODS 2.1. Experimental

Design

All reagents were made up in deionized distilled water (ca 18 Mohm) and deoxygenated by bubbling with oxygen-free nitrogen. Sulfide solutions were prepared from a stock solutions of 0.1 M NaZS made up from reagent-grade Na,S 9H20 and stored for up to 24 hrs in a glove box also filled with oxygen-free nitrogen. Iron solutions were prepared from 0.1 M stock solutions made up from analytical grade FeS04.(NH,),S0,‘6H,0 (Mohr’s salt). Mohr’s salt is the preferred reagent of experimentalists with aqueous iron(I1) since it is relatively resistant to oxidation. The experimental flow-through cell (T-Tube) is illustrated in Fig. 1. It is manufactured in glass and capillary inputs and outflows were used in order to reduce the amount of reactant solutions used and to promote laminar flow in the outlet in order to reduce the effects of turbulence on the electrodes. Sulfide and iron(H) solutions were pumped through the opposite arms of the cell with a Verder V.150.12/2032 magnetic drive gear pump for measurements of < 130 ms and with two Watson Marlow 502s standard variable speed peristaltic pumps for measurements > 130 ms. The flow rates were standardized by measuring the volumes flowing through the system at different pumping speeds. The solutions were mixed into a microsecond mix, a chamber which is carefully designed with tangential capillary inflows into a spherical mixing area. Calculations based on flow rate and the known volume of the mix demonstrates calculated residence times of less than 3 ms. Measurements were made with AgAg$, pH, and calomel reference electrodes.

iron

As-42s electrode

Agar-KCI bridge to reference

(1)

This suggested that an iron bisulfide phase was involved in the Stage 1 (i.e., <400 ms) precipitation process. The present paper reports the results of a study using a development of the original T-tube system in which pH is measured independently of dissolved sulfide concentration and the reaction is accessed down to less than 30 ms of reaction time. The results are discussed in terms of their implications for iron( II) sulfide formation in natural systems as

ifiput

FIG. 1. Experimental flow-through cell (T-tube). Sulfide and iron solutions are pumped through the arms of the T, mixed and ejected through the stem capillary of the T. S(I1) activity and pH are measured with Ag-Ag,S and micropH electrodes connected to a calomel reference electrode through and Agar-KC1 bridge. The reaction time is varied by varying the pumping speed of input fluids.

Kinetics

4369

of Fe sulfide precipitation

equivalent to the molar concentrations. The individual ion activity coefficients for HS - are listed in Table 1. The ionic strength of the initial Na2S and FeSO.,. ( N&),S04 solutions is determined by

TABLE 1. Calculated individual ion activity coefficients for HS- in standard solutions at 25°C in aqueous solution according to the Davies approximation to the extended DebyeHuckel equation.

Z = 0.5Z,c,zf

= 0.5( [cNa+]

+ [cHS-]

+ 4[cFe2+]

+ 8[cSO:-1.

+ 2[cNH:]],

(4)

where c is the molarity. However, if iron- and sulfide-bearing ions are removed from solution, which is the situation approached in the experimental runs, the ionic strength becomes Z = 0.5( [cNa+]

+ S[cSO:-]

+ 2[cNH;]].

(5)

The individual activity coefficient at 25°C for HS - is listed in Table 2 for the ionic strengths of the experimental runs.

The Ag-Ag,S electrode was made by soldering silver wire to a copper wire attached to a coaxial cable. It was standardized by passing standard solutions with known iodiometrically standardized, sulfide concentrations down the tube. The results of the Ag-Ag$ electrode standardization are presented below. pH was measured with an MI-405 pH microelectrode (Microelectrodes Inc ) and was standardized by passing standard buffer solutions down the tube. The reference electrode was an Orion Research Model 90-01 single junction reference electrode attached to the T-tube via an agar-KC1 bridge. The flow-through system allows the electrode measurement at any time to be measured over a long interval until stability is achieved. That is, the measurement is independent of the response time of the electrode. Rickard ( 1989a) discussed various sources of error in the original T-tube design. The experimental design itself resolves most of these problems, including spurious junction potentials, since the behavior of the system with known solutions can be continuously monitored. The major problem concerns the effect of turbulent flow on the electrode potentials. The T-tube design involves a capillary exit tube (4 = 1.2 mm) after the mix which promotes laminar flow in the tube. The effect of flow rate is examined by increasing pumping rates until the electrode response becomes erratic. This effect begins to occur in this experimental design at less than 10 ms reaction time, where electrode response is similar to that in the mix itself (<3 ms reaction time) and is thought to be due to turbulence. pH and mV measurements were made with an Orion 902 pH/ millivoltmeter. Temperature control of the system was achieved through burying the cell in a sandbath and is within ?O.l”C. The experiments reported in this paper were all run at 25°C. 2.2. Sulfide Measurement The results of electrode standardization runs, discussed in Appendix 1, give an equation for the silver-silver sulfide electrodes used in this experimentation: mV = -28.4

(pH + log[aHS-])

- 445.

(2)

2.3. Activity Coefficient The activity coefficient was calculated according modification of the Debye-Htickel equation log y = A&\/I/(

1 + dZ) - 0.21),

to the Davies

(3)

where A = e = T= Z=

1.82 x 10”(~T)~“*, dielectric constant, temperature, ionic strength = 0.5C,

3. RESULTS The results are listed in Table 3 and displayed in Figs. 27. A feature of the experimental design is that electrode measurements provide extremely large dynamic ranges. For this reason most plots are log-log and their regression lines are power relationships. Certain linear axes plots are displayed (Figs. 3 and 5); however, these are less satisfactory since many of the observed values cluster around the origin.

3.1. Rate Calculation The measurements, including pH and aHS -, were calculated according to Eqn. 2, for various reaction times. The data were listed and calculated in EXCEL@ and converted to LOTUS@@spreadsheets before being transferred to GRAPHER@@ for plotting and computation of correlation statistics. Curvefitting was carried out with TURBOCURVE@@. Throughout this work it is assumed that the reaction H,Sc*HS-

+ H+

(6)

TABLE 2. Individual activity coefficients for HS for the range of ionic strengths of experimental runs and standardisation experiments.

Ionic Strength

Davies approx

lw 0.000 10 0.00055 0.00090 0.00100 0.00100 0.00180 0.00500 0.00505

-0.00503 -0.01161 -0.01473 -0.0155c -0.0155c -0.02053 -0.033 11 -0.03326

0.01000 0.05000 0.10000

-0.04525 -0.08793 -0.11211

c,zf. I

The Davies equation was used since it is useful for mixtures of electrolytes with ionic strengths up to 0.2 M. Standard solutions were made up at lo-‘, lo-‘, lo-‘, and 10e4 M with NazS. 9HZ0. In the pH range of interest, the dissolved species include Na+, HS -, and H,S. The ionic strength of the solutions are

0.90 104 0.8 1672 0.77249

3410

I

diverges

0.080

9.91

I

-550 I

I

at extreme pH values.

I23E-IO

I 6.188.07

I 9 26E-01

Likewise

between

I 6.678-07

comparison

The comparison

closely the rate model satisfies the observations.

model rates is 90[H2S] + 1.3 x 107[aHS]*.

I 6.68E-07

between

7 60E-10

I

The run

-duH,S/dt

and the sum of the

8.43E-09

I 6.35E-06

6 78E-06

rates and -dZS/dt

6 35E-06

/

log

5 14E-06

shows how the rate

rates and the sum of the model rate shows how

rates -duHS-ldt

the sum of the observed

the sum of the observed

initial pH. rl + r, is the sum of the observed

1 x lo-“.

the second to the negative

where lE-10 is equivalent

log of the initial ZS content,

Results are listed in computer-speak

the first figure refers to the negative

results for Stage 1 of the reaction.

gives the initial solution compositions:

of the initial XFe and the third to the approximate

numbering

Table 3. Experimental

Kinetics of Fe sulfide precipitation

4371

lE-4 11’

1

?j IE-7 cn $ lE-8 F ,;

IE-9

d E IE-10

1E-7

_

I.-/ lE-7

lE-6

IE-11 lE-5

IE-12

I

11111ll

I

l//111

I lllllli

IE-13 IE-12 IE-11 IE-10 IE-9

aHS

r

I

lE-9

_, lE-7

lE-6

a H2S FIG. 2. Log-log plot of rate (-d[nHS-I/&) vs. [aHS] for experiments where pH > 8 and aHS > H,S. The regression line shows a slope of 2.32 (? = 0.96) and the model slope of 2.0 is shown with the dotted line. The deviation of the observed dependence from two results form the complex nature of the observed rate constant at these pH values (see text).

is fast, equilibria are set up instantaneously between protonated S(B) species and protons, and S2- is insignificant (Schoonen and Barnes, 1988). Activity-time plots for each run condition were inspected to determine the onset of reaction stage 2, where the HSincreased. It had previously been shown (Rickard, 1989b) that this increase was reproducible and not artifactual. Originally the increase was thought to be through some quirk of the experimental design. However, repeated runs under varying conditions of flow rate, reagent concentrations, electrode design modifications, and change in electrode location in the outflow tube, demonstrated that the increase was not only real but quite reproducible. The loglog plots of aHS _ vs. time for reaction stage 1 closely approximate a straight line suggesting that the decrease in

FIG. 4. Log-log plot of rate (-d[aH,S]/dr) vs. [nH2S] for runs where aH,S > aHS_. Experimentally, aH$ is indistiguishable from cH2S and the experimental rate is in units of in units of moles.liter. moles.liter-’ . s-’ and the concentration The regression line shows a slope of 1.26 (? = 0.99) and the deviation from unity is caused by the involvement of substantial quantities of HS- in the system at pH > 6. The theoretical line with a slope of 1.0 is dotted. The result suggests a first order dependence of the rate on cH2S.

HS - could be described by a power relationship. The best fit regression line for this was obtained through GRAPHER@ and the coefficient of regression, r2, listed in each case as an indication of the uncertainty. The regression line formula is of the form y=u.x”,

cm0

a30

lE-12

J

2E-12

(aHS-)* FIG. 3. Linear plot of rate (-d[uHS]/dr) vs. [aHS]* for Stage 1 of the reaction where aHS- > aHZS. The coefficient of regression is 0.99 for this plot which suggests a second order dependence of the rate on aHS_. If the experimental units arc moles. liter-’ . sm ’for the rate and moles. liter for aHS_, the second order rate constant of 1.3 X 10’ 1iters’molesC .s-‘.

1E-7

2E-7

3E-7

a H2S FIG. 5. Linear plot of rate (-d[aH,S]/dt) vs. [aH,S] for reaction Stage 1 where aHZS > aHS. Experimentally no distinction can be made between aH2S and cHZS and the units of rate are moles. liter-’ f se’and the units of concentration are moles.literr’. Although the linear plot appears to distort the dependence of the regression line on points with high rates, the computer program takes account of this. The slope is very robust and the removal of high value points makes no significant change to the slope. The regression coefficient for the line is 0.99 and the slope is the observed first order rate constant of 90 SC’.

4372

D. Rickard

since S ‘- is negligible in solution under the conditions experimentation (Schoonen and Barnes 1988). The electrode measures aHS _, where uHS and y is the individual water. Then

of this

= y[cHS] ion activity

cHS

coefficient

for HS

in

= [aHS]ly

and zE z

CS = [uHS--]ly

rrm('I T I- l-rrrml IE-10 Ii-9 lE% IE-7 Ii% Ii-5

lE-12 I’ IE-13lE-IZIE-11

+ cH$.

At these concentrations with ionic strength, ( H2S ) is close to unity, and

ZS =a H2.S + a HS FIG. 6. Plot of log model rate vs. log ZS for all Stage 1 data points. The model rate is -d[H,S]/dr - d[uHS-]/dt = 90[H,S] + 1.3 X lO’[aHS-]* and displays a first order dependence on X.8 with a

(8) I < 0.1 M, y

= uHZS.

cH$ Then

pseudo first order rate constant of 15 s-‘. The coefficient of regression for this line is 0.98.

ZS = [uHS-l/y

+ cHZS.

(9)

For the reaction where y is the aHS, is the slope. Then

x is the time, a is the intercept,

-dyldx

and m

H,S(aq)

= abt”~‘.

[aH,S]

= [aHS]

uHS

lE%

lE% 1E-9

0.00

(11)

+ [aHS][uH+]/lO~’

(lo-’

+ y[aH’]

)lylO-’

(12)

= ZSylO-‘/(

10m7 + y[uH+]}.

(13)

sulfide concentration,

CS, can then be cal-

(w

(a) 0337 0437

(10)

and

lE-5 IE-7 ~_

= [aHS][uH+]/10m7.

ZS = [uHS]ly

The total dissolved

_

= [uHS-][uH+]/[uHZS]

Then

+ cH,S,

lE%

10-7

and

(71

The concentration of HS is in moles per liter and thus the formally dimensionless aHS can be represented on a moles per liter scale for experimental convenience. Time, t, is in seconds and the unit of rate is moles. liter -’ . s _ ’. aHS is calculated from Eqn. 2. Since y (HS -) is known, cHS can be calculated. If XS is sum of the molarities of the dissolved sulfide species ZS = cHS

zz

( Murray and Cubicciotti, K, = lo-’

-d[aHS-]/dt

+ Hf.

constant at 25°C and 1 atm., K, 1983 )

The equilibrium

= amY_

= HS

--v

1

1.00

nme ~e~orid.3 FIG. 7. Plots of log [nH2S] vs. time for runs with excess Fe(R) (a) and limited Fe(H) (b). The shaded areas are the excursions in dissolved S(H) concentrations which mark the onset of reaction Stage 2 and the condensation of Fe(SH)2 to FeS. Note that the excursions are more marked in (a) than (b) and that there appears to be a consistency in the cH,S value for the onset of the excursion (arrowed) for each series of between IO-” and lo-l4 for (a) where CFe is between lo-’ and 10m4 M, and between lo-“’ and in (b), where ZFe is around lo-’ M. This suggests the establishment of a kinetic equilibrium in the system involving FeS.

4373

Kinetics of Fe sulfide precipitation culated. Using the same methods as with HS, the rate - d[ CS] ldt can be calculated. The concentration of HPS at any time is calculated simply by the difference between ZS at any time and cHS - and a rate in terms of -d[cH,S]ldt, and, therefore, -d[aH,S]ldt is calculated. 3.2. Rate Dependence

+ H+

is pH dependent with aHS = aH,S at pH = 7 at 25°C. This provides an opportunity to use the method of isolation to determine the rate dependence on aHS - vs. that on aH$, since the change in relative activities with pH is exponential. The rate in terms of - d[ uHS ]/dt vs. uHS _ was measured for those systems where uHS - > uH$ (Fig. 2). It was found that as uHS became much greater than uH,S, the rate clearly depended on the square of the uHS _ (Fig. 3 ) : -d[uHS-]ldt

= k;[uHS12,

(14)

with k;, the observed second order rate constant of 1.3 x lo7 liters. mole ’. s ’. The rate constant, k; , is apparent because it describes the rate wholly in terms of the component uHS -, and may in itself include terms due to other components. The same procedure applied to reaction regions where pH < 7 and uH$ > uHS gives a rate with respect to uH2S. In this case (Figs. 4 and 5) the rate equation follows a first order plot such that -d[uH,S]ldt

-d[H2S]ldt

- d[uHS-]ldr

= 9O[H$]

+ 1.3 x lO’[uHS]*

The use of any of these functions of rate vs. a dissolved sulfide species concentration, (e.g., -d[ ZS]ldt vs. CS or - d[ aHS ] ldt vs. a[ HS -1) , for all experimental runs give a correlation with some scatter. In particular it was noticed that there is some systematic grouping of experimental points according to pH. It is apparent that the experimental results include an implicit function of pH. The equilibrium H,S+‘HS

tal points (Table 3) _ A plot of the sum of the experimental rates (Eqn. 14 + Eqn. 15) vs. the total dissolved sulfide (Fig. 6) shows an excellent correlation. Using all data points, the process gives a regression coefficient of 0.98 and follows a relationship

= k:[uH,S],

(15)

with kit the observed first order rate constant, being measured as 90 + 10 SK’. The nice thing about these plots is the high regression coefficients obtained: r2 = 0.991 for Eqn. 14 and 0.990 for Eqn. 15. These are excellent correlations since, although results from extreme pH regions have been employed in the calculations, the components are not entirely isolated. In particular, the large difference between the magnitude of the second order and first order rate constants, suggests that bisulfide is affecting the rate to below pH = 6, where uHS- constitutes 10% of the total dissolved sulfide. The slopes are very robust and are not affected significantly by selecting different sets from the measured data to test whether very high or very low data points significantly distort the results. In addition to the measured data points, the slopes are also constrained by the condition that -d[uH,S]ldt = -d[uHS-]ldt + 0 as t + 0. Most of the experimental measurements are from the intermediate region of the process around pH = 7, where both reactions are occurring. The system provides a concise method of checking the validity of the above interpretation by calculating the sum of both model rates for all experimen-

= 15.48[ZS]“.98.

(16)

The 0.98 power dependence is near enough to unity to suggest that it can closely be approximated by a first order equation, with a pseudo first order rate constant of 15 s-’ . This compares with a value of 48 + 9 s -’ derived by Rickard ( 1989b) in buffered systems for a first order plot in terms of - d[ XS] / dt The relationship between the model rate and - d[ ZS] ldt can be observed by inspection of Table 3. The model rate approximates the measured - d[ ZS ] ldt values except in more extreme pH regimes (6 < pH > 8) where the individual components of the rate equations dominate. A simple plot of rate in terms of total sulfide -dZSldt vs. ZS displays significant scatter with a coefficient of regression of 0.92 for the same data. In other words the model rate describes the variation in the experimental system more closely than the measured total rate in terms of the disappearance of total S (II). 3.3. Uncertainties A rigorous treatment of errors in this experimentation is not possible. Certain random errors have been determined by repeated measurements, but systematic errors and errors through calculations can only be estimated. All mV measurements are given by the mean of repeated measurements. Experimentally, measurements were repeated until stable readings were obtained. Repeated measurements of buffer solutions give a 2u error of 20.05 pH units. This is equivalent to a total relative error of 12% or ?6% on any individual reading. The errors in pH measurements contribute to the errors in uHS measurements through Eqn. 2. Errors in ZS concentration in the initial solution preparations are within 22.5% relative. K,[ HS] is assumed to be known and y[HS-] is estimated to within +2.5%. The sum effect of the uncertainties can be estimated with respect to the results of standardization of Ag-Ag,S electrodes, as shown in Fig. 8. In that plot r2 = 0.99 and it appears that the regression line explains 99% of the observed variation. The systematic errors in the electrode measurements are large but mainly irrelevant, since the experimental system is repeatedly standardized. In summary, it is difficult to evaluate rigorously the magnitude of the uncertainties in the rate constants derived from this experimentation. I am presenting the results in terms of a best estimated uncertainty of + 10%. This suggests that the rate constant are 90 + 9 SK’ for k: and 1.3 ? 0.1 x 10’ liters.mole-' . SC’for k;. The apparent uncertainties in these rate constants can furtber be estimated in Fig. 7, where the sum of the model rate equations explains some 98% of the total experimental variation. 3.4. Second Stage Kinetics Second stage kinetics are surnrnarized in Fig. 7. The Stage 2 process is defined as commencing when the rate in terms of

4314

D. Rickard K,,, is mainly dependent on the charge of the reacting species, in a medium of constant ionic strength. Thus, although ligand substitution involving H2S is attractive from a steric viewpoint (i.e., H$ simply replacing HZ0 because of its similar configuration), it is inhibited relative to HS - because of the charge considerations, leading to the significantly lower rate constant observed experimentally for the H2S pathway. It is possible that a neutral outer sphere iron( II) bisulfide complex forms before the inner sphere complex. However, the extreme nucleophilicity of HS (cf. Schwarzenbach and Gschwend, 1990) suggests that this route is unlikely. More probable is a route involving direct formation of a charged inner sphere bisulfide complex:

FIG. 8. Standardization curve for the Ag-AgZS electrode at 25°C in terms of mV vs. (pH + log aHS_). The best fit equation for the curve is shown (coefficient of regression, r’, 0.99) for 43 measurements giving a slope of 28.4 mV per decade.

moles per liter dissolved sulfide per second becomes positive. This phenomenon was reported and established by Rickard ( 1989b). The Stage 2 process is complex. It consists of an increase in dissolved sulfide followed by an approximately symmetrical decrease until the rate follows the same form as in Stage 1. The return to the Stage 1 form occurs within 1 second total reaction time. There is a suggestion that this phenomenon is repeated as the reaction time increases and the Stage 2 reaction-time curve is essentially sinusoidal superimposed on Stage 1 kinetics. After 1.3 seconds the change in sulfide concentrations become so small that the uncertainty in the measurements tend to outweigh the observations. In the present experimentation, in which pH measurements were made independently of sulfide, the increase in dissolved sulfide is accompanied by an increase in [H ‘I. However, no simple relationship has been discovered for the position or magnitude of the onset of Stage 2 kinetics in this experimentation. It is not observed at less than 400 ms at 25°C. The amount of dissolved sulfide and [H+ ] produced in the first fluctuation can be measured by integrating the activity-time curves between the onset of Stage 2 and the point in which the rate falls back to its previous form using TABLECURVE’@. The results are listed in Table 4.

Fe(H,O)h.HS+

= Fe(HS).(H,O):

+ HZO.

The rate is determined by the removal of inner sphere water molecules, k. w, at a rate which is characteristic for iron( II) and independent of the ligand. For the hexaquoiron (II) complex log km, = 6-7. The rate of formation of the complex Fe( HS) ( H*O):, ignoring water molecules, is d[Fe(HS)+]ldt

= k,[Fe*‘][HS-1,

(20)

where k, = K,,k_,. There is no direct evidence for the magnitude of K,, . However, simple electrostatic models (Stumm and Morgan, 198 1) suggest that for opposite charged ions the log of the stability constant for ion pairs is between 0 and 1. Since log km, = 67, this implies that k, is around 107. In this experimentation, the initial concentrations of [Fe*+] and [ HS - ] are characteristically around 10-j M. Integrating Eqn. 5, with the condition that Fe(HS)’ + 0 as t -+ 0, implies that lo-’ M FeSH+ (i.e., 100% reaction) occurs within 0.1 ms. Within this experimental design, therefore, the formation of FeSH’ is very fast, the concentration of FeSH’ in the system can be closely approximated by KFeSH+, and the equilibrium constant for the overall reaction system (excluding water molecules) is Fe*+ + HS-

= FeSH+,

(21)

where K+sH+ = [FeSH+]/[Fe2+][HSm].

4. DISCUSSION

4.1. Theoretical Treatment of the Bisulfide Pathway The mechanism proposed for iron( II) sulfide precipitation from aqueous solution at 25°C from observations of fast precipitation time curves can be treated in terms of a standard Eigen-Wilkins substitution reaction (cf. Eigen and Wilkins, 1965 ) . Two alternative routes are possible both of which start with the formation of an outer sphere complex of aqueous iron ( II ) and bisulfide: Fe(H,O)g+

+ HS-

= Fe(H,O),.HS+,

where K,,, is the stability constant plex:

(17)

for the outer sphere com-

K,,, = [Fe(H20),.HS’]I[Fe(H,0)~‘][HS].

(18)

(19)

(22)

Luther and Ferdelman ( 1993) measured a conditional stability constant, log P(FeSH+) = 10’.‘. Then Fe( HS )2 is formed directly from the charged inner sphere FeSH + complex. Fe(HS).(H,O);

+ HS-

= Fe(HS).(H,O);

.(HS-)

(23)

[Fe(HS).(H,O),]‘.[HS

-1.

(24)

-) = Fe(HS)*

+ 5H20,

where Ki, = [Fe(HS).(H,O);

.(HS-)]/

Then Fe(HS).(H,O),]+.(HS the rate of which is determined molecules, k w.

by the rate of loss of the water

Kinetics

4375

of Fe sulfide precipitation

TABLE 4. Stage 2 kinetic data. The quantities of aHS-, aH,S, CS, and H+ produced are calculated by integrating the concentration-time curve between the onset of the rate excursion, r,,,,. and the re-establishment of the Stage 1 curve, r,,,,,. The values of aHS, azS, ZS, and H+, at the onset of Stage 2 behaviour are also listed and denoted with the subscript,,,,,..

run

‘min

tnux 1aHS_rnin (oH2Smin)

ESmin

The rate of Fe( SH)2 formation

d[Fe(SH)2]ldt

= k_,Ki,[FeHS+][HS] = km, K’:, KpeSH+[Fe*+][HS-1’.

(25)

I assume Fe( SH)2 is a solid phase. There is a lack of evidence for an Fe( SH), complex in solution (cf. Luther and Ferdelman, 1993) and a rapid nucleation reaction would not be detected in the present experimentation if it were not rate-limiting. 4.2. Iron Dependence The theoretical rate Eqn. 25 is of a similar form to the observed rate Eqn. 14 apart from the dependence on Fe’+. The involvement of Fe” in the rate expression is anticipated. This experimentation does not permit independent measurements of Fe*+ concentrations with time. It might be possible to acquire these data with a stop-flow system involving measurements of extremely low Fe*’ concentrations with ICPMS. Even then, the problem of the extremely fine particulate Fe( II) sulfide material would make the uncertainties in the measurements very large. In the absence of dissolved sulfide, Fe’+ speciation in the experimental systems is controlled by these equilibria ( Stumm and Morgan, 198 1) : log K Fe(OH),(s)

= Fe*+ + 20H-

Fe(OH),(s)

= FeOH+

+ OH-

-14.7

produced

I-I+ mm

magnitude greater than OH- (Schwarzenbach and Gschwend, 1990). With minimum initial ZS of 1O-4 M, this suggests that pathways involving OH- do not become competitive until pH > 11. In natural systems with lower CS, the OH mechanism might be important in extreme environments with pH > 9. The iron (II) hydroxycomplexes may be important in the present experimentation if Fe(I1) is in excess of ZS and is, therefore, not competing with Fe( SH)* formation. The mass balance suggests that this will occur where XFe > OSXS. This situation occurs only in experiment 3410. In these runs excess Fe( II) is precipitated as Fe( OH), above pH = 8 and the dissolved Fe(I1) concentration for the runs above this pH will be controlled by Fe( OH), solubility. At pH = 9.8 (Table 3) the total dissolved Fe( II) in the experimental runs will be of the order of lo-’ M. More significantly for the results of this experimentation, the dissolved Fe( II) concentration will be approximately constant. In surnrnary, the dissolved iron concentration in the experimental runs is approximately constant. In those runs where CFe < OSCS (series 447,337, and 437) the experiments have excess Fe and the dissolved iron content varies between lo-“ and lo-’ M. In series 3410, the dissolved Fe(I1) content is controlled by Fe(OHb and is about lo-’ M. 4.3. The Nature of the Observed Second Order Rate Constant, k; The theoretical rate equation is similar in form to the rate equation derived from the present experimentation. Here

-9.4 -d[aHS]ldt

Fe(OH),(s)

+ OH-

= Fe(OH).;

= d[Fe(SH),]ldt

= k$[aHS-I*

(26)

-5.1.

The magnitude of these equilibrium constants suggest that Fe’+ is the dominant Fe( II) form in solution below pH = 8.7 and that Fe( OH), will precipitate at around pH = 8.4 at Fe*+ = lo-’ M and pH = 8.6 at Fe*+ = 10m4 M. The actual values for freshly precipitated Fe( OH), , with a high surface free energy are poorly known, and may lie within a log unit of these values. This suggests the possibility that the hydroxylation of Fe(I1) occurs before the reaction with bisulfide in alkaline systems and that the iron reactant is a hydroxyl complex. In the Eigen-Wilkins interpretation, the rate of formation of FeOH.(H,O): is similar to the rate of formation of FeSH.(H,O): since both depend on the rate of removal of water from the inner hydration sphere. However, the nucleophilicity of HS for alkyl halide SN’ reactions is almost a

and ki = k_,K~,K,,sH+[aFe2+].

(27)

Then ki is constrained between 107. 10. 105.5[Fe2+] = 10’3.5[Fe2’] and 106. 1. 105.5[Fe2+] = 10”.5[Fe2”]. This endmember rate is measured in alkaline systems where [Fe*+] is determined by Fe(OH)* solubility and is approximately constant around lo-’ M. This theoretical calculation suggests that the observed rate constant k:, according to an EigenWilkins model, should be around lo6 liter. mole-’ . SC’within 2 one magnitude, which is satisfyingly close to the measured value of the observed second order rate constant in this experimentation. I conclude that the observed second order rate constant, ki, is a composite constant which involves [Fe*+] and can be modelled by a classical Eigen-Wilkins substitution

D. Rickard

4376

process. The data suggest that the rate equation might be written -d[aHS]!dt

= d[Fe(SH)*Jldt

(28)

= k*[Fe2+][HS-]2,

where the logarithm of k*, the Eigen-Wilkins constant, is 12.5 % 1 liters *~mole~*~s~‘.

reaction

rate

4.4. The Hydrogen Sulfide Pathway The competitive hydrogen a first order Eqn. 15: -d[aH,S]ldz

d[FeS]ldt

sulfide pathway

is described

As mentioned above, theoretically this reaction, which involves a neutral molecule, should be far slower than the reaction involving bisulfide, which agrees with the observations. As with the bisulfide pathway, the apparent rate constant is a complex constant. It probably includes [aFe*+] dependence at least. For the same reasons as given above, no iron dependence has been determined in the present experimentation. In the endmember systems with pH < 7, Fe*+ is high and approximately constant at lo-’ to 1O-4 M which probably gives rise to the apparent rate constant. Using the same systematics as above, the reaction probably follows mechanisms involving the exchange of inner sphere H*O molecules with H*S followed by the release of protons. Luther and Ferdelman ( 1993 ) found evidence for the existence of the FeH,S *+ complex up to pH = 6, strongly supporting the proposal that the mechanism involves the production of this inner sphere complex, before loss of protons and the formation of FeS. The theoretical rate, according to Eigen-Wilkins kinetics, is

Fe(H*O)g’

= k_,KA,,

(29)

+ H*S = Fe(H*O),.H*S*‘,

(30)

with Kb, =

[Fe(H*O)h~H*S*+l/[Fe(H*O)~fl[H*Sl,

(31)

Fe(H*O)6.H*S2’

= FeH*S(H*O):‘,

(32)

= k_,K~,[aFe*‘][aH*S].

(33)

where d[a(FeH*S)*+]ldt Finally, (FeH*S)*+

= FeS + 2H’

and d[FeS]ldt

= -d[a(FeH*S)‘+]ldt = -k_,K&[aFe]*+[uH*S].

The form of this equation 15 where -d[aH*S]ldt and the observed

= d[FeS]ldt

is similar to the observed = ki[uH*S]

ki = -k_ wK’“C[aFe*‘].

(34) Eqn.

= k:[cH*S]

first order rate constant k i is complex

= -d[cH*S]ldt

= -d[aH*S]ldt

by

= k:[aH,S].

d[FeS]ldt

The calculated value for k: using the limiting values of k_, and K:, given above, together with [aFez+] between lo-4 and 10el M is constrained between 106. 1. 1O-4 = 10’ so’ and 107. 10. lo-’ = lo5 ss’ which is consistent with the experimentally measured value of around 10’ s-‘. The observed kinetics are, therefore, consistent with an Eigen-Wilkins reaction in which the rate is described by

and (35)

= kl[aFe2+][uH*S], where the logarithm of k, , the theoretical Eigen-Wilkins reaction rate constant, has a value of about 7 -C 1 liters.mole~‘.s~‘. 4.5. Second Stage Kinetics: The Formation

of FeS

Although there appears to be no obvious systematic relationship between amount of sulfide released during stage 2, the pH and the time, inspection of Table 4 results suggest that the H*S value at the onset of the sulfide release phase is systematic. The H*S value is related to the reaction progress through the condensation model for Stage 2 (Rickard, 1989b) which proposes a reaction of the type: Fe(SH)*

= FeS + H*S.

(36)

The FeS in this case is the more familiar amorphous FeS or proto-mackinawite. If the reverse reaction occurs, then a kinetic equilibrium will be set up with an apparent equilibrium constant of K’ = [H*S].

(37)

The net result should be that where the H*S concentration reaches a certain fixed value, FeS should begin to form. Inspection of the H*S-time plots in Fig. 7 shows that, in the absence of excess dissolved Fe( II) (i.e., where the initial dissolved Fe( II) concentration was 10m4 M), the concentration of H*S approximates closely to IO-” M independent of other factors, such as pH. This is consistent with the reaction in Eqn. 36. Where Fe( II) is in excess in the experiments (Fig. 7a), the increase of dissolved sulfide is marked and occurs at an H*S concentration of ca lo-” M. In this case, the total Fe(II) concentration approximates to 10m3 M throughout Stage 1 of the experiment. Where the initial CS concentration is IO-‘, the Fe(I1) concentration after the production of Fe( SH)* approaches 0.5 x lo-’ M. Where the initial ZS concentration is 10-4, the Fe( II) concentration after the production of Fe(SH)* approaches 0.9 X lo-’ M. In the case of excess Fe( II) in solution, Stage 2 kinetics occur at H*S = 1O-‘7 M which closely approximates lo-‘” X 10m7, where lo-‘” value for [ H*S] for the onset of Stage 2 in the absence of excess Fe( II) and 10 -’ is the approximate concentration of dissolved iron. This suggests that the reason the condensation reaction occurs at lower H*S concentrations is the presence of excess Fe( II). In the presence of excess dissolved Fe( II), H*S continually re-reacts with dissolved Fe( II) in the Stage 1 reaction until the ratio of [H*S]/[Fe(II)] is less than lo-“.

4371

Kinetics of Fe sulfide precipitation 4.6. Application to Natural Systems From the experimental observations, the overall rate of formation of iron sulfides from solution can be described simply in terms of the total dissolved sulfide concentrations in systems with total dissolved iron( II) of between lo-’ and 10m4 M to an acceptable degree of precision. Thus, d[FeS]ldr

= k[[aH,S],

d[Fe(SH),]ldt

= k;[aHS]‘,

-d[cXS]ldt

= ko[cZS],

solved iron concentration. However, greater total dissolved iron concentrations will increase the rates of both processes. 5. CONCLUSIONS The fast precipitation reaction between dissolved iron( II) and sulfide in aqueous solution displays complex behavior within the first second of reaction. The total rate can be modelled by two competitive processes

-d[aH,S]/dt

and, overall,

= d[FeS]/dt

= k([aH,S],

where k: = 90 + 10 s-’ (38)

where k0 is the pseudo first order rate constant for this equation of 15 s -’ at 25°C. This implies that the disappearance of total dissolved sulfide with time, in sediments for example, follows an exponential rate law. Integrating Eqn. 38 ZS - CSO =c -lrot, where ZS, is the total dissolved sulfide concentration at t = 0. -d[CS]ldt

= d[FeS]ldt

= k,[aFe*+][aH$],

where log k, is 7 +- 1 liters. mole _’ s ~’. For the bisulfide pathway this is d[Fe(SHh]ldt

= d[aFe(SH)*]ldt

= k2[uFe2+][aHS]‘,

where log k2 is 13 ? 1 liters*.mole~*.s-‘. These generic rate laws are applicable to all environments at 25°C within a precision similar to that attained in many equilibrium thermodynamic estimations. The laws suggest that the pathways and rates of precipitation of FeS is controlled as described above by pH and ZS. The relative concentration of dissolved Fe(I1) will have no effect on the pathways since it affects each rate law equally. This is possibly the reason why the experimentally determined rate could be approximated by a law which is independent of the total dis-

= k$[aHS]*,

where k; = 1.3 ? 0.1 X lo7 liter.mole-‘.s-‘. The results show good agreement with a classical EigenWilkins process. In this interpretation, k; and k; are pseudo constants incorporating an [ uFe*+ ] dependency. Then d[FeS]ldt

= -d[cH,S]ldt

= -d[uH,S]/dt

+ d[Fe(SH),]/dt

and the rate of removal of ZS is equivalent to the rate of formation of FeS and Fe( SH)*. The effect of the competitive reactions is shown on Fig. 8. Here all three rate laws are plotted from Eqns. 14, 15, and 16. The result show that relative dominance of the H$ and the HS pathways depends on ZS. At ZS > lo-’ M, the bisulfide pathway dominates above pH = 6 (CS = lo-” M) and pH = 5 (ZS = 10-l M). At higher pH values, FeS is still being formed directly although the bisulfide pathway dominates. The overall rate increases by two orders of magnitude above pH = 7 at CS > 10 -’ M. However, because of the competitive kinetics, the curves have complex responses to ZS. At CS < lo-’ M the H,S pathway increases in importance, until at ZS = 10m6 M, the direct formation of FeS is not dominant up to pH = 8, but is also faster. The results are intuitively correct and provide an alternative, kinetic, explanation for the formation of sulfide-rich iron complexes at higher dissolved sulfide concentrations. The observed results are consistent with Eigen-Wilkins models of the processes which lead to general rate laws in which the rate is a direct function of the ion activity products. For the H2S pathway this is d[FeS]ldt

-d[uHS-]ldt

= k,[uFe2+][uH2S] with a theoretical rate ter.mole-‘.s-’ and -d[uHS]ldt with

a theoretical

constant,

= d[aFe(SH)2]ldt rate constant,

k,, approaching

10’ li-

= k2[uFe2’][uHS-]2 k2, approaching

10” liboth suggest that the rates are a direct function of the ion activity products of the iron sulfide precipitates. Corroborating evidence for this is obtained from the experimental observation that the rate of the Fe( SH)* reaction is best described in terms of uHS _ rather than cHS -, It was not possible to distinguish between uH$ and cH2S in this experimentation to make a similar distinction for the FeS reaction, since y (H,S) = 1 for the experimental conditions. The results suggest that the first stage kinetics of this reaction can be modelled entirely in terms of solution kinetics without recourse to nucleation theory. This may result from a small energy change between aqueous Fe( HS k and solid Fe( HS)2 and between intermediates like aqueous FeSH+ and solid FeS. The lack of any observed lag phase in the reaction is consistent with this interpretation. In fact, of course, I have no direct information from this experimentation that Fe( SH h is necessarily a solid phase. All the observations provide is the evidence for removal of HS from solution. Particles are not observed within the T-tube because of the low concentration, although they can be collected in the outflow. The interpretation of a solid phase is preferred because of lack of evidence for a Fe( SH)* complex in solution (cf. Luther and Ferdelman, 1993) and the Fe:S ratio of analyzed products. Filtering the outflow gives an amorphous iron( II) sulfide product with an Fe:S ratio of less than one (cf. Bemer, 1967; Rickard, 1969; Morse et al., 1987) consistent with a mixture of FeS and Fe( SH)2. According to the mechanistic interpretation of the rate, the concentration of total dissolved iron affects each pathway similarly. The rate of removal of total dissolved sulfide through the formation of iron( II) monosulfides in natural systems, such as sediments, with total dissolved iron in the mil-

ter’ . mole -*. s -’ . These theoretical rate expressions

D. Rickard

4378

total dlssdved

pendence in the micromolar to nannomolar range the value of k0 can be decreased proportionally to a first estimation. Thus, generally, k0 can be approximated as 15 X 10~m4/[CFe2+] where [ ZFe’+ ] is the total concentration of dissolved Fe( II). The result will probably be precise to within rt one magnitude. The net result of the competitive pathways in natural systems is a strong dependence on the pathway for iron (II) sulfide formation on pH and total dissolved sulfide concentration (Fig. 9). In environments with dissolved sulfide concentrations above the ppm (or PM) level, the bisulfide pathway will dominate at neutral and alkaline pH values. In sub-ppm (or ,uM) level sulfide-bearing environments, the direct route dominates in neutral to weakly alkaline environments. Interestingly, this direct route, in sulfide-poor environments becomes actually faster than the bisulfide pathway. The Fe( SH), condensation reaction is relatively slow at 25°C. Thus in environments with medium level dissolved sulfide concentrations, above the ppm (or PM) level, there is a standing concentration of Fe(SH)2 in natural system, especially above pH = 7. It is important to note that the condensation of Fe( SH)* is only one of the reactions Fe( SH)2 may undergo. If any other reaction is faster, for example reaction with more Hz!3 to form pyrite (D. T. Rickard, unpubl. data), then FeS need not be a major product. Mackinawite crystallisation from the initial precipitate has a half-life in terms of tens to hundreds of days at 25”C, although some long-range ordering may be detected after two days. Even so, if sedimentary pyrite formation is faster than this, then mackinawite may not be a common precursor to low temperature pyrite formation. The reaction region between below pH = 7.5 with medium levels of dissolved sulfide is of particular interest in this context. Here H2S makes up a significant part of the total dissolved sulfide whilst kinetically, the Fe(SH), pathway dominates. D. T. Rickard (unpubl. data) has found that the kinetics of the reaction between iron(U) sulfides and HzS is relatively fast at 25”C, with a half-life measured in hours. This might suggest that iron( II) bisulfides like Fe( SH), could be significant intermediaries in sedimentary pyrite formation.

rultld-a =lO-'M

--7-y lE+5

lE-9

total dbmolved wlflde b

= 10%4 9

10

11

w

.

PH FIG. 9. Plot of total model rate vs. pH. The total rate is plotted for CS = lo-‘, lo-’ and 10-O M, the two endmember rates, the H&r,) and the HS (rz) pathways, are indicated and the regions where each pathway dominates are shaded. The plot shows that the rate of the HS pathway equals the rate of the HZS pathway at pH = 6 at CS = 10ml, pH = 8 at ZS = 10mh and pH = 5 at ZS = IO-‘. With CS = 1O- ’M and above pH = 7, the rate is dominated by the bisulfide pathway, and is some two magnitudes faster than in more acid solutions. However, at ZS < IO-? M the H2S pathway is faster and dominates up to pH = 8.

limolar or sub-millimolar range, can, therefore, scribed by an overall rate law -d[CS]l& where k,, = I5 s ~-I. In systems

be closely de-

= L”[CS], with total dissolved

iron de-

Acknowledgments-The work was supported by UK Natural Environment Research Grant GR3/7564. I thank Anthony Oldroyd for experimental assistance. John Morse, Bill Davison, George Luther, and Hu Barnes commented on an earlier version of the manuscript. GCA referees Goldhaber, Schoonen, and Barnes (again! ) exceeded the bounds of normal reviewing effort to knock the submitted version into shape. Support by Editor Ohmoto was appreciated. Edirorial

handling: H. Ohmoto REFERENCES

Baas Becking L. G. M. and Moore D. ( 1961) Biogenic sulfides. Econ. Geol. 56,259-272. Bemer R. ( 1967) Thermodynamic stability of sedimentary iron sulfides. Amer. J. Sci. 72,293-306. Bemer R. A. ( 1970) Sedimentary pyrite formation. Amer. J. Sci. 268, l-23. Davison W., Buffle J., and De Vitre R. ( 1988) Pure Appl. Chem. 60, 1535-1548. Eigen M. and Wilkins R. G. ( 1965) The kinetics and mechanism of formation of metal complexes. In Mechanisms of Inorganic Reactions; ACS Symp. Ser. 49, 55-80.

Kinetics

4379

of Fe sulfide precipitation

Gammon C. H. and Barnes H. L. ( 1989) The solubility of Ag,S in near-neutral aqueous sulfide solutions at 25 to 300°C. Geochim. Cosmochim. Acta 53,279-290. Luther III G. W. ( 1991) Pyrite synthesis via polysulfide compounds. Geochim. Cosmochim. Acta S-5,2829-2849. Luther III G. W. and Ferdelman T. G. ( 1993) Voltammetric characterization of iron( II) sulfide complexes in laboratory solutions and in marine waters and porewaters. Environ. Sci. Tech. 27, 1154-I 163. Morse J. W., Miller0 F., Comwell J. C., and Rickard D. ( 1987) The chemistry of the hydrogen sulfide and iron sulfide systems in natural waters. Earth Sci. Rev. 24, l-42 1. Murray R. C. and Cubicciotti G. ( 1983) Thermodynamics of aqueous sulfur species to 300°C and potential-pH diagrams. J. Electrochem. Sot. 130,866-869. Rickard D. T. ( 1969) The chemistry of iron sulfide formation at low temperatures. Stockholm Cont. Geology. 20,67-95. Rickard D. T. (1989a) An apparatus for the study of fast precipitation reactions. Mineral. Mag. 53, 527-530. Rickard D. T. ( 1989b) Experimental concentration-time curves for the iron (II) sulfide precipitation process in aqueous solutions and their interpretation. Chem. Geol. 78, 315-324. Schoonen M. A. and Barnes H. L. (1988) An approximation of the second dissociation constant for HZS. Geochim. Cosmochim. Acta 52,649-654. Schwarzenbach R. P. and Gschwend P. M. (1990) Chemical transformations of organic pollutants in the aquatic environment. In Aquatic Chemical Kinetics (ed. W. Stumm), pp. 199-234. Wiley. Stumm W. and Morgan J. J. ( 1981) Aquatic Chemistry. 2nd ed. Wiley. Sweeney R. E. and Kaplan I. R. (1973) Pyrite framboid formation: laboratory synthesis and marine sediments. &on. Geol. 68, 618634.

plexes relative to the total dissolved sulfide concentration gible in this experimentation. The electrode reaction may be written AgS

is negli-

+ H+ + 2e = 2Ag” + HS-.

For this reaction pe = pea - ‘/*(log [aHS] For a plot of mV vs. (log [aHS]

+ pH).

+ pH), at the intercept

(log [aHS_]

+ pH) = 0

and pe” = pe. The results of electrode standardization runs are shown in Fig. 8. The equation for the electrodes in this experimentation is mV = -28.4(pH

+ log [aHS_])

- 445.

(1)

At 25°C the theoretical value for the slope. is -29 mV/decade and the measured value of 28.4 is consistent with theory. It demonstrates that the electrodes are behaving in a two-electron transfer reaction suggesting the appropriateness of the proposed equilibrium reaction: Ag,S + H+ + 2e = 2Ag

+ HS-.

From data listed in Schoonen and Barnes ( 1988) and Stumm and Morgan ( 1981) the logarithm of the equilibrium constant for this reaction is -9.1, where Ag,S is the stable a-form, acantbite. Selected data from data listed in Gammons and Barnes ( 1989) gives -9.2. Since E” = -445

mV,

pe’ = -44510.059

at

25°C

= -7.5.

APPENDIX pe’ = l/n log K, Silver-Silver Sulfide Electrode Systematics

log K = -15.1.

Gammons and Barnes ( 1989) found a value of K = -3.82 at 25°C for the solubility of AgS according to the reaction ‘/,A@

+ ‘12HzS + HS-

which means that the concentration

= Ag(HS-)*,

of dissolved

silver sulfide com-

The conclusion is that the silver sulfide forming on the electrode is not acanthite or argentite but another phase. This conclusion is supported by the observation that the phase is X-ray amorphous at 25°C. In terms of solubility the phase is far less soluble than aAg,S, which would imply that it is the stable phase at 25°C.