Thermodynamics and kinetics of hydrogen sulfide in natural waters PDF

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Marine Chemistry, 18 (1986) 121--147 121 Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands THE THERMODYNAMICS AND KINETICS OF THE HYDROGEN SULFIDE SYSTEM IN NATURAL WATERS* F R A N K J. MILLERO Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, ...

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Marine Chemistry, 18 (1986) 121--147 Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands

121

THE THERMODYNAMICS AND KINETICS OF THE HYDROGEN SULFIDE SYSTEM IN NATURAL WATERS* F R A N K J. MILLERO

Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Miami, FL 33149 (U.S.A.) ABSTRACT Millero, F.J., 1986. The thermodynamics and kinetics of the hydrogen sulfide system in natural waters. Mar. Chem., 18: 121--147. The thermodynamics and kinetics o f the H2S system in natural waters have been critically reviewed. Equations have been derived for the solubility and ionization of H2S in water and seawater as a function of salinity, temperature and pressure. Pitzer parameters for the interaction of the major cations (Na +, Mg2+ and Ca 2+) with HS- have been determined to allow one to calculate values of pK~ in various ionic m e d i a The limited data available for the interaction of trace metals for HS- are summarized and future work is suggested. The kinetics o f oxidation of H2S have also been examined as a function of pH, temperature, and salinity. The discrepancies in the available data are largely due to the different [ O 2 ] / [ H S - ] ratios used in various studies. Over a limited pH range (6--8) the pseudo first order rate constant for the oxidation is shown to be directly proportional to the activity of HS-. Further studies are suggested to examine the effect of ionic media and temperature on the rate o f oxidation.

INTRODUCTION

At the interface between oxygen and hydrogen sulfide in natural waters large changes occur in the state of metal ions. This is due to the changes in redox conditions, solubility conditions and bacterial activity. Areas where these reactions control the chemical processes include pore waters, hydrothermal waters, and waters of anoxic basins. Recent workers (Gardner, 1973, 1974; Davison, 1980; Jacobs and Emerson, 1982; Boulegue et aL, 1982) have been examining the equilibrium and kinetic factors that are important at this interface. Although equilibrium models only approximate the real system, they are useful in examining the trends in field data (Jacobs and Emerson, 1982). The kinetic behavior is difficult to completely characterize due to varying rates of oxidation and adsorption above the interface and to varying rates of reduction, precipitation and dissolution below the interface (Boulegue et al.,

*Presented at the VIII International Symposium on the Chemistry of the Mediterranean, Primosten, Yugoslavia, May 1984.

0304-4203/86/$03.50

© 1986 Elsevier Science Publishers B.V.

122

1982; Jacobs and Emerson, 1982). Bacterial catalysis may also complicate the system (Jacobs and Emerson, 1982). Since fundamental data on this system are important and needed to characterize the natural conditions, we have attempted in this review to critically analyze the existing thermodynamic and kinetic data available on the hydrogen sulfide system in natural waters. More complete reviews of the sulfur cycle are given elsewhere (Goldhaber and Kaplan, 1974; Nriagu and Hem, 1978). This review will concentrate on the thermodynamics of H2S solubility, ionization and complexation with metals The kinetics of the oxidation of H2S in natural waters will also be examined. The effects of pH, ionic strength and catalysts will be considered. Some of the future work needed to clarify the thermodynamics and kinetics of the H2S system will also be discussed. THERMODYNAMICS

O F H2S IN A Q U E O U S SOLUTIONS

Thermodynamic data on the H2S system in pure water are available in the compilations of Sillen and Martell (1964, 1971); we, thus, do not plan to review these data in detail. Instead we wish to discuss critically the thermodynamic data important for marine systems Solubility o f H2S in water and seawater

The most extensive measurements on the solubility of H2S in water and seawater are those of Douabul and Riley (1979). They made measurements from 2 to 30°C and salinities of 0 to 40. They analyzed the solutions using iodometric techniques. The precision was estimated to be 0.2%. The effect of temperature on the solubility of H2S in water and seawater ( S - - 3 5 ) is shown in Fig. 1. The solubility decreases with increasing

2.5 Ose0water 2.3

2.1 0

c=

1.9

1.7

5~ I. 3.2

3.3

3.4

3.5

3.6

3.7

p / T ) fo' , K

Fig. 1. T h e e f f e c t o f t e m p e r a t u r e o n t h e s o l u b i l i t y o f H2 S in w a t e r a n d s e a w a t e r (S = 35 ).

123 2.5 25"C 2.3

2.1 -In C 1.9 2°C

1.7

I.,5

0

5

I0

15

20

25

30

35

40

S

Fig. 2. The effect o f salinity on the solubility o f H2S at 2 and 25°C.

temperature in water and seawater. The decrease is larger in water than seawater. This means that the enthalpy o f solution (Zl/-/so~, = 4.53 kcal tool- ] ) in water is greater than that in seawater (zl/-/~o~ = 4.35 kcal tool- 1). The addition o f sea salt to water causes a decrease in the solubility o f H2 S. This salting out is similar to other gases. The effect o f salinity o n the solubility is s h o w n in Fig. 2. These results can be represented by the S e t c h e n o w equation

in(C°/C)

kS

=

(1)

Where C o and C are the solubilities in water and seawater, k is the salting TABLE I Values of the salting out coefficient for H2S in seawater at various temperatures Temp. (°C) 103k a

2.1 1.702

5.05 1.555

10.19 1.350

15.04 1.153

20.10 1.032

24.72 0.921

aEquation 1.

1.5

k I0" I

0.5 5

I0

15

20

Z5

30

t, °C Fig. 3. T h e effect o f t e m p e r a t u r e o n the salting out coefficient for H2S in seawater.

29.82 0.831

124 coefficient and S is the salinity. Values of k are given in Table I and shown plotted versus temperature in Fig. 3. The salting out coefficients become smaller in magnitude at higher temperatures and can be represented by 10ak = 1 . 8 0 6 - - 5.2297 × 1 0 - 2 t + 6.6066 x 10 - 4 t 2

(2)

(where t is in °C) with o = 0.009. Douabul and Riley (1979) fit their solubility results using the equation of Weiss (1970), T = 273.15 + t. lnC

=

--

41.0563 + 66.4005(100/T) + 15.1060 In(T/100)

+ S[-- 0.60583 + 0.379753(T/100) -- 0.602340(T/100) 2]

(3)

which is valid when the fugacity of H:S is 1 attn. The results of Douabul and Riley (1979) in H20 agree with the results from earlier studies to + 0.5%. A comparison of the Setchenow salting coefficients for H2S in seawater with other gases using the equation log(C°/C)= kI is shown in Table II. The values of k and 7g = C°/C are both lower than those found for other gases, but similar to HaPO4 in 0.7 rn NaC1 (k = 0.052 and ~,g = 1.09). Since the activity coefficient of H2S is near 1.0, the interactions between the major sea salts and H2 S are quite small The Henry's law constant, Hs (atm kg H20 tool -1 ) over a wide range of temperature can be estimated (Clarke and Glew, 1971) from l o g H s = 1 0 2 . 3 2 5 - 4 4 2 3 . 1 1 / T - - 36.6296 log T + 0.13870T

(4)

This equation is valid from 25 to 260°C. Measurements of the solubility H2S in binary solutions are not generally available (Gamsjager and 8chindler, 1969) and results at high ionic strengths are non-existent. Since the salting coefficient is quite small, this is not a serious limitation for most dilute natural waters. New measurements of the solubility of H:S in brines and at high temperatures are needed. Spedding and Vujcick (1982) have measured the exchange coefficient for H2S across the air--sea interface as a function of pH. TABLE II The salting out and activity coefficients

of gases in

seawatera

Gas

k'

7g

Gas

k'

7g

H2S He CO2 Ne O2

0.020 0.092 0.095 0.101 0.121

1.03 1.16 I. 17 1.18 1.22

Ar Kr CH4

0.121 0.128 0.129 0.131 0.134

1.22 1.23 1.24 1.24 1.25

N2

CO

aWhere log(C°/C) = log 7g = k'I (Millero and Schreiber, 1982).

125

Ionization o f H2S in water and seawater A knowledge o f the ionization of H2S is needed for equilibrium and kinetic calculations in anoxic waters. Dissolved H2S is generated by bacteria under anoxic conditions SO~-+2H

+ = H2S+202

(5)

and is a constituent o f pore fluids of sediments and stagnant basins (seas, lakes, etc.). Because metal sulfides are highly insoluble, the production of H2S can control their sedimentary geochemistry (Berner, 1967). Since H2S can dissociate H2S = H++HS-

(6)

HS- = H + + S 2-

(7)

the various forms are a function o f pH. The kinetic reactions of H2S are also pH dependent. It is important, therefore, to have reliable values for the ionization of H2S in natural waters, pK1 for the ionization of H2S in water at 25°C has been measured by a number of worker~ Almgren et al. (1976) tabulated the values given in Table III. A mean value of pKI = 7.01 + 0.02 was selected by Almgren et al. (1976). The large scatter of the results is related to the experimental errors o f the various spectrophotometric and potentiometric m e t h o d s used by various authors (see Table IV). Another problem with these results is that the extrapolations to infinite dilution were not made in a consistent manner. The value of K1 is related to the appropriate activity coefficients by KI

= K *1('yH'~HS/'~/H2S)

(8)

where K~ is the stoichiometric constant and 7~ are the activity coefficients. From the pK~ measurements of Almgren et al. (1976) in NaC1 solutions, it is TABLE III Values of PK1 for the ionization of H2S in water at 25°C a pK1

Reference

pK1

Reference

7.07 7.06 7.05 7.04

Tumanova et al. (1957) Loy and Himmelblau (1961) Ringbom (1953) Brunet and Zawadzki (1909), Thiel and Gessner (1914) Ellis and Golding (1959)

7.0 6.00

Goates et aL (1952) Kubli (1946), Konopik and Leberl (1949), Pohl (1962) Khodakovskii et aL (1965) Wright and Maa~ (1932a, b) Kapustinskii (1940) Latimer (1952)

7.02

6.98 6.97 6.96

7.01 + 0.02 mean aFrom Almgren et al. (1976).

126 TABLE IV Values of pKI for the ionization of H2S obtained by various methods pK 1

Method

Reference

6.97 6.99 7.06 6.96 7.02 6.985 6.98

conductometric calculated glass electrode calculated spectrophotometric glass electrode spectrophotometric

Wright and Maass (1932a, b) Kubli (1946) Kubli (1946) Latimer (1952) Ellis and Golding (1959) Berner (1967) Goldhaber and Kaplan (1975)

possible t o d e t e r m i n e pK1 using Pitzer's e q u a t i o n s ( 1 9 7 3 ) t o estimate t h e activity c o e f f i c i e n t s (Millero, 1983a). T h e r e a r r a n g e m e n t o f eq. 8, b y transferring all t h e k n o w n p a r a m e t e r s t o t h e l e f t . h a n d side o f t h e e q u a t i o n , gives Y = - - In K~ - - In 7H + In 7H, S - - In 7 H s ( M E D ) = - - In K I + 2m~O~Hs + f l ~ H S

(9)

w h e r e In 7HS = In 7HS (MED) + 2rn~°aHs + f'~N~HS, In 7Hs-(MED) includes all t h e k n o w n Pitzer t e r m s f o r t h e m e d i u m , t h e values o f ~OaHs and ~ , H s axe Pitzer i n t e r a c t i o n p a r a m e t e r s (Millero, 1 9 8 2 ) and f l = [1 - - e x p (-- 2mV2)(1 + 2 rnl/2)]. T h e various t e r m s n e e d e d t o calculate Y axe given elsewhere (Millero, 1983a). A n o n l i n e a r least squares fit o f t h e d a t a gives pK~ = 6 . 9 7 6 -+ 0 . 0 0 5 , /~OaHs = - - 0 . 1 0 3 + 0.02 a n d /~IN~Hs = 0 . 8 8 4 + 0.05 at 25°C. T o d e m o n s t r a t e t h e reliability o f these p a r a m e t e r s a p l o t o f Y ' = y _ f l ~ a ~ s versus m is s h o w n in Fig. 4. O u r value o f p K I = 6 . 9 8 -+ 0.O1 is in e x c e l l e n t a g r e e m e n t w i t h t h e r e c e n t values o f B e r n e r ( 1 9 6 7 ) a n d G o l d h a b e r and K a p l a n ( 1 9 7 5 ) (see T a b l e IV). 16.2

The IonizQflon of H2S in NaCI Solutions

161 16.0 15.9

15.80

dZ

d.4

d6

d.8

I'.0

mNoCI Fig. 4. A plot of Y' = Y (eq. 9 ) - - fl ~NaHS 1 versus molality of NaCl obtained from the ionization of H2S measurements of Almgren et al. (1976).

127 TABLE V Pitzer parameters for HS- salts at 25°C a Salt

~Mx

~MX

NariS KHS Mg(HS)2 Ca(HS)2

-- 0.103 --0.337 0.466 0.069

0.884 0.884 2. 264 2. 264

aCalculated from the measurements of Almgren et aL (1976). The results for K H S were determined from the measurements of Goldhaber and Kaplan (1975). The ~I terms for K + and Ca 2+ were equated, respectively, to N a + and M g 2+.

Measurements of H2S in more concentrated NaCl solutions are needed to

obtain more reliable higher order terms and information of the interactions of C1- and H8-. Almgren et al. (1976) also made measurements of pK~ in NaCaC1 and seawater solutions. From these results it is possible to calculate Pitzer (1973) parameters for the interactions of Ca 2+ and Mg 2+ ions with HS-. The results of these calculations are given in Table V, along with values for NariS and KHS (Millero, 1983a). The Pitzer parameters for these salts are of the same order of magnitude as the appropriate chloride; thus ~/HS is similar to 7c~ (Herr and Helz, 1976). Ionization constants for HS- in water show a wide range of variations (Goldhaber and Kaplan, 1975) (see Table VI). Part of this disagreement is related to the extrapolations of the measured values to infinite dilution. This can be seen from Fig. 5 (Goldhaber and Kaplan, 1975). A simple linear extrapolation of this data gives a value close to the average value (13.8) given in Table VI. TABLE VI Values of pK2 obtained by various workers a Temp. (°C)

pK2

Method

Reference

20

12.44 13.10 14.0 14.15 14.0 17.1 14.92 13. 78 13.85

potentiometric colorimetric spectrophotometric potentiometric spectrophotometric spectrophotometric solubility potentiometric spectrophotometric

Kubli (1946) Konopik and Leberl (1949) Ellis and Golding (1959) Widmer and Schwarzenbach (1964) Ellis and Milestone (1967) Giggenbach (1971) Knox (1906) Maronny (1959) Muhammad and Sundarahm (1961)

25 30

mean: 13.78 -+ 0.74 aFrom G oldhaber and Kaplan (1975).

128 146

eGoldhober and Koplon OMaronny oEIlis end Gelding &Ellis and Milestone

x

~x

x

x

13.8

pK,

~x ~

0

•

0

•

OD

0

0

130

12.6 0.2

0.4

Q6

0.8

I

i'/, Fig. 5. The effect of ionic strength on the PK2 for ionization o f H2S at 25°C (Goldhaber and Kaplan, 1975).

Since activity coefficients of Na2S or K2S are not available, it is difficult to extrapolate these results properly to infinite dilution. If Na2CO3 is used as a model, one might expect the values for pK: in water to be as high as 14.6. Errors due to the use of different ionic media and oxidation of S 2- with oxygen are also important. Recent workers (Meyer et al., 1 9 8 3 ) h a v e suggested that the high pK2 = 17.1 of Giggenbach (1971) may be more reliable than the low values obtained by others. Since S:- probably forms strong complexes with divalent ions, pK~ in natural waters may be a lot lower. Further work is needed to clarify these discrepancies. Fortunately for most natural waters (pH 6--9) the S 2- species is not very important. This can be shown from the fraction of various species in water found using pKl = 6.98 and pK2 = 14.6 (see Table VII). The effect of temperature on the ionization of H2S in water has been measured by Ellis et al. (1967) Ellis and Giggenbach (1971) and Tsonopoulos et al. {1976). Ellis and Giggenbach (1971) obtained data to 276°C using TABLE VII The speciation o f H2S in various ionic media at 25°C and pH 8.1 a % o f species Species

H20

0.7 m NaC1

Seawater (S = 35)

H2S HSS:-

7.05% 92.95 2.9 × 10 -s

4.00% 96.00 1.9 X 10 -4

3.07% 96.93 1.9 × 10 -4

aCalculated using pK1 = 6.98, 6.72, 6.60 and pK2 -- 14.6, 13.8, 13.8, respectively, in H20, NaC1 and seawater.

129 80

'°0 "0

I o I 7705 0

':"

"°

0

;'°,,.E. 0o..,,".. . . . .

"°

0EllisandGiggenboch 0Tsonopouloul ~ oFm r Colorimetry •

pK,

65 60179

2

270 (I/-r)ld

320

570

Fig. 6. The effect of temperature on the pK* of H2S in water. spectroph.otometric methods. Tsonopoulos et al. (1976) made measurements to 150°C, also using spectrophotometric methods. As shown in Fig. 6 the two studies are not in good agreement above 75°C. These deviations are probably due to errors in the assignment of pH (Barbero et al., 1982). Recently, Barbero et al. (1982) estimated the effect of temperature on the ionization of H2S using t h e r m o d y n a m i c data (AH and ACp ). For the neutralization o f H2S H2S + OH- = HS- + H20

(10)

They found (with an adjustment for pK 1 = 6.98 at 25°C) log K~ = 1 9 . 8 3 + 9 3 0 . 8 / T - - 2.800 In T

(11)

near the steam saturation point. The estimated uncertainty is + 0.47 in log K~ at 300°C. These results can be converted to values for pK1 using values for pKw for the ionization o f water (Olofsson and Hepler, 1975). These values (Barbero et al., 1982) are given in Table VIII. Values at other temperatures can be estimated from pK1 = 32.55 + 1 5 1 9 . 4 4 / T - - 15.672 log T + 0.02722T TABLE VIII Equilibrium constants for the ionization of H2S in water at various temperatures t(°C)

pK 1

t(°C)

pK1

0 25 50 75 100 125 150

7.40 6.98 6.73 6.57 6.51 6.49 6.52

175 200 225 250 275 300

6.61 6.73 6.89 7.10 7.33 7.61

(12)

130

As shown in Fig. 6 the values of pK1 determined from thermodynamic data are in reasonable agreement with the results of Tsonopoulos et al. (1976), but differ considerably from the work of Ellis and Giggenbach {1971). Further measurements are needed to clear up these discrepancies. We feel that the values determined from thermodynamic data are more reliable than experimental measurements due to the failure of both studies to characterize the pH of the solutions. Measurements of pK1 for H2S in seawater have been made by Goldhaber and Kaplan {1975) and Almgren et al. (1976). The results of Goldhaber and Kaplan (1975) are on the NBS pH scale (Bates and Culberson, 1977), while the results of Almgren et al. (1976) are on the total proton concentration scale (Hansson, 1973). The apparent constants (K') of Goldhaber and Kaplan (1975) are defined by K'I = an [HS-] T/[H2S ] W

(13)

while the stoichiometric constants (K~)of Almgren et al. (1976)are defined by g~ = [H]T [HS-]T/[H2S]T

(14)

The t...