Biogenic Sulfur in the Environment - American Chemical Society

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of

18

Thermodynamics and Kinetics Hydrogen Sulfide in N a t u r a l Waters Frank J. Millero and J. Peter Hershey Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149-1098

The thermodynamic and kinetic measurements recently made on the H S system in natural waters have been critically reviewed. Thermodynamic equations are given for the solubility and ionization of H S 2

2

in water, seawater and brines. Pitzer interaction coefficients are given so that the pK for the ionization can be calculatedfrom0 to 50°C and I = 0 to 6m in natural waters containing the major sea salts (Na , Mg , Ca , K , Cl-, SO4 ). The kinetics of oxidation of H S with oxygen and hydrogen peroxide 1

+

2+

2+

+

2-

2

has also been examined as a function of pH, temperature and ionic strength. Equations are given for the second order rate constants for these oxidation reactions as a function of these variables. At the levels of O (200 μΜ) and H O (0.1 μΜ) in 2

2

2

surface sea waters, the oxygen oxidation is 70 times faster than peroxide oxidation. In rain waters, however, the concentration of hydrogen peroxide (100 μΜ) is great enough so that it is the dominant oxidant for H S. 2

The formation of H S occurs in a variety of natural waters. It is formed by bacteria under anoxic conditions 2

0097-6156/89/0393~0282$09.00/0 « 1989 American Chemical Society

In Biogenic Sulfur in the Environment; Saltzman, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

18. MILLERO AND HERSHEY

H£ in Natural Waters

283

This bacterial production occurs in the pore fluids of sediments and in stagnant basins (seas, lakes,riversand fiords). At the interface between anoxic and oxic waters the H S can be oxidized. This oxidation is frequently coupled to changes in the redox state of metals CL2) and non-metals (2). Another major interest in the H S system comes from an attempt to understand the authigenic production of sulfide minerals as a result of biological or submarine hydrothermal activity and the transformation and disappearance of these minerals due to oxidation (4). For example, hydrothermally produced H2S can react with iron to form pyrite, the overall reaction given by 2

2

2S0 - + 4H+ + l l F e S i 0 — - > FeS2 + 7 F e 0 + H S i 0 + 2 H 0 2


4

2

4

3

4

2

(2)

2

The oxidation of pyrite (FeS ) is thought to involve the dissolution of FeS and subsequent oxidation of HS" and F e . Recently, workers (5) have been examining the equilibrium and kinetic factors that are important at the oxic-anoxic interface. The kinetic behavior is difficult to characterize completely due to varying rates of oxidation and absorption above the interface and varying rates of reduction, precipitation and dissolution below the interface (2.5). Bacterial catalysis may also complicate the system (I). Although one can question the importance of abiotic thermodynamic and kinetic processes at this interface, we feel it is useful to use simple inorganic models to approximate the real system. Recently, the thermodynamics and kinetics of the H S system in natural waters has been reviewed (£). From this review it became apparent that large discrepancies existed in rates of oxidation of H S and the thermodynamic data was limited to dilute solution. In the last few years we have made a number of thermodynamic (7.8) and kinetic (9.10) measurements on the H S system in natural waters. In the present paper we will review these recent studies. The results will be summarized by equations valid for most natural waters. 2

2

2 +

2

2

2

Thermodynamics of W S ip AqWQtfS Solutions 2

The chemistry of H S in natural aqueous solutions is characterized by the following reactions 2

H 2

S ( g ) - - > H S(aq)

(3)

2

HS

> H

+

2

+ HS-

HS"

> H

+

+ S"

(4)

2

(5)

The concentration of H2S gas in solution ( C , mol kg" ) at equilibrium with various gas fugacities (f|i2s) be determined from 1

0811

C* = f H s / H 2

S

(6)

where He is the Henry's law constant. For pure water the value of Hg (atm - kg 1

H 0 mor ) can be determined from (1L12) 2

log H = 103.70 - 4455.94/T - 37.1874 log T + 0.01426T s

(7)

where T is the absolute temperature (°K) and the equation is valid from 25 to 260°C(a = 0.001).


284

BIOGENIC SULFUR IN THE ENVIRONMENT

The most extensive measurements of the solubility of H S in seawater were made by Douabel and Riley (12). Their results from 2 to 30°C and 0 to 40 salinity [I = 19.92S/(10 + 1.005 S)] have been refitted to 2

3

In K (mol l-l atm-l) = -44.6931 + 71.4632/T + 16.8818 In (T) + s

S[0.87627 - 0.40081/T - 0.13037 In (T)]

(8) 1 a

t

m

H

where K = 1/H and the results are valid for fu2S = °f ? S (* = 0.5%). The decrease in the solubility of H S with the addition of salt or the salting out can be represented by the Setchenow equation s

S


2

ln(Cb/C) = ln

=kl

7 g

(9)

where CQ and C are the solubilities in water and salt solution, 7 is the activity coefficient of the gas, k is the salting coefficient and I is the ionic strength. The value of k for seawater can be determined from g

l(Pk = 87.43 - 2.5317t + 3.1982 x 10-2t

2

(10)

3

where t is in °C and the a = 0.4 x 10* in k. The value of y is 1.03 for average seawater (S = 35 or I = 0.723) at 25°C. This is similar to the value found for other acids ( = 1.0 for H F (14)). The value of 7 for other ionic media can be estimated from the solubility of H S in NaCl solutions (15). Results at 25°C are given by (8) g

7 g

g

2

k25 = 0.1554-0.008061

(11)

Values of 7 ^ at other temperatures can be determined from log 7

2

H 2

2

S - 1*25 - 2.5321 x 10-3 (t-25) + 3.1984 x 10-5 (t -25 )] I

(12)

which uses the temperature dependence of k in seawater (2). New measurements of the solubility of H S in the major sea salts as a function of ionic strength and temperature would be useful, but since NaCl is the major salt of most natural brines, this is not a serious limitation. Since 7 is near 1.0 for seawater, the interactions of H S and the major sea salts are quite small. Since H S dissociates in aqueous solutions (equations (4) and (5)), it is necessary to have reliable equilibrium constants tor the ionization. These constants are defined by 2

g

2

2

K

x

= ([H+][HS-]/[H S])( 7 H S A H S ) 2

7H

(!3)

2

1 4

K = ([H+][S2-]/[HS-])( 7S/7HS) ( ) where [i] and n are the concentrations and activity coefficients of species 1. As discussed elsewhere (£), experimental results for the K of H S cover a wide ranee of values (pK = 12.4 to 17.1 near 25°C). Recent work of Meyer et al. (10 supports the higher value of p K = 17.1 measured spectroscopically by Giggenbach (12). The lower values are apparently in error due to the oxidative formation of polysulfides that interfere with the determination of pKo. Since we feel this higher value is correct and in the pH range of most natural waters the concentration of S * is quite small, we will not consider the second dissociation of H S any further. 2

7H

2

2

?

2

2

2


18. M I L L E R O A N D H E R S H E Y

H^S in Natural Waters

285

The thermodynamic first dissociation constant for H S at infinite dilution can be determined from (g) 2

pK = -98.080 + 5765.4/T + 15.0455 InT

(15)

x

which is valid from 0 to 300°C. The equation has a a = 0.04 from 0 to 100°C and is thought to be valid to ± 0.1 above 100°C (IS). Measurements of the first dissociation constant for H S in seawater have been made by a number of workers. The measurements of Savenko (12) and Goldhaber and Kaplan (2Q) were made using the National Bureau of Standards (N.B.S.)pH scale (21) Downloaded by UNIV OF MINNESOTA on June 4, 2013 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch018

2

K i =aH[HS-]/[H S] 2

(16)

T

where a u ' is the apparent activity of the proton obtained with N.B.S. dilute solution buffers. The measurements of Anngren et al. (22) arid Millero et al. (2) were made using the total proton scale (22) r^IH+lTlHSIx/IH^T

(17) +

where the subscript T is used to denote the total concentration, i.e., [H ]x = [ H ] + [HSO4 ] + [HF]. The two scales are related by (24) +

F

+

a ' - f [H ] H

H

(18)

T

where fjj is the apparent activity coefficient of the proton. This value includes effects of liquid junctions, the definition of the N.B.S. scale and the activity coefficient ot the proton (24). The apparent constants of Savenko (12) and Goldhaber and Kaplan (20) have been fitted to p K i « p K + A ' SV2 + B'S

(19)

t

where A ' = 0.0057-19.98/T

(20)

B' = 0.0028

(21) 1

with a a = 0.019 in pK^ (mol kg-SW' ). A n examination of the residuals between the measured and calculated results as a function of T and S is shown in Figure 1, demonstrating that the two studies are in good agreement and that the electrode systems used give similar values of fj|. The results of Millero et al. (2) were combined with the adjusted pKi values of Savenko (12) and Goldhaber and Kaplan (2Q) to yield the consensus equation pK*x = pKx + A* SV2 + B*S

(22)

where A* - -0.1498

(23)

B* = 0.0119

(24)


286



0.08

Figure 1. Values of AJ>KI using the data of (O) Goldhaber and Kaplan (2Q) and (O) Savenko (12)fittedto Equation 19 as a function of (A) T and (B) S.




287

1

with a a = 0.028 in pK*! (mol kg-SW* ). The values of pK* at 25°C from the two studies are shown in Figure 2. The experimentally determined values of fa of Mehrbach et al. (25), Culberson and Pytkowicz (2fi) and Millero (22) were fitted to x

f

2

= 0.739 + 3.07x 10-3 + 7.94x 10*5 S +

H

6.443 x 10-5T -1.17 x 1(H TS

(25)


which has a a = 0.006. The values of fn from this equation were used to calculate the pK*x from the pK^ using pK*! = pK

, 1

+ log f

(26)

H

It should be pointed out that the pK% results of Almgren et aL (22) were 0.07 ± 0.02 higher than other workers and were not used to obtain the consensus equation. The residuals of errors for the pK*i fit for various workers are shown in Figure 3. These residuals demonstrate that the three studies are in good agreement when adjusted to the same pH scale. In our earlier work (28.6) we demonstrated how Pitzer parameters can be generated from pK% measurements in various ionic media. Recently we have extended these calculations to higher ionic strengths from 0 to 50°C (2). The activity coefficients for m and 7HS using the Pitzer (22) equations are given (22^21) ln H = f

7

+ s2m (BHx + E C H X + ^ M ^ X ^ ' M X + C M X )

7

x

+

(2*MH

+

M

In7HS = f? + s 2 m ( B M

2 7

X *HMX) M H S

( )

+ E C M H S ) + ^ M ^ x ( B ' M X • + CMX)

2

+

2 +

(28)

2 +

where X = Cl% S0 % etc. and M = N a , M g , C a , etc. The definition of the Debye-Hiickel slope, fr, and the interaction parameters, B^x* C M X -> are given in Appendix I. The parameters needed to calculate the values of TH and 7HS f ° various natural waters are given in Table I. These parameters yield calculated values of pK*i in NaCl, KC1, MgCl and CaCl solutions from 5 to 45°C and I = 0 to 6 to ± 0.02 in pK*!. The reliability of these parameters can be demonstrated by comparing the measured and calculated values of pK* for seawater. The differences, ApK* , are shown in Figure 4. The agreement is quite good and well within the standard error of the experimental data (a = 0.026). Measurements of pK* in artificial Dead Sea brines (22) gavepK*x = 7.25 ± 0.03 at 25°C compared to a calculated value of pK*x = 7.30. Tne agreement is quite good and indicates that the parameters are valid to I = 6.0. Since the 7 H S is approximately equal to 7C1 (22)> a reasonable approximation of pK*i can be made to high temperatures using the temperature coefficients for CI" salts. Future measurements using spectrophotometric techniques should be made on the p K * i in the major sea salts at high temperatures. The effect of pressure on the Ki can be estimated from 4

ETC

r

2

2

x

x

x

0

l n ( K i y K i ) = - ( A V X / R T ) P + 0.5 ( A K J / R T ) P

2


(29)


288


8.0

7.5-

GL

1

2

Figure 2. Values of pK*x versus S / at 25°C from the present work and adjusted values of (•) Savenko (12) and (O) Goldhaber and Kaplan (2Q)and (CI) the present work. Fitted curve determined from the values of the present work.


MILLERO AND HERSHEY



18.


289


290


Table I. Pitzer Coefficients used to Calculate Ion Activity Coefficients for H and H S a

HCl q cfe q q q q q x

4

6 7

9

1 0

b

KC1«>

0.32779 3.88370 -5.478xl(H -0.14553 -1.4759x10-3 1.523xl(H 2.1725x10-5

0.22518 -5.9309x10-3 -0.22796 1.4763x10-3 -1.5852x10-3 2.4993x10^

NaCl

c

NaHS

d

KHS M g H S C a H S

d

25.7819 0.3662 0.6371 0.170 -0.105 -777.03 -67.54 -138.5 8.946x10-3 . . . 0.1528 2.78 3.43 6.161x10-5 . . . -0.63337 -0.01272 -0.1935 33317 . . .

= 91 + q i / J + Ch InT + q + qs «J) = q + q T + q g ^ 4

6

b. c. d.

7

Calculated from the mean activity coefficients tabulated in Harned and Owen (61). Values of = -4.4706, C|5=-3.3158xl0- , q»=1.0715X10" , q =9.421x10-2 9.12=-4.655x10-5 are also from Silvester and Pitzer (£2). Calculated at 25°C. 6

6

u


18.

MILLERO AND HERSHEY

HJ5 in Natural Waters

0.03


0.02H Q.

Products 2

(34)

2

has been studied by a number of workers (9.34-40V The oxidation kinetics are complicated and tne results of various workers are not in good agreement (6). The overall rate equation is given by d[H S] /dt = -k [H S]a[02]b 2

T

(35)

2

where n = a + b is the overall rate of the reaction. Although Chen and Morris (41) found a = 1.34 and b =0.56, most workers have found the reaction to be second order (first order with respect to H S and 0 . When [OJ > [H S] the reaction is pseudo-first-order 2

2

2

d[H S] /dt = -ki[H S] 2

T

(36)

2

where k i = k[0 ] and the half-time, tin = (In 2)/k/. As discussed in an earlier review (£), the values of tin vary from 0.4 to 65h (see Table II). We have made a number of measurements on the oxidation of H S by O j as a function of temperature, ionic strength and pH to resolve these discrepancies. In our first series of measurements we determined the pseudo-first-order rate constant (k\) for the oxidation of IhS in water and seawater (S = 35) as a function of temperature at a pH = 8.0. Our results for the overall rate constant k = k'j/[02>] were calculated from these results using the values of [0 ] determined from the equations of Benson and co-workers (44.45^. The results are shown plotted versus 1/T (°K) in Figures 5 and 6. The energies of activation, E , for the oxidation calculated from 2

2

2

a

E = (dlnk/dT)RT>

(37)

a

1

were found to be E = 56 ± 4 kJ moH and E = 66 ± 5 kJ mol" , respectively, for water and seawater. Within the experimental error (0.18 in log k) a value of E = 57 ± 4 kJ mol can be used to represent the effect of temperature on the oxidation of H S in water and seawater. This energy of activation is slightly higher than the value of E = 46 kJ mol" at a pH = 12 in water (26). The a

a

-1

a

2

1

a



18.


MILLERO A N D HERSHEY

293

Table II. Comparisons of the Half-Times for the Oxidation of H S in Air Saturated Solutions at 25°C and pH = 8.0 2

Media

ti/

References

Water

50 37 50 18 26 27 10-40 65 6-28 2-5 0.4

2

h

a

b

Seawater

a

c

Our results O'Brien and Birkner(42) Chen and Morris(41) Avrahami and Golding(26) Our results O'Brien and Birkner(42) Sorokin(2S) Skopintsev et al.(25) Cline and Richards(22) Almgren and Hagstrom(42) Ostlund and Alexander(24)

a) Water results extrapolated to I = 0, seawater results at I = 0.7. b) A t a p H = 12. c) At 9.8°C.


294



4.0

00 I 2.9

1 3.1

'

1

•

1

3.3

3.5

>

1 3.7

1000A

Figure 5. Values of log k for the oxidation of H S in water versus 1/T at pH = 2

4.0

1.CH

1000/T

Figure 6. Values of log k for the oxidation of H S in seawater (S = 35) versus l / T a t p H = 8.0. 2




295

difference could be related to the changes in E as a function of p H and possibly due to the strange p H behavior of the oxidation of H S above a pH = 10 found by earlier workers (41). In our next series of measurements we determined the effect of pH on the oxidation of H S in buffered dilute solutions. The measurements were made at 55°C to speed up the acquisition of data. The results are shown in Figure 7. The results from pH = 2 to 8 are similar to the earlier measurements of Chen and Morris (41). Above a p H = 8 we find the rate to be independent of pH unlike the results of Chen and Morris (41) who find a complicated p H dependence. This could be related to trace metal impurities in the buffers used by Chen and Morris (41). Hoffmann and Lim (4&) have examined these trace metal effects and the base catalysis of the oxidation of H S. As discussed elsewhere (6,9.46). the effect of pH on the oxidation of H S can be related to the reactions a

2

2


2

2

HS +0 2

HS- + 0

2

2

— > Products

(38)

— > Products

(39)

where ko and ki are, respectively, the rate constants for the oxidation of H S and HS*. The observed rate constant is related to these values (£) by 2

K

= V H

2

4

S + M H S

( °)

The fraction of H S and HS* are given by 2

" H S = V ( l + Ki/IH+D

(41)

2

+

° H S - V ( l + [H ]/Kx)

(42)

where K is the thermodynamic dissociation constant for the ionization of H S. The rearrangement of equation 40 yields the linear equation x

2

k/aH s = ko + kiKi/IH+J

(43)

2

+

Values of k / a m j plotted versus 1/[H ] are shown in Figure 8. The least squares straight Tine gives b) = 80 ± 17 (kg H 0 ) mol" hr* and k = 344 ± 7 (kg H 0 ) mol*l h r using pKi = 6.68 (fi). The values of k determined from 1

2

x

1

2

k = (ko + k x K x / I H + M l + KiAH+D

(44)

are shown as the smooth curve in Figure 7. The standard deviation between the measured and calculated values of log k is 0.10. We have also determined the effect of ionic strength on the oxidation of H S in NaCl solutions. The values of log k measured at 45°C are shown as a function of I / in Figure 9. They can be represented by 2

1 2

log k = 2.33 + 0.50 I V

2


(45)



296

2.8

1.6H 0

.

1 2

.

1 4

«

1 6

«

1 8

«

1 « 1 10 12

1 14

PH Figure 7. Values of log k for the oxidation of H S in water versus pH in water at 55°C. Fitted curve determined from Equation 44. 2


MILLERO AND HERSHEY

HjS in Natural Waters


18.


297



298




299

with a a = 0.12 in log k. The slope of 0.50 ± 0.08 can be compared to a value of 0.49 ± 0.2 obtained at 25°C by O'Brien and Birkner (42) from 0.16 to 1.78 in NaCl solution. The agreement is good and within the combined experimental error of the measurements. All of our experimental measurements at a pH = 8.0 can be combined to yield the equation 1

log k = 11.78 - 3.0 x 1(P/T + 0.44 I /

(46)

which has an overall a = 0.18 in log k. The slope of log k (0.44 ± 0.06) versus I / for seawater found over the entire temperature range is the same within experimental error as found for NaCl (0.50 ± 0.08) to saturation at 45°C. A comparison of our results expressed as half-times with other workers is given in Table II. Our results for water are in good agreement with the work of O'Brien and Birkner (42) and Chen and Morns (41). The lower half times obtained by Avrahami and uolding (26) may be related to the high p H = 12 used for the measurements. Over a pH range of 11 to 14, thev found large changes in the half-times (an increase in pH of one unit decreased the half time by two). Thus, the extrapolation of their results to a pH = 8 would increase the half time eight times. We have used the U.V. spectra method at a pH = 8.0 and obtained halftimes that are in reasonable agreement with the values obtained with the methylene blue technique (see Figure 10). Our seawater results are in good agreement with the work of O'Brien and Birkner (42) in NaCl solutions at 0.7 m and in fair agreement with the seawater work of Sorokin (22) and Skopintsev et al. (25). The seawater results of Cline and Richards (22) show a wide range depending upon the experimental conditions used (47.48). A n average value of t i / = 12 ± 7 h is obtained at 9.8°C and [O2] = 225 /iM from all the experiments except for the addition of iron (4g). At 25°C this would give a tin = 4 h which is much lower than our results. We have no logical explanation for this difference. The lower half-times determined using the emf technique (34.43) requires some discussion. In our earlier studies of the H S oxidation, we made numerous seawater measurements using this emf technique at a pH = 8.0 and 25°C. As found by Ostlund and Alexander (24) and Almgren and Hagstrom (42) in low concentrations of [H S]x = 20 M M , reasonably linear plots were obtained (see Figure 11). We obtained half-times of 2 to 3 hours at 25°C that were only slightly dependent upon salinity. The results were quite variable and we frequently obtained a non-linear behavior of the emf and dramatic changes if the experiments were carried out over long time periods. A methylene blue analysis of the solutions after a run (« 6 hours) showed only small changes in the (H S]x giving t i / « 24 h compared to 2.5 h with the emf technique. This led us to believe that the emf technique was sensing the disappearance of electrochemically active sulfur (S ") due to the formation of polysulfides in the solution or on the surface of the electrode. This was demonstrated by the changes in the emf after the addition of 0.01 M tributylphosphine (which breaks S-S bonds) to the solutions. Although we cannot state with certainty the exact cause of the observed effects, we feel that the emf method does not give reliable results for the oxidation of H S with O?. It is interesting to note that similar emf measurements of the oxidation of H S with 1000 M M fl 0 (Figure 12) gave half-times (14 to 30 min) for seawater that were in good agreement with the U . V . spectra technique (see Figure 13). These half-times are sufficiently fast to avoid the problems of deactivation of the electrode or formation of polysulfides. More will be said about the oxidation of H S by H 0 in the next section. 1


2

2

2

2

2

2

2

2

2

2

2

2

2

2

2



300

o.o-o o

o o

o

o o o o o

o O Oo

-.5-

E

-565-

E 0)

-575

-585

Time/min

Figure 11. Values of emf versus time for air oxidation of H S with 0 at pH 8.0 in seawater (S = 35) where [H S]° = 20 fM. 2

2

2



301


-560

-570

> E

>

-580

E Downloaded by UNIV OF MINNESOTA on June 4, 2013 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch018

0)

-590

-600 Time/min

Figure 12. Values of emf versus time for the oxidation of H S with 1000 fM H 0 a t 2 5 ° C a t p H = 8.0. 2

2

2

-1.5

-3.0-

10

r-f-r 15

20

25

30

Time/min

Figure 13. Values of In absorbance at 229nm versus time for the oxidation of H S with H 0 in water at 25°C at pH = 8. 2

2

2


302


Since Products 2

2

(49)

2

has been studied by a number of workers (49-53). The most extensive measurements were made at 25°C by Hoffmann (42) as a function of pH (2 to 8.1). We became interested in the oxidation of H S by H 0 due to the findings of Zika and co-workers (55-56) of 0.1 M M concentrations of H 0 in surface waters. The concentrations in rainwater can be higher (100 fM); thus, peroxide may be the preferred oxidant in rainwaters and marine aerosols. To elucidate the kinetics of oxidation of H S by H ^ ^ we have made measurements on the effect of temperature, ionic strength and pH on the reaction (2). In our first series of measurements we determined the pseudo-first-order rate constant (k\) for the oxidation of H S by H 0 ? in water at a p H = 8.0 (0.01M borax) and 25°C as a function of [ A s i ^ r = 23 to 200 /*M at [ H P J = 5000 /iM and as a function of [ B j O J = 500 /iM to 60 mM at [ H S ] = 25)*M, where the superscript (°) indicates initial concentration. The pseudo-firstorder behavior as a function of [H S]° is shown in Figure 14. The value of k\ was found to be 0.13 ± 0.02 min* . This first order behavior relative to [H S]° agrees with the earlier findings of Hoffmann (4£). The order with respect to H 0 was examined by plotting log k'i versus the log [ H 0 ] ° as shown in Figure 15. The slope is 0.94 ± 0.(M which is essentially first order. If the reaction is assumed to be first order the value of k = ii/lRjfM = 30 ± 5 min M is found for the 27 measurements made at pH = 8 and 25°C. These findings are also in reasonable agreement with the results of Hoffmann (4£) who found k = 10 to 87 min" M-^ between pH = 6.8 to 8.1 and 25°C. In all our subsequent discussions we will examine the overall rate constant k for 2

2

2

2

2

2

2

2

0

0

0

2

T

2

1

2

2

2

2

T

2

0

-1

_ 1

1

d[H S] /dt = -k[H S] [H 02] 2

T

2

T

2


(50)




•

303

25/iM

•

50*1*1

v

100/iM

Time/hr

Figure 14. Values of In [HoSfr versus time for the oxidation of H S with H2O2 for different values of [H S] ° (pH = 8.0, in 0.01 M Borax at 25°C). 2

2

T

0.5

log [ H 0 ] ° 2

2

Figure 15. Values of log k i versus log [H2O2] for the oxidation of H S with H ^ O (kj is the pseudo first order rate constant) (pH = 8, in 0.01M borax at 0

2

?


304


In our second series of measurements we examined the effect of ionic strength on the rate of oxidation at a pH = 8 and at 5, 25 and 45°C. These results are shown plotted versus the square root of ionic strength in Figure 16. Over most of the ionic strength range the values of log k were found to be linear functions of I / independent of whether the measurements were made in seawater or NaCl. The slopes were almost independent of temperature and ranged between 0.04 to 0.12 (average of 0.08 ± 0.04 from 5 to 45°C). The slopes were smaller than the values of 0.44 ± 0.06 found in our measurements for the oxidation of H S by 0 (2). As mentioned earlier, extensive measurements made in seawater, using the emf and spectrophotometric technique as function of salinity shown in Figures 12 and 13, give results that agree with the more recent results (1Q) and also demonstrate that the rate constants are nearly independent of ionic strength. We also made a few measurements as a function of ionic strength at pH = 3 and 13. The results at p H = 13 gave log k = 1.33 ± 0.01 min" M ' for four measurements between I = 0 to 3m. At a pH = 3 in dilute solutions below 0.04M, no ionic strength dependence was found; however, at I = 3.0m, the rate was ten times faster that at I = 0. We attribute this increase in rate to the presence of trace metals. A l l of our runs at pH = 8 to 13 were made with enough borax to complex these trace metals and suppress the catalytic effect. A n experiment at pH = 11 without borax was completed within 5 minutes compared to 1.5 hours with 0.01 M borax. These results support our contention that the effect of ionic strength on the rates of oxidation are independent of pH if the catalytic effects of trace impurities are avoided. In our next series of measurements we examined the effect of temperature on the rate of oxidation of HoS by H 0 . These results are shown plotted versus the reciprocal of the absolute temperature (1/T) in Figure 1/. The energies of activation for seawater and NaCl were found to be E = 39 ± 1.2 kJ mol"^ independent of ionic strength. The energy of activation for H^S oxidation with HoOj is lower than the value ( E = 57 ± 4 kJ moH) found in our earlier work (§) for the oxidation of H S with 0 . A l l of our measurements at pH = 8.0 in seawater and NaCl have been fitted to the equation 1

2


2

2

1

2

1

2

a

a

2

1

log k = 8.60 - 2052/T + 0.0841 /

2

(51)

2

(with a a = 0.07 in log k. This equation should be valid for most natural waters from 0 to 50°C and to I = 6.0 near a pH of 8.0. The effect of pH on the rate of oxidation of H S with H 0 was determined from pH = 2 to 13 at 5, 25 and 45°C. These results are shown in Figure 18. Our results at 25°C from pH = 5 to 8 are in good agreement with the results of Hoffmann (4£) (See Figure 19). At lower values of pH, his results are faster than ours. This may be due to problems with the emf technique he used. For the slower reactions of H S with Oo or H 6 , the emf technique may yield unreliable results due to problems with the electrode response. The effect of pH on the oxidation of H S at various temperatures can be divided into two linear portions: from pH = 2 to 7.5 and from pH = 7.5 to 13. The increase between 2 to 7.5 has been fitted to (a = 0.18) 2

2

2

2

2

2

2

log k = 6.38 - 3420/T - 0.902 pH

(52)

and the decrease between 7.5 to 13 has been fitted to (a = 0.13) log k = 12.04 - 2641/T - 0.186 pH


(53)

18. MILLERO AND IIERSHEY

11

•

•

305


-

•

••

• B


•

—

a

— T

5

" ^ o

o

0 o

o

n

• o

.0 I • 0.0

0.5

i . . . . i • . . . I 1.5 2.0 2.5

1.0

Vi Figure 16. Values of log k versus I / for the oxidation of H S with H 7 O 2 seawater (+) and NaCl at 5, (O) 25 ( • ) and 45°C ( • ) (pH = 8.0, in 0.01M borax). 1

2

i n

2

1000 A

Figure 17. Values of log k' versus 1/T (T°K) for the oxidation of H S with H2O2 for seawater (A) and 6m NaCl (•) solution. 2


306



3.0

,

-3.0H 0

,

,

2

,

,

4

,

,

6

,

,

8

, 10

.

,

. 1

12

14

PH Figure 18. The effect of pH on the log k for the oxidation of H S with H 0 at 2

5 ( 0 ) , 2 5 Q ) a n d 4 5 0 C (A).

2

2

3.0 2.01.0o» o

0.0-

-O.U1

1

0

, 2

.

, 4

.

, 6

,

, 8

.

, 1 , 1 1 10 12 14

PH Figure 19. Values of log k versus pH for the oxidation of H S with H Oo compared to the experimental values at 25°C: ( • ) present work; ( • ) Hoffmann; (—) fitted curve accounting for ans" and OH202» ( - ) fitted curve accounting for a . 2

H S


2



307

These linear fits of log k as a function of pH are given in Figure 18. The effect of temperature on the results above pH = 7.5 is the same as found for the results in NaCl at pH = 8 (equation 51). The effect of temperature on the results below pH = 8 is different because of the effect of temperature on the ionization of B>S that occurs in this pH range. From a pH = 2 to 8, the rate increases in a near linear manner with increasing pH. This is related to the ionization of H?S and indicates that the HS" species is more reactive than H S. It is noteworthy that log k determined in this study does not appear to level off at low pH values as was found by Hoffmann (4£) for the oxidation of H?S by H2O2. The leveling off at low pH was also observed for the oxidation of HjS by oxygen (2). The leveling off at low values of pH can be related to the difference in the rates of oxidation of H S and HS- according to equation 40. A plot of k/c*H2S versus ki/[H ] is shown in Figure 20. The intercept kg = 0 at all temperatures is within the experimental error. The slopes give k = 12.0 ± 0.5, 36.2 ± 0.4, and 211 ± 5 mm* M * , at 5, 25 and 45°C, respectively. The values of In ki at the three temperatures have been plotted versus 1/T in Figure 21 and fitted to 2


+

2

x

1

1

In k! = 25.0 - 6306/T

(54) 1

which gives an energy of activation of E = 51 ± 3 kJ mol" for the oxidation of H S. This is larger than the value given earlier at a p H = 8 ( E = 39 ± 2 kJ) because it does not contain terms due to the effect of temperature on the dissociation of H S. The overall rate constant, k, is related to k by k«a ki. Thus, the differential of k with respect to T contains terms due to the effect of T on a^s and ki. The effect of temperature on a is related to the A H ° for the ionization of Ii S. The simplest mechanism suggested by the pH dependence between 2 and 8, is a rapid pre-equilibrium of the dissociation of H?S followed by a nucleophilic attack of HS" on H 0 with heterolytic cleavage of OH" in the rate determining step a

2

a

2

x

HS

H S

2

2

H S —> H 2

+

2

+ HS"

(55)

HS" + H 0 — > HSOH + OH" 2

(56)

2

where rate = -kxtHS-HH^]

(57)

Additional steps are the formation of polysulfides HS - and their subsequent oxidation by HSOH (4j&). By substituting the expression for [HS*], the following rate equation can be derived n

rate = - k i K x l H i S M H ^ / ^ ! + [H+])

(58) +

where the second order rate constant should be equal to k i K / ( K + [H ]). Using a value for k = 36 min M * and p K = 6.98 at 25k: (£), Figure 19 illustrates the p H dependence based on this simple mechanism. This mechanism predicts that when [H ]> >K that is, at the lower values of pH, the slope of log k vs pH should be a straight line with a slope of one. The 1

1

1

x

x

+

1?




308


18. MILLERO AND IIERSIIEY


309

experimental values of log k are within experimental error of this line at all three temperatures. The experimental points are lower than the calculated curve at pH values above 8.0 and falling off in a near linear manner. At pH>ll the [H2O2] is reduced due to its dissociation H 0 = H+ + H O f 2

(59)

2

where pKu202 = H-6 (58). The formation of HO2" causes the rates to decrease above a pH « 8.0 apparently due to the slow reaction of HS with HO2". If we assume tnat the reaction between HS" and HO2" is small, the decrease in k can be attributed to Downloaded by UNIV OF MINNESOTA on June 4, 2013 | http://pubs.acs.org Publication Date: April 27, 1989 | doi: 10.1021/bk-1989-0393.ch018

-

k =k a a o 1

H S

H 2

(60)

2

where +

«H^-IH ]/([H+] + K H ^

2

)

(61)

The 25°C results (dotted line in Figure 19) show that the addition of the correction for H2O2 ionization does improve the fit above a p H = 10, but does not explain the nearly linear decrease above pH = 8. The 5 and 45°C results shown in Figure 22 look slightly better. Obviously, this simple explanation does not completely explain the near linear dependence above pfr = 8. Other factors such as the formation of polysulnde ions (HS" ) and S " may be important. 2

n

3.0

pH

Figure 22. Values of log k versus pH for the oxidation of H^S with H2O2 at (A) 45°C; O 5°C; fitted curve accounting for OHS- and c*H202 (Equation 60).


310


Over the entire range of pH and temperature studied there was little or no dependence of the rate on ionic strength, that is, no salt effect. This result is consistent with the simple mechanism in that the slow step does not involve two ions. With at least one neutral molecule in the slow step, transition state theory predicts that the rate of the reactions will be independent of ionic strength. The half-life for the oxidation of sulfide in seawater with oxygen was 30 hours at 25°C. If one uses the [ H 0 ] = 1.0 x 10" M found (54.55) for surface seawater then the half-life for the oxidation of sulfide by peroxide in seawater would be 2800 hours. At concentrations of H C>2 > lfr* M , the oxidation of H2O2 with H2S becomes competitive with O2. Such concentrations of H2O2 are found in rain waters (58); thus, peroxide oxidation of H2S may be more important than oxygen oxidation in aerosols or rainwaters. 7

2

?


2

APPENDIX I The activity coefficients for 7 and 7HS using the Pitzer (29.59) equations are given (202128) by H

ln

= tf + s 2 m ( B H X + E C H X + ^ S H I M ^ X ( B ' M X + C M X )

7 H

x

+ sm (2* + m x ^ H M x ) M

ln

(

M H

A 1

)

s = & + ^ ^ ( B M H S + E C M H S ) + 2sm m (B x+C x) ,

7 H

M

X

M

M

2

2

+ E m ( * X H S + niM^MXHs)

(A )

X

where M and X are cations and anions, respectively, and -A*[I /2/(i+i.2lV2)+(2/1.2)ln(l + 1.2lV2)]

fr=

1

B = 0(0) + (2)8(l)/a2l)[l - (1 + ajVfyxpi-a^ / ) 1 2

1

(A3) (A4)

B ' = (2 8(l)/a 2l2)[.l + (1 + l V 2 + 2 I)exp(-a lV2)]

(A5)

C = CV2|Z Z |V2

(A6)

1

i

M

a i

a

1

1

X

and E = l / 2 S|m:Z:| where CM = 1.2 and the Debye Hiickel limiting law A * = l/3(2irN d /1000) /2( 2/DkT)3/2 has been previously defined (52). The parameters 0 and represent interactions between ions of the same charge and triple interactions, respectively. The Pitzer parameters have been fitted as a function of temperature to the following equations 1

o

0(0) =

w

q

i

e

+ q ^ T + q^nT + q + q s T

2

4

= Q6 + q?T + q T*

(A8)

8

& = 09 qio/T + qnlnT +

(A7)

q i 2

T

(A9)

The values of qj are riven in Table I. Further details For the method used for determining the Pitzer parameters are given by Pitzer (52), Millero (28.311 Harvie and co-workers (30.6m.




311

Acknowledgement The authors wish to acknowledge the support of the Office of Naval Research (N00014-87-G-0116) and the Oceanographic Section (OCE-8600284) of the National Science Foundation for this study.


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