Equilibrium constants and thermodynamics of ionization of aqueous hydrogen sulfide

293

Hydrometallurgy, 2 (1976/1977) 293-299 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

EQUILIBRIUM CONSTANTS AND THERMODYNAMICS OF IONIZATION OF AQUEOUS HYDROGEN SULFIDE

S. RAMACHANDRA RAO and LOREN G. HEPLER

Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, TIK 3M4 (Canada) (Received July 19th, 1976)

ABSTRACT

Ramachandra Rao, S., Hepler, L.G., 1977. Equilibrium constants and thermodynamics of ionization of aqueous hydrogen sulfide. Hydrometallurgy, 2 : 293--299. First (K,) and second (K~) ionization constants for aqueous hydrogen sulfide reported by various investigators have been reviewed, along with results of related calorimetric measurements leading to corresponding enthalpies of ionization. Following critical analysis of the published results, we have selected what we regard as "best" values for the ionization constants and related thermodynamic quantities. We call particular attention to significant uncertainties in these quantities for the higher (above 25°C) temperatures that are generally most important in hydrometallurgy.

INTRODUCTION Rational development of procedures for hydrometallurgical treatment of sulfide ores and for use o f h y d r o g e n sulfide as a h y d r o m e t a l l u r g i c a l reagent (for e x a m p l e , Simons, 1 9 6 3 ) b o t h d e p e n d o n k n o w l e d g e o f the i o n i z a t i o n o f a q u e o u s h y d r o g e n sulfide at the t e m p e r a t u r e s o f interest. Here we p r e s e n t a critical s u m m a r y o f the i n f o r m a t i o n t h a t is available for b o t h t h e first a n d s e c o n d i o n i z a t i o n c o n s t a n t s o f a q u e o u s h y d r o g e n sulfide over a wide range o f t e m p e r a t u r e . Results o f s o m e n e w t h e r m o d y n a m i c analyses are also presented. IONIZATION OF H2S(aq) In Table 1 we p r e s e n t a s u m m a r y o f published values o f the equilibrium c o n s t a n t K, f o r the first i o n i z a t i o n o f H2S(aq). These same published K, values are d i s p l a y e d (log K , vs. 1/T) in Fig. 1. We have c o n s i d e r e d earlier reviews and all o f the results s u m m a r i z e d in Table 1 in o r d e r t o arrive at o u r choices f o r the following " b e s t " values:

294

TABLE 1 E q u i l i b r i u m c o n s t a n t s for H : S ( a q ) = H÷(aq) + HS-(aq) T e m p . (°C)

K l x 107

ref.

0 5 10 15 18 20 22 25 30 35 40 45 50 55 60 90 109 167 228 276

0.27, 1.0 0.47 0.55, 0.58 0.75 0.58 t o 3.3 0.83 t o 1.3 0.95 0.85 t o 1.6 1.0, 1.3 1.0, 2.2 1.6 2.9 1.2 to 2.0 2.1 2.4 2.8 2.3 1.2 0.36 0.15

a, b c c, d c e, f, g, h, i c, i, j, k, 1 m b--d, n - - t c, u d, i c i b--d j d m j j j j

a. b. c. d. e. f. g. h. i. j. k. 1. m. n. o. p. q. r. s. t. u.

J e l l i n e k a n d Czerwinski, 1922. L o y a n d H i m m e l b l a u , 1961. Wright a n d Maass, 1932. T u m a n o v a et al., 1957. Paul, 1899. Walker a n d C o r m a c k , 1900. A u e r b a c h , 1904. E p p r e c h t , 1938. G o l o v i n , 1 9 5 8 a n d 1959. Ellis a n d Golding, 1959. Kubli, 1946. W i d m e r a n d S c h w a r z e n b a c h , 1964. Ellis a n d Milestone, 1967. B r u n e t a n d Zawadski, 1 9 0 9 a n d 1910. Ellis a n d A n d e r s o n , 1961. Ellis a n d G o l d i n g , 1959. Ste-Marie et al., 1966. Thiel a n d Gessner, 1914. Yui, 1951. C a l c u l a t e d b y K u r y et al. ( 1 9 5 3 ) f r o m Kubli (1946). M u h a m m a d a n d S u n d a r a m , 1961.

295

-6.6 68 -TO

Z c

72 74 Z6 -78

200C 210 I ; 2.2

110C ;1 ; 214 26 2.8 ( 1 / T ) x 10 ~

60C I 3.0

312

25C I 3.4

i 3.6

Fig. 1. Graph of log K~ vs. l I T for the first ionization of aqueous hydrogen sulfide. Lines indicate ranges o f / ~ values reported at some temperatures and dots indicate single K, values reported at some temperatures.

H2S(aq) = H÷(aq) + H S - ( a q ) logK~ =--6.99

[25°C; 2 9 8 K]

(1)

K1 = 1.02 X 10 -7

A G ] = 9 . 5 4 kcal m o l -~ = 3 9 . 9 2 k J m o l -~ /XH~, = 5.3

kcal mo1-1 = 22.2

k J mo1-1

/xS] = - - 1 4 . 2 cal K -1 m o l -~ = - - 5 9 . 4 J K -1 mo1-1 C o m b i n a t i o n o f o u r " b e s t " values a b o v e w i t h t h e a p p r o x i m a t i o n t h a t o

ACp = 0 f o r r e a c t i o n (1) leads to

log g l = - - ( 1 1 5 8 / T ) - - 3 . 1 0

(2)

mad t h e s t r a i g h t line d i s p l a y e d in Fig. 1. We regard e q u a t i o n (2) as giving the " b e s t " values f o r K~ at t e m p e r a t u r e s n e a r e n o u g h t o 25°C t h a t setting /x C~ = 0 does n o t i n t r o d u c e serious e r r o r a n d suggest t h a t this range e x t e n d s f o r o n l y a b o u t 10 ° a b o v e a n d b e l o w 25°C. We m a y i m p r o v e on e q u a t i o n (2) a n d the resulting s t r a i g h t line in Fig. 1 b y allowing AC~ ¢ 0. In the a b s e n c e o f c a l o r i m e t r i c results t o give us i n f o r m a o t i o n a b o u t AC~ f o r r e a c t i o n (1), we t e n t a t i v e l y t a k e ACp = - - 7 5 cal K -1 m o l -a and o b t a i n t h e following: /~H~ = 2 7 6 6 1 - - 75 T

[cal m o F 1]

(3)

/xS~ = 4 1 3 . 1 - -

[cal K -1 mo1-1]

(4)

751n T

A G ] = 2 7 6 6 1 - - 4 8 8 . 1 T + 75 T I n T

[cal mo1-1]

log K~ = - - ( 6 0 4 5 . 2 / T ) + 1 0 6 . 6 7 - - 3 7 . 7 4 4 log T

(5) (6)

296

Equation (6) leads to the curved line in Fig. 1, which is reasonably consistent with reported K1 values over a wide range of temperatures. But it should be noted that AC~ = --75 cal K -1 mo1-1 is considerably more negative than is c o m m o n (Larson and Hepler, 1969) for ionization reactions of type HA(aq) = H*(aq) + A-(aq) near 25°C. Choosing AC~ less negative than --75 cal K -1 mo1-1 for reaction (1) leads to calculated log K~ values that fall between the straight line and the curved line in Fig. 1. Further investigations (equilibrium and calorimetric) are needed in the temperature range above 25°C that is generally of greatest importance for hydrometallurgy. In Table 2 we present published values of the equilibrium constant K2 for the reaction HS-(aq) = H+(aq) + S=-(aq)

(7)

These same K2 values are displayed (log K2 vs. 1/T) in Fig. 2. There are very large discrepancies between results of different investigators and no certain way to resolve these discrepancies w i t h o u t doing more (better) measurements. The NBS Tech. Note 270-3 (Wagman et al., 1968) lists AG~ values that correspond to log K2 = --12.92 and K2 = 1.2 X 10 -13 at 25°C. Their AH~ values correspond to AH~2 = 12.1 kcal mo1-1. We use this AH~ and their log K2 at 25°C with the approximation that AC~ = 0 for reaction (7) to obtain the straight line in Fig. 2. All of this is in good agreement with the work of Kury, Zielen, and Latimer (1953), w h o made calorimetric measurements on the heat of neutralization of H2S(aq). Interpretation of their calorimetric results was based on log K2 = --12.94 at 25°C. We have found that use of any log K2

II 12

Y.~

.

14 u~ c

15

-16 -17

4,

1 -18

i!8

225C :1

2o

~12

125°C ~

2'4 126

~

28

60 °C I

3o

312

25 °C "~' I~

3.4

;

36

( 1/T ) x 703

Fig. 2. G r a p h o f log K 2 vs. 1/T for t h e s e c o n d i o n i z a t i o n o f a q u e o u s h y d r o g e n sulfide. L i n e s i n d i c a t e r a n g e s o f K 2 values r e p o r t e d at s o m e t e m p e r a t u r e s , d o t s i n d i c a t e single K 2 values r e p o r t e d at s o m e t e m p e r a t u r e s , a n d a r r o w s i n d i c a t e u p p e r limits o n K 2 r e p o r t e d for some temperatures.

297

TABLE 2* Equilibrium constants for HS-(aq) = H÷(aq) + S 2 -(aq) temp. (°C)

K 2 x 10 '4

ref.

0 10 14 18 20 22 24 25 30 35 40 50 60 70 75 90 100 125 150 175 200 225 250 300

0.006 to 3 25 < 0.00016, 0.0006 0.12, 6.0 0.71 to 36 2.5 < 0.0008 0.12 to 63 1.4, 17 89 25 13 to 120 52 < 0.004, 0.004 1.0 100 < 0.01, 2.5 5.0 7.9 13 16, < 30 20 25, < 60 < 100

a, v--y d j, z ~, k, l, p, ~, m z d, j, n, q, r, v, x,~, u, 5 d 6 d, m, v, 5 5 j, z v m j, v v v v j, v v j, v j

* Reference letters a through u are the same as in Table 1. v. Dickson, 1966. w. Jellinek, 1933. x. Maronny, 1959. y. Wasastjerna, 1922. z. Giggenbach, 1971. ~. Knox, 1906. ~. Kilster and Heberlein, 1905. 7. Konopik and Leberl, 1949. 5. Zavodnov and Kryukov, 1960. Calculated by Kury et al. (1953) from results of Kubli (1946) and Konopik and Leberl (1949).

s u b s t a n t i a l l y m o r e n e g a t i v e t h a n - - 1 3 ( s u c h as - - 1 7 ) is i n c o n s i s t e n t w i t h t h e concentration dependence of the calorimetrically measured heats of neutralizat i o n , w h i c h is i n d i r e c t e v i d e n c e t h a t l o g K2 is less n e g a t i v e t h a n - - 1 7 , c o n t r a r y t o t h e c o n c l u s i o n s o f G i g g e n b a c h ( 1 9 7 1 ) a n d Ellis a n d G i g g e n b a c h ( 1 9 7 1 ) . Stephens and Cobble (1971) have made calorimetric measurements of heats of s o l u t i o n o f K H S ( c ) in s o l u t i o n s c o n t a i n i n g d i f f e r e n t c o n c e n t r a t i o n s of O H - ( a q ) . T h e y h a v e i n t e r p r e t e d t h e i r r e s u l t s a t 25°C w i t h l o g K2 = - - 1 3 . 7 8

298

and have f o u n d AH~ = 13.1 kcal mol -~. Their results also are inconsistent with log K2 = --17. Stephens and Cobble (1971) have carried out furt her calorimetric measurements at 95°C with results that pe r m i t t e d them to calculate an average AC~ = --25 CaloK-1 mol -~ for reaction (7) over the t em perat ure range 25 to 95 C. This ACpis less negative than is c o m m o n (Larson and Hepler, 1969) for ionization reactions of t y p e HA-(aq) = H÷(aq) + A 2 -(aq). In spite of uncertainties, AC~ = --25 cal K-' mo1-1 is surely an i m p r o v e m e n t over/xC~, = 0 as used in obtaining the straight line in Fig. 2. Calorimetric results from Juza and U p h o f f (1956) also lead us to AH~ = 13 kcal mol -~ for reaction (7). We have used log K2 = --13.78 at 25°C, AH~ = 13.1 kcal mo1-1 at 25°C, and an average AC~ = --25 cal K -~ mo1-1 from Stephens and Cobble (1971) to obtain an equation t ha t is nearly the same as their equation (18) and thence the curved line in Fig. 2. Retaining AC~ = --25 cal K -~ mol -~ to still higher temperatures leads to A/-/~2 = 0 and thence to a m a x i m u m in log K2 at T = 822 K (549°C), which is o f f the left side of our Fig. 2. Although we believe that the best overall interpretation of published results is consistent with log K2 = --13 and A/4~: = --12 or --13 kcai moF 1 at 25°C, we are unable to justify com pl e t e rejection of the results of Giggenbach (1971) and Ellis and Giggenbach (1971) and their m u c h more negative values of log K2; fu r th er measurements are needed. ACKNOWLEDGMENTS

We are grateful to the National Research Council o f Canada and the Whiteshell Nuclear Research Establishment (Atomic Energy of Canada Limited) for s u p p or t o f this work.

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299

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