The New Low Value for the Second Dissociation Constant for H2S Its History, Its Best Value, and Its Impact on the Teaching of Sulfide Equilibria Rollle J. Myers University of California. Berkeley, CA 94720 The value of the equilibrium constant Kz for the second dissociation of H2S %qi
@
H w t + ?S-,,
(1)
has always been subject t o considerable uncertainty. Most textbooks have used values between 10-'3 and lO-I4 (pK, = 13-14), and the S2- ion has been treated as if i t were a principal species in basic aqueous solutions. In their critical literature review dated 1976, Smithand Martell (1) chose for 25 OC and zero ionic strength the value pK. = 13.9 f 0.1 or K2 = 1.3(f 0.3) X 10-la. In 1971 Werner F. Giggenbach, a staff member a t the D e ~ a r t m e nof t Scientific and Industrial Research (DSIR) ,~~ . in M ' h g t o n , New Zealand, reported (20) that pK, = 17.1 f 0.2 at 2.1 "C. He had niadr ultraviolet liehr absnrution measolutions that did surements on very concentrated N ~ O G not contain any dissolved oxygen. At first, he had tried to repeat the measurements of some other DSIR workers (3). They had reported that the HS- absorbance near 230 nm would decrease, in what they thought were deoxygenated solutions, when [OH-] = 0.5 M. From this decrease they reported a room-temperature K2 value close to 10-14. Giggenbach completely excluded oxygen from his solutions and he could find no decrease in the HS- absorbance region even in 5 M NaOH. He could also not observe the absorbance near 365 nm which other workers ( 4 ) , who used oxygen-containing solutions, had reported for S2-. Giggenbach found an absorbance near 250 nm, which appeared as a shoulder on the more intense HS- absorbance, which he assigned to S2-. He used this absorbance to determine his new low value for /.Thesemeaiurement?i haverlearly demonstrated that the usls derrense in the HS- ahorbanre and the ~ r e \ ~ i ~ ~assigned S2- absorbance were the result of dissolved oxygen-and these effects were most likely due to the formation of polysulfides (26). . . I t now seems clear that K2 for H2S is much less than 10-l4 and that S2- is never a principal species in even moderately concentrated NaOH solutions. We will first review the other evidence for a low value and give our best estimate for Kz. We will then show that a low K2 value for HzS is very logical if we consider trends in the Periodic Table. An explanation of the traditional high values for K2 will be given, and lastly we will show how our teaching of sulfide equilibria should be modified in light of the new low value of K2. ~
~
~~
The Best Value of K2
Another independent measurement has recently appeared that confirms the low value for Kz. Meyer et al. (5) observed the H-S stretch of HS- using modern Raman methods. For 16.9 M NaOH they observed an approximate 50%decrease in the [HS-] and in 8.9 M NaOH they reported that the [HS-] was from 67 to 100% of its low OH- value. Their samples were handled under N2 gas and after the HzS gas was added they were sealed in uacuo. From a limited analysis of their measurements Meyer et al. selected a pK. = 17 f 1. There are a few older measurements in the literature that
have given Kz values lower than 10-15. Most of these are based upon sulfide solubilities ( 6 ) ,but the most direct estimate for a low K Z value were the titrations repoked by Tsonopoulos et al. (7). They were determining the first constant K1 using indicators for pH and with Ar gas to protect against 02, but they also reported that 0.1 M HCI gave identical curves when titrated against 0.28 M Na2S and 0.28 A4 NaOH. This would require complete protonation of SZand they estimated that K2 5 2 X 10-16. From all the evidence for a low Kz value, Brewer selected pK. = 17 f 2 in his recent thermodynamics review (8). Giggenbach's value of 17.1 f 0.2 is based upon two treatments of his data. In his first evaluation he used a completely empirical equation to extrapolate the apparent pK. values in his 8-18 M NaOH solutions down to a dilute solution value, this extrapolation gave him pK. = 17.1, but he acknowledged that this was most likely a lower limit. In the second publication (2b) they state that pK, 2 17.1. Giggenbach liked the value of 17.1 because his second treatment also gave this value. His second treatment used the acidity function H- which is defined for basic solutions of a very weak acid HB by
In this equation pK, is the dilute solution pK. value with [B-] and [HB] the indicated equilibrium molarities in the basic solutions. All the nonidealities in the acid-base equilibrium
go into the values of H- which result from using eq 2 for particular basic solutions. I t is very difficult to determine values for H- since it reauires an ex~erimentaldetermination of the pK. values, [H'I and [HH] ioraseriesoivery u,eak acids d~.;.olved in runwntrated h'aOII snlutions. These acids are usually a series of substituted organics possessing a chromophoric group. Giggenbach used the H- values determined by Yagil (9). From his own measurements Giggenbach determined that [HS-] = [S2-] in 15 M NaOH. This gives the result that for eq 1 its pK. = H- for 15 M NaOH. Yagil's value for H- in 15 M NaOH is 17.1. There are several difficulties with usine aciditv functions. They are not thermodynamic quantities since various types of a~proximationsare used in their determination. However. t h e i a r e the best method available for treating equilibria in concentrated acids and bases. As they are defined, all the nonidealities in the solution are contained in the acidity function, and Giggenbach should have used the acidity function H2- instead of H-. The Hz- function is defined for use with a doubly charged base A2- as [AZ? Hz_= PK. + log [HA-I
The current literature (10) contains only a few determinations of Hz-, but Yagil's values in KOH (9)showed that HzVolume 63 Number 8 August 1986
687
> H-. The reasons for this can be seen if we write down these acidity functions in terms of the activity coefficients yi
In these equations all the activity coefficients appear as corrections to convert the pH into the acidity functions. From our knowledge of activity coefficients in concentrated solutions we can say, on the basis of the charges alone, that
and this gives Hz- > H-. Values for HZ- have not been determined in NaOH solutionsup to 15M. The difference Hz- - H- from Yagil's KOH data extrapolated to 15 M gives an Hz- - H- equal to 1.2, which corresponds to HZ- = 18.3 in 15 M NaOH. The Hzdata of Halle et al. (11)uo to 12MNaOH a t 20°C can also he extrapolated to 15 M to obtain Hz- = 19.3 a t 20 "C or 19.1 at 25 O C . The proper value of an acidity function depends upon the detailed nature of the weak acid and can vary from acid to acid. Since the charges are highly localized in S 2 when compared t o any doubly charged organic base, a larger value for Hz_is the more logical choice for eq 1.With this in mind, we recommend pK. = 19 f 2 as the best current estimate for the second dissociation constant for H2S. Perlodlc Trends In his 1958 paper on the Kz value for HzS, Wood (12) showed how the pK, values for the Group VIA hydrides varied from one member to the other. In Table 1we reproduce Wood's table except that we have corrected pKz for H2Sfrom 14 to 19 and we include Latimer's estimate (13) for PKZfor HzO. We can see from Table 1that a high value for pKn for HzS is necessary if these pK values follow a simple pattern in the Periodic Table. The values for H2Te and H2Se are presumably free from an oxygen error since i t has been traditional with such compounds to work in vacuum systems. The difference pK2 - pKI has a special significance. In their theory of weak acids, Branch and Calvin (14) would ascribe this difference to an inductive effect due to formal charge. The pK differences that they ascribed to a change of one full unit of formal charge was 12.3, and this is very close to the difference seen for H2S and H2Se. We would assume that this inductive charge effect should be larger for smaller ions consistent with the trend shown in Table 1. One reason that workers were satisfied with pK2 - pK1 = 7 for H2S was that they had seen differences such as 5 for acids like H3P04 and H2S03and a value of 7 was just a little larger. However, the charges in HzP04- and HP04Z-are spread over several oxygens and not totally concentrated as it is in HS- and HO-. The trends shown in Table 1 clearly show that a pKz value of 19 for HzS is much more consistent with what we know about acids than the old value of 14. In hindsight, it is surprising that the old KZvalue was not questioned on this basis alone. The Source of the Incorrect High Value The measurement of Kz for H2S has a long history (15). Knox's value (16) from 1906, Kz = 1.2 X 10-15, was used for many years. He measured the E M F of cells containing HgS in Na2S solutions. In 1931 I. M. Kolthoff (17) pointed out that some of the solubility values for metal sulfides were in error due to what he thought were metal oxides on the sulfide surface, but he did not consider that polysulfides 888
Journal of Chemical Education
Table 1.
A
Comparison of the Group VIA Acld Dlssoclatlon Constants In Waterd
dunlessotherwise i~imsd. value8 horn refs land 72. bRet 13.
Our estimate.
could also he introduced into sulfide solutions. The values of K2 determined after 1940 with modern instrumentation were generally higher than Knox's value, and it became accepted that K2was between lo-" and 10W3based upon a variety of measurements. The oxidation of sulfide solutions first yields polysulfide ions with the general formula of S,S2-. These ions are in fairlv, r a.~ i deouilihrium with each other but thev are all relati\.ely strong acids I~pcausethe negative charge is highly dAmlized. T h r eouilihria hrtween theseions has beenmost extensively investigated by Giggenbach (18-20). From a general viewpoint, the problem of measuringK2is that of determining the equilibrium constant for OH-
+ HS- ~1S2- + H 2 0
(5)
where i t was generally thought that Kg -1. In polysulfide solutions with [OH-] -1 M there are three important equilibria OH-
+ HS- + 3S,SZ- s 4S3SZ-+ H 2 0
(6)
+ HS- + S,SZ- e 2SS2- + H,O
(8)
OH-
where Giggenbach (18) determined for 20 OC that Kg = 4.0 X and Kg = 2.0 X These equilibria all lo5,K7 = 1.8 X mimic eq 5 and the decrease in HS- reported by ref 3 with increasing [OH-] can be explained by eqs 6 and 7 when [OH-] -1 M. The increase in absorbance a t 365 nm, which was reported by ref 4 and used by them to determine the IS2-1. can be ascribed to the SS2- s ~ e c i e son the basis of i;igienbach's in\.estigatinns ( I & ) . ~ h polysulfides c are unstable with n-svert toSK&,~-,hut it has bwnshown (201that this requires &rage for years a t room temperature. The literature does contain some simple experiments which, a t first glance, supports a high KZ value. However when examined more closely they do not provide strong evidence to support any particular value for Kp. Figures 1 and 2 show the titration curves published by Kubli (21). He followed these titration pH values with a glass electrode. Figure 1 looks to be a typical diprotic base titration curve, but if we assume that pKz is larger than 14, the sulfide would hydrolyze completely S2-
+ HZOe HS- +OH-
(9)
The first part of Figure 1 from points 0 to B would then represent only the titration of the OH- from eq 9, and this was confirmed by the authors of ref 7 who used indicators instead of a elass electrode. The two eouivalence mints shown i n Ftgurr I seem to tw stoirhiometrirnllv fairly acruriltv. Kuhli (211tried toexcludr oxvaen and volvsulfidej do not seem to have affected these t i t z i o n s . he ialue of pKz reported by Kubli was 12.44 a t 20 OC, but its accuracy depends entirely on how much the curve OR deviates from the titration of a 0.04942 M NaOH solution. The pH of point 0
Figure 1 me fwst tnation clnve hom Kublo s 1946 amcm m whch 20 mL of 0 4942 MNa,S was t rated with 0 5233 NHCI at 20 OC At f rst glance, ths appears to be a typical cuwe for an ordinary diprotic base
Figure 2. Kubli's second tihatian curve. in which 20 mL of 0.08425 MNaHS was titrated with 0.5233 NHCI at 20 'C. The pH at point B gave a K2 which agreed with mose of points 0 and A in Figure 1.
measured by Kubli was close to 12.4 while 0.05 M NaOH would have its pH close to 12.7. Kubli's pK2 values depend entirely upon this small shift and the Na+ error in glass electrodes a t pH > 12 could account for such a shift. Nevertheless, Kubli obtained pK2 = 12.44, 12.46, and 12.41 from his points 0, A, and B. This precision was clearly improbable and his experiments were not properly designed to actually measure pKz. We can conclude that most of the methods used to measure the value for Kz for H2S were either mined by the presence of polysulfides or were simply not designed to detect the fact that its Kz value was much lower than the expected values of 10-l3 or 10-14.
this using the values in ref 1 for reactions 12.13, and 14 for ZnS we obtain
The Teachlng ol Sulllde Equlllbrla
From the previous parts of this paper, we can reach two important conclusions 1) The species 5%-is never a principal apecies in normal aqueous
solutions. 2) The value of Kz for HIS is highly uncertain and the equilibrium value for [Sz-1 in a solution is known to very low accuracy.
Because of these facts, Sz- should assume the same role that O2- has had. They are both present in solid lattices, but they have no role in elementary discussions of aqueous solution chemistry. In the case of 0 2 - we do not include i t in equilibria. The solubility product for MgO, for example, is written ( I ) as
Since the incorrect value for 1/K13or Kz was very close t o K ~ or K,, our final K,, value for eq 11is close in value to the old K,? value based upon eq 12. The modern value for eq 12 usmg Kz = 10-I9 would be close to but its uncertainty is very high and it should not be used. The value of 1.5 X for eq 11 is probably quite accurate. Metal sulfide solubilities are usually determined in acid solutions and polysulfides do not readily form in acid solutions. Table 2 shows some of these corrected K,, values for various metal sulfides based upon the values listed in ref 1 . While eq 11is the correct way to treat metal sulfides if we follow the practice set for metal oxides, it is a clumsy equation. Most sulfide equilibrium calculations are done in acid solutions where the O H and HS- species would be protonated. In the basic solution where the HS- and O H would actually be present the ZnZ+would be present as Zn(OH)42-. In acid solutions the solubilization of ZnS comes from the reaction
The related reaction for a sulfide such as ZnS would be ZnSC8,+ H20 3 Znzt + OH- + HSK, = [Zn2+] [OH-][HS-]
(11)
Table 2.
Corrected Solublllty Product Exprerslons for Metal Sulfides st 25 ' C
Equation 11can he written as the sum of three reactions ZnS,,, e ZnZ++ SZ-
(12)
The published values for the equilibrium constant for eq 12, previously called its K, value, have largely been calcnlatedvalues which were based upon an assumed value for eq 13. This is becausae eq 13was measured indirectly by the effect of acid upon the solubility of the metal sulfides. Such an indirect measurement depended upon a value for K13 that we now know was incorrect. In this way, the older K,, values were calculated using an assumed value for Kz. We can reverse this calculation and remove the error that was introduced when the incorrect value for eq 13 was used. If we do
for MSiq + H a d M2+ + HS- + OH~ I ~ M S , . , +~iZM H~++ + H , S , ~ ,
Volume 63 Number 8
August 1986
689
the new constant, called K, or K., in acid, can be used instead of the K,, of eq 11for all sulfide equilibrium calculations. It is more convenient than eq 11in such calculations and it still avoids all the uncertainties involved in the use of eq 12. Table 2 also gives these K,,. values based upon the value of DKI = 7.02 ( I ) . The values of KO. and K-.. differ hv almost exactly a factor of loz1. ~ulfid; with v&ei greater than 10-2 are readilv soluble in acid. - The significance of the low Kz value and the use of K,, will he illustrated in the following examples.
xps
Example 3: What is the Equilibrium Value for [ C @ ] if H&g) is Bubbled Into a CuSOdSolution until AN the Possible CuS,,, is Precipitated? Assume that the Final [ W ] = 0.30 M. Thlsprohlrm isuften wurked by first iolvinp, fur [HS 1, then IS2-1 and finally [Cu'']. using theold K,,valut fm CuS .I. Since K1 isnor knuwn r ~ much r accuracv i t is best to amrid IS7-] by using K,,..
for saturated
Example 1: What are the Equilibrium Concentrations in a 0.050 M Solution of Naps? Since S2- is a very strong hase eq 9 goes to completion, and we ohtain
[OH-] = [HS-] = 0.050 M, [Nat]
= 0.10 M.
The [Ht] and [HzS] can he readily calculated and 52- should be treated as having no appreciable concentration.
Example 2: What are the Equilibrium Concentrations in a 0.050 M Solution of NaHS? We will first use a net reaction approximation and then justify this with the exact method. The usual disproportionation reaction determining the [Ht] in salts such as NaHzP04and NaHC03 applied to NaHS would he 2HS-
+ H,O
+
e HzS S2-
Since S2- is a very strong base, we must modify this reaction to of a simple hase reaction with K = K,IK1
HS-
one
+ H20 e H2S+ OH-
This equation is a result of the fact that HS-, like OH- or NH2-, is only a base and it has no acidic properties in water. With this net reaction we ohtain
[H,S]
= [OH-],
[HS-1 = [Na'] - [OH-]
and approximately [HS-] = [Nat]
H2S, [HzS] = 0.10 M, and
Similar calculations can he done to ohtain the [H+]that would be necessary to separate Zn2+from Fez+or other problems common to sulfide separations. By using our values for K., or K,,., we can completely avoid the large variations in equilibrium constants that will result if we insist on using S2- as an intermediate species for sulfide calculations.
An analysis of the literature and our knowledge of acids clearly supports a low value of Kz for H2S. Our best estimate is that pK2 = 19 f 2. With such a smallvalue we should learn to treat S2- as an unimportant species in aqueous solutions. The literature on the determination of K2 contains many systematic errors due to the presence of polysulfides. But it should also serve as an excellent example, for teaching purposes, of experiments which were often designed to ohtain . the expected, hut inaccurate, results. Acknowledgment I would like to thank L. Brewer, who first brought the Kz problem to my attention, and D. S. Noyce for helpful information about the theory of weak acids.
Literature Cited (11 Smith,R. M.; Martel1.A.E,"CriticdStabilityConrfants. Val. 4: Inorganic Complexes": Plenum: New York. 1976. (21 1.1 Chenbach. W. lnori. Cham. 1971, 10, 1333. lbl Ellis. A. J.: Gippenbaeh. W. Geochim. Cosmorhim. Acts 1971,35,247. (3) Ellis,A. J.: Miiedone,N. B. Oeochim. Cosmochim. Aeto 1961,31,615.See also Ellis, A.J.: Galding, R. M.J.Chhm. Sot. 1959,127. (41 BBlsnder,M.J.; Gz0sr.J. M.;Symons, M . C. R. Trons.Forodoy Soi. 1964.60.494, (51 Meyor,B.;Ward, K.;Kwhlhlasp,K.:Pofer,L.lnorg.Chem. 1981.22.2345, I61 See for oxemple, Aumerao, M. Compf. R. H. Acad. Sci. 1926,186,1724,aod ~ i e k s o n ,
This is a satisfactoryresult for 0.050 M NaHS. The exact mass and charge balance equations are
[Nat]
+ [Ht] = [OH-] + [HS-]
If we neglect the [Ht] in the charge halance equation, we have our net reaction result. These calculations give pH = 9.96 for a 0.084M NaHS solution. In Figure 2 Kubli (21) obtained, for point B, pH = 9.54 at 20 'C. This is again only slightly displaced from the theory with Kz very small, and only a small error in the equivalence point or NaHS puritywould give complete agreement. This again shows that the shape of Figures 1and 2 are completely consistent with a small K z value, and they do not, within their accuracy, give any information about the value of K2.
690
Journal of Chemical Education
191 Yagil, G.J.Phys. Cham. 1967.71.1034, 1101 C0r.R. A.;Yetes.K.Con.J. Chem 1963,61,2225. I111 Halle, J.~C.:Terrier.F.:Schaal. R.Bull.Soc.Chim.PI. 1969.4569. (121 Wood. R.H. JAmW Chrm.Soc. 1958,80,1559. (131 Latimer. W. M. "The Oxidation States of the Elements and their Potentialsin Aqueous Solution': 2nd ed.; Prentice-Hell:Englewood Cliffa, NJ. 1952:g 34. (141 Branch, G. E. K.; Calvin, M. "The Theory of Organic Chemistry": Prentiee-Hdl: Englewwd Cliffs, NJ. 1%": p 204. I151 Sillen. L. G.; Martell. A. E, %tability Constlnfs of Metal-Ion Complexes". Spec. Pub! No. 17.2nded.;ChemiealSoeiety London, 196%pZiM6. I161 Knox, J. Z.Electrochem. 1906,12,477. (171 Kolthaff.1.M.J. Phyr. Chem. 1931.35.2711. (181 Giggenbseh. W.lnorg. Chem. 1912.11.1201. (191 Giggenbneh, W.F.Inarg.Chem. 1974,13,1724. (201 Giggenbach, W.F.Inorg. Chem. 1974,13,1730. I211 Kubli, H. Hdu. Chim. Acto L946.29.1962.
