Anal. Chem. 1987, 59, 1222-1225
1222
Thermometric Titration of Polysulfides John W. Stahl' and Joseph Jordan* Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802
A novel calorimetric approach has been developed for analyzing mixtures of sulffdes and pdysull;kles in aqueow, solution, where the moleties HS-, S l - , Sa2-, S t - , and S5'- are in dynamic equilibrium. Advantage Is taken of their Lewis base reactivities wlth the organomercury Lewis acld zwitterion -OOCPhHg+. On the basis of judkious thermochemical consideratlons, samples are titrated to thermometric end polnts with standard p -hydroxymercuribenroate. Quantitatlon of sulfidic and poiysulfidlc sulfur concentrations is feasible In a single experiment. Sulfldlc sulfur can be estimated at concentratlon levels as low as 0.0001 M. Polysulfldlc sulfur is amenable to determination even in the presence of a more than 40-fold excess of sulfide. CapaMlltles of the method are documented by the analysis of synfuel process stream specimens. Precision and accuracy of 1-3% were attained.
Polysulfide anions, Sx2- (z = 2, 3, 4, 5), are troublesome contaminants in many industrial processes. Aqueous condensates from coal liquefaction processes ( l ) coke , oven ammoniacal liquors (2), and Kraft paper pulping liquors (3) are all subject to contamination by polysulfides. Analytical determination of individual polysulfide species in aqueous solution is practically impossible, due to facile rearrangement reactions of the type
3SS2- + HS-
+ OH- + 4S4'- + H2O 2S42-+ HS- + OH- + 3SS2-+ H2O SS2- + HS- + OH- + 2S22- + H20
(1)
(2) (3)
which may be generalized as (X
+ HS- + OH- == (x:- l)Sz-12-+ H2O
- 2)SX2-
(4)
Classical schemes for analyzing mixtures of polysulfides (4, 5) have resorted to a formalism that circumvents the difficulty caused by these rearrangements. Results are expressed in terms of "sulfidic sulfur", S(-11), and "polysulfidic sulfur", S(O), whose molar concentrations are defined as follows: 5
[S(-II)] = [HS-] + C[S,2-] x=l
[S(O)l =
5 C ( X x=2
- 1)[Sx2-1
(5) (6)
The quantities [S(-11)] and [S(O)] are not affected by rearrangements of the type illustrated in eq 1-4. The method described in this paper is capable of determining in a single experiment both [S(-II)] and [S(O)] in an aqueous mixture of polysulfides. This represents a capability that is unmatched by any other approach. The present method was developed from considerations of the reactivity of sulfide and the polysulfides as "soft" Lewis bases. As such they can form adducts with the mercury(I1) Present address: Department of Chemistry, Geneva College, Beaver Falls, PA 15010.
benzoate zwitterion, which is a Lewis acid. The reagent of choice was the anion (4-carboxylatophenyl)hydroxymercurate(1-) which is commonly and hereafter referred to as p-hydroxymercuribenzoate, p-HMB. The ortho isomer, o-HMB, has long been recognized by Wronski (6-8) as a reagent which is selective for sulfur in the -11 oxidation state. The para isomer of the sodium salt was used in this work because of its commercial availability and superior stability. The usefulness of HMB as a titration reagent is predicated (in part) by the presence of only one available coordination site on the mercury, which yields straightforward, simple stoichiometries. Wronski has made use of metallochromic indicators and manual titration methods. In the present work, an instrumental end point determination was used under judiciously controlled experimental conditions, viz., thermometric enthalpy titration (TET). EXPERIMENTAL SECTION Apparatus. Thermometric titrations were performed in a custom-built isoperibol calorimeter (9-11), where virtual adiabaticity prevailed. The reaction vessel was a specially designed Dewar flask of 7-13-mL capacity. The titrant was delivered at a constant rate with the aid of a motorized syringe drive (Model 234-3, Sage Instruments, Orion Research, Cambridge, MA) which depressed the plunger of a 2.5-mL gas-tight syringe (Hamilton Co., Reno, NV). The calorimetric readout (temperature, expressed as millivolts of unbalance potential of a dc Wheatstone bridge containing a thermistor sensor) was amplified and plotted in analog form on a strip chart recorder. Concomitantly the data were digitized and stored with the aid of a minicomputer (Model 11/24, Modcomp, Fort Lauderdale, FL). More recently this computer system has been replaced with a microcomputer (Model II+, Apple Computer, Inc.). The digital data were computer corrected for background and extraneous sources of temperature change by using established procedures (11,12). Corrected titration data were plotted as heat evolved vs. moles of titrant. Reagents. The titrant was an aqueous solution of approximately 0.05 M sodium p-hydroxymercuribenzoate (Aldrich Chemical Co., Milwaukee, WI) in 0.01 M NaOH. The p-HMB solution was standardized by thermometric titration into standard thiosulfate buffered at pH 9.2 (9). Sodium sulfide solutions were prepared from large clear crystals of NazS-9Hz0which were rinsed with deoxygenated water under nitrogen. Tetrasulfide solutions were prepared by dissolving NazS4,96% (Alfa Products, Danvers, MA), in an oxygen-free carbonate-bicarbonate buffer. Solutions containing mixtures of HS-, S2-,and various polysulfides, SZ2-, were prepared by dissolving known amounts of elemental sulfur in the NaOH and NazS stock solutions. The composition of each polysulfide-sulfide mixture at equilibrium was calculated from the equilibrium constants of reactions 1-3 (13). Procedures. Thermometric titration curves ("enthalpograms") using p-HMB as the titrant were obtained for solutions of Na2S and of Na2S, and for solutions containing mixtures of the ions HS-, S2-,and SZ2-in the presence of sodium hydroxide. All experiments were performed in aqueous solutions in a range of temperatures between 24.9 and 25.1 O C . RESULTS AND DISCUSSION Sodium Sulfide. When p-HMB was titrated into a solution of Na2S in 0.01 M NaOH (where S2- is predominantly hydrolyzed to HS-,as discussed below), the enthalpogram shown in Figure 1was obtained. The two end points in that figure, El and E2, corresponded to the mole ratios (p-
0003-2700/87/0359-1222$01.50/0 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 8 , APRIL 15, 1987
1223
Table I. Composition of Typical Mixtures of Sulfide and Polysulfide Species and the Data Resulting from Thermometric Titrations of Those Mixtures with g-Hydroxymercuribenzoate (p-HMB) row micromoles used to make up 10.0 mL of solution calculated composition of solution at equilibrium: micromoles present in 10.0 mL
1 2
3 4 5 6 7
Na2S elemental S HS- plus S2S?-
33.7 31.5 21.0 6.6 6.1
mobsd,lc
2.95 0.16 0.015 7.25 20.2 -80
-80
mobsd,2d
-54
-56
S2El" Ezb
12
10.0
0.14
S32-
concn of NaOH (mol/L) data derived from enthalpograms of the type illustrated in Figure 3
solution B
9.75 6.75
S,2-
8 9 10 11
solution A
1.00 23.5 68.0
"The first thermometric titration curve end point, expressed in pmol of p-HMB. *The second end point, expressed in pmol of p-HMB. AHob+ = heat of the reaction occurring prior to the first endpoint, E,, in kJ mol-' of p-HMB. m & d , 2 = heat of the reaction occurring immediately after the end point, El, in kJ mol-' of p-HMB.
54-
I
I
I 2 3 Mole ratio between titrant (HMB) added and tetrasulfide initially present
0
I 2 3 Mole rotio between titrant (HMB) added and sulfide initially present
0
Flgure 1. Enthalpograrn for the titration of p-HMB into 10 rnL of an aqueous solution containing 8.5 rnM Na,S and 0.01 M NaOH.
Enthalpograrn for the titration of D-HMB into 10 mL of an aiueous solution c6ntaining 7 . 4 rnM Na,S,.
HMB/HS) = 1.0 and (p-HMB/HS) = 2.0. These stoichiometries are entirely analogousto the results obtained by Wronski for the ortho isomer of HMB (6). From the slopes of the two regions of the enthalpogram identified in Figure 1,heats of reaction were evaluated. The relevant reactions and corresponding values of AHo' are given in eq 7 and 8, where Mo' denotes formal assignments corresponding to the prevailing conditions, in this instance 0.01 M sodium hydroxide at 25 "C.
(or both!) was actually the reacting species in the thermometric titrations. Fortunately, the analytical validity of the method described below is not compromised by this ambiguity. Reactions 7 and 8 were fast compared to the rate of titrant addition: no change in end point stoichiometry was observed when the rate of titrant addition was varied from 5 to 20 pmol min-l. Sodium Tetrasulfide. The typical titration of Na2S4with p-HMB yielded the enthalpogram shown in Figure 2. The salient feature of that curve is that a single end point, having a stoichiometric ratio of (p-HMB/S4,-) = 2.0 was obtained. At the conclusion of the experiment, a very fine white precipitate of colloidal sulfur was found in the reaction vessel. The precipitate was collected, dried, weighed, oxidized to sulfuric acid, and determined as barium sulfate. For every mole of tetrasulfide, Sd2-,originally present, 3 mol of sulfur, S(s), were found. This corresponded to the polysulfidic sulfur content ([S(O)] as defined in eq 6) of the titrate. A titration reaction equation consistent with these findings is
-0OCPhHgOH
+ HS- == -0OCPhHgS- + H 2 0
(7)
AH,"'= -79 kJ mol-' -0OCPhHgOH
+ -0OCPhHgS- e (-OOCPhHg)2S
+ OH-
(8)
A","'= -54 kJ mol-l Some discussion is appropriate concerning the actual ionic species present in aqueous solutions of Na2S. The value of the second pK, for H2S is a matter of some controversy in the literature, ranging from 17 (14,15)to 14 (16-18). Depending o n that value, Na2S, dissolved in water, hydrolyzes more or less completely, viz.
S2- + H,O
6
HS-
+ OH-
(9)
Accordingly, aqueous solutions of NazS are referred to as "solutions of HS-" in this write-up. However, in solutions of 1M NaOH, as much as 50% of the Na2S dissolved may exist as S2- if pK,, = 14 were the correct assignment. Because the heat of reaction 9 is small (16), AHH,' < 1 kJ/mol, it was experimentally impossible to discriminate whether HS- or S2-
2-000CPhHgOH + SX2-+ (-0CCPhHg)zS +
(X
-
l)S(s) + 20H- (10)
AHlo"' = -62 kJ mol-' where x = 4. Mixtures of Sulfide and Polysulfides. When mixtures containing both HS- and various polysulfide ions, Sx2-,were titrated with p-HMB, enthalpograms of the type shown in Figure 3 were obtained. Corresponding data for representative solutions are listed in Table I. Several points are significant. The first end point, El (row 9 in Table I), corresponds roughly
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 8, APRIL 15, 1987
6t
Table 11. Average Experimental Polysulfide Number (a f) Observed during Thermometric Titrations with p -Hydroxymercuribenzoate ( p -HMB) at Various Hydroxide Concentrations NaOH concn," mol/L
n'b
0.015 0.100 1.00
3.7 f 0.2 3.3 f 0.1 3.0 f 0.1
All experiments performed at a titrant addition rate of about 10 wmol of p-HMB min-'. *ii' defined in eq 14 and determined experimentally using eq 15. Values are recorded as the mean plus or minus the standard deviation. I
(but not exactly as will be discussed later) to the amount of HS- (plus any S2-) calculated to be present (row 3 in Table I). Row 11 corresponds to the heat of reaction 7 . Therefore, El was assigned to the completion of reaction 7 . The second end point, E2 (row 10 in Table I), corresponds to twice the amount of sulfidic sulfur, i.e., to 2([HS-]
0
E 2 / 2 ~= [HS-] + [S2-]
Clearly, for any given polysulfide ion, n = x - 1. Appropriate substitutions from eq 6 and eq 13 in eq 14 yield
(11)
+ [S2'-] + [S32-]+[St-] + [S:-] (12)
(4
-El)!
U =
[S,2-]
+ [S32-]+ [S42-]+ [S52-]
where El and E2 are expressed in millimoles of p-HMB and u is the initial titrate volume in milliliters. Additional experiments showed that, at a fixed hydroxide concentration, the relative concentrations of the various polysulfides during the titration were constant without regard to their initial distribution before the titration. This was quantitatively expressed by the invariance of the AVERAGE EXPERIMENTAL POLYSULFIDE NUMBER, ii ', defined below, for a given set of experimental conditions (sodium hydroxide concentration and rate of titrant addition) 5
R'=
5
C(x - 1)[Sx2-]/C[Sx2-]
x=2
x=2
3
Figure 3. Enthalpogram for the titration of p-HMB into 10 mL of an aqueous solution containing Na,S and a mixture of polysulfides in 1 M NaOH.
A precipitate of colloidal sulfur was observed in the region of the titration between E, and EP. Therefore, this second region of the titration curve (Figure 3) was assigned to the overlapping occurrence of reactions 8 and 10. Assuming that reaction 8 predominates initially, the heats of reaction, AH8'' = -54 kJ (moles of p-HMB)-' and AHlo'' = -62 kJ (moles of p-HMB)-', are consistent with the observed heat, AH,,,2 (row 12 in Table I), and the upward curvature in Figure 3 between El and E,. The small difference in reaction heats between solutions A and B in row 12 is of uncertain origin, although it might be attributed to the difference in ionic strength of these two solutions (determined primarily by the NaOH concentrations, row 8, which differ by almost 2 orders of magnitude). The end points were correlated to molar concentrations as follows:
[HS-] + [S2-]
I
I
and total sulfidic sulfur, S(-E), initially present
+ [S2-]+ [SZ2-]+ [SS2-]+ [S,*-] + IS,"])
El/u =
I
I 2 Mole ratio between titrant (HMB) added
(14)
For a given experiment, ii'was calculated from eq 15. [S(O)] was available from the known composition of the solution, and El and Ez were the end points derived from the corresponding enthalpogram. The invariance of ii'may be rationalized on the following considerations. The disproportionation and rearrangement equilibria among the polysulfides (reactions 1-3) are dependent on [HS-] and on [OH-]. During the first part of the titration with p-HMB, HS- is being removed from these equilibria by reaction 7 . Therefore, the equilibria are shifted to the left, that is, toward longer chain lengths, during the first part of the titration. Furthermore, the extent of this rearrangement is pH dependent. A lower hydroxide concentration favors rearrangement to longer average chain lengths. In addition, it is apparent from heats of formation data (17) that the heats of reactions 1-3 are small. Consequently, the rearrangements will not significantly affect the heat observed during a thermometric titration. A series of thermometric titrations of HS- and S,2- mixtures of known composition in the presence of various concentrations of hydroxide were performed to verify this interpretation. The data, summarized in Table 11, show that rearrangement to longer average chain lengths does indeed occur at lower hydroxide concentrations. These rearrangements were found to be reproducible and constant for a given NaOH concentration regardless of the initial polysulfide distribution. Another series of experiments were performed to determine if these rearrangements were kinetically controlled processes. An HS- and SX2-mixture of known composition was titrated with p-HMB at various titrant addition rates. In all cases the medium consisted of a solution of 1 M NaOH. Within the experimental error, E' was found to be equal to 3.0 and in-
Table 111. Accuracy, Precision, and Dynamic Range for the Analysis of Polysulfide Solutions by Thermometric Titration with p -Hydroxymercuribenzoate determination of
[S(-II)], sulfidic sulfur = [H8]+ E.,=15[S,2-] [S(O)],polysulfidic sulfur = ~ z = ~ -( 1)[SZ2-] x
% re1 accuracy
% re1 precisionb
0.5 3
fl *3
dynamic range lower limit upper limit
x 10-5M 0.02[ s(-11) 1 t)
none none
"Based on the known amounts of pure sodium sulfide and elemental sulfur used in preparing reference standards. *Expressed as the standard error of the mean B = s jN'12.
ANALYTICAL CHEMISTRY, VOL. 59, NO. 8, APRIL 15, 1987
dependent of titrant addition rate over the range of 10-24 pmol of p-HMB min-’, suggesting a relatively rapid rearrangement of polysulfides during the titration. Thus, the rearrangement of polysulfides during the titrations was found to occur to a constant and reproducible average chain length in 1 M NaOH. From the analytical viewpoint, this is advantageous, as both quantities necessary to characterize a polysulfide mixture, viz., [S(-II)] and [S(O)], can be obtained from a single thermometric titration with p-HMB, viz. [S(-II)] = E , / ~ u
[S(O)] = - - -E1 u
(16)
)
where El and E2 are expressed in mmol of p-HMB, u is sample volume in milliliters, and ii’ = 3.0 in 1 M NaOH. Fundamentally, the resolution of two end points in the titrations of mixtures containing HS- and polysulfides is possible because of an appreciable difference in the Lewis basicities of S2-and SX2-toward the Lewis acid -OOCPhHg+. The reagent p-HMB is the adduct of the dipolar ion -OOCPhHg+ and OH-. Considering the order in which reactions 7,8, and 10 predominate in the titration of a mixture with p-HMB, the following order of Lewis basicities (toward -OOCPhHg+) may be assigned:
S2->> -0OCPhHgS- > S,*-
(18)
Of the other Lewis bases which might possibly be present in sulfur-containing water samples (I),only cyanide is of any consequence as an interference. Species such as thiosulfate, sulfite, and thiocyanate did not interfere due to the relatively small equilibrium constants of their reactions with p-HMB
(9). Precision, Accuracy, and Significant Applications. Precision and accuracy were assessed by analyzing solutions made up ad hoc from known amounts of pure sodium sulfide and elemental sulfur. Thus, “true” reference concentrations of sulfidic and polysulfidic sulfur were available. These standards were subsequently analyzed by the thermometric titration method described earlier. Results of replicate determinations are summarized in Table 111. A lower limit of 0.00008 M [S(-II)] in the dynamic range is accounted for by the sensitivity of the thermistor circuits used for temperature measurements. On the other hand, [S(O)]is evaluated from the difference between two thermometric end points, in accordance with eq 17. The absolute variances are additive when a result represents the difference between two quantities, viz., E2/2and El in this instance. Consequently, the lower limit of detection of polysulfidic sulfur is given by that ratio of [S(O)]/ [S(-II)] which satisfies the following requirement:
(:
- E ~ =)
[(
)+
( O . O O ~ E ~ ) ~ ] ~(19) ”
where the factor 0.005 represents the relative standard deviations of the end points El and E2 which are shown in Figure 3. Substituting appropriately from eq 11and 13 and solving, the resulting ratio is [S(O)]/[S(-II)] = 0.02
(20)
Consequently, the lower limit of the dynamic range for [S(O)] is 2% of the concentration of S(-11). Two representative samples of synfuel effluent streams were analyzed by the method outlined in this paper. The same specimens were also analyzed by classical procedures ( 4 ) and by a polarographic method (19-22). Results are reported in Table IV. All values for S(-11) and S(0) are seen to agree to within the experimental error. Since the three methods used
1225
Table IV. Summary of Results (Moles per Liter) of Determination of Sulfur Species in H-Coal “Sour Water” Samplesa sample LO-2097b
method thermometric titration electrochemical classical (wet) procedures‘
sample LO-2098*
sulfidic sulfur
polysulfidi c sulfur
sulfidic sulfur
polysulfidic sulfur
S(-II)
S(0)
S(-11)
S(0)
0.78 f 0.01 0.55 & 0.02 1.77 & 0.02 0.75 f 0.02 0.53 f 0.01 1.79 & 0.04
