H. L.
264
L O Y AND
D. M. HIMMELBLsU
Vol. G5
THE FIRST IONIZATION CONSTANT OF HYDROGEN SULFIDE I N WATER BY H. L. LOYAND D. M. HIMMELBLAU Department of Chemical Engineering, The University of Texas, Austin I d , Texas Received J u l y 1.4, 1960
Recent developments in radioactive tracing techniques and the availability of radioactive tracers have been exploited together with standard conductance techniques to determine the thermodynamic first ionization constant of hydrogen sulfide: KI = [(mH+)(mHS-)/(mHnS)] [( yn+)(~ H S - ) / ( Y R z S ) ] . The apparent ionization constant of H2Swas determined at successively lower concentrations of H2S in the range of 1 X 10-3 to 16 >r: 10-3 molal, and a true thermodynamic constant evaluated by extrapolation to infinite dilution. Water with a conductivity of 0.25 x 10-6 mho a t 25” was obtained by distilling deionized water under a hydrogen atmosphere directly into the reaction flask and proceeding with the experiment as soon as the water reached thermal equilibrium with the thermostat. The values obtained for the first ionization constant were f 4%, 0.87 X lo-: f 4%, and 1.52 X lo-’ It 70jo.at 0, 25 and 50°, regpectively. These values are in 0.271 X general agreement with values obtained by previous investigators, taking into account the high ionic strengths employed by them.
Introduction In the last GO years there have been a number of investigators’-$ employing various techniques who have measured and reported widely varying values for the first ionization constant of hydrogen sulfide. Thermodynamic interpretation and evaluation of the reported values have been uncertain because of the high ionic strengths employed and because of the lack of reliable activity coefficient data when activity corrections were applied. The purpose of this investigation was to determine the first ionization constant of hydrogen sulfide by exploiting recent developments in radioactive tracer equipment and the availability of radioactive chemicals. With these new techniques it was possihle to determine concentrations of hydrogen sulfide as low as molar within an accuracy of about 3%. When hydrogen sulfide ionizes in an aqueous solution according to equation (1) (hydration of the proton is assumed but not written down in the analysis given) H&aq)
J_ H + HS-
(1)
the first ionization constant is defined by Kl
= ( a H c ) (aHS-)/(aHzS)
=
(r)(Kl’)
(2)
where I’, the activity coefficient product, is defined as
r
= (TH+)(YHS-)/(~H*S)
and K’, the apparent ionization constant, is defined as K‘l = (mEi+)(mHS-)/(mHzS)
K1’ has no thermodynamic significance, but is a convenient value to measure in the evaluation of K1 since a t infinite dilution, where by definition the activity coefficients are equal to unity, K1 = K1’. By collecting experimental data suitable for the calculation of K1’ a t various diminishing molalities, K1 can be found by plotting K1’ against some (1) Th. Paul, Chem. Z., 535 (1899). (2) J. Walker a n d R’. Comack, J. A m . Chem. Soc., 22, 5 (1900). (3) F. Z. Auerbach, Phys. Chem., 49, 217 (1904). (4) IC. Jellinek and J. Czerweski, 2.physik. Chem., 102, 438 (1922). (5) R. €1. Wright and 0. Maass, Canadian J . Research, 6 , 888 (1932). (6) A. G. Epprecht, Hela. Chim. Acta, 21, 205 (1938). (7) H. Kubli, ibid., 29, 1962 (1946). (8) N. Yiu, Sei. R p t s . Tohoku Unia., Fzrst Series. 86, 53 (1951). (9) T. 4 . Turnanova and K. P. Mishenko, Zhur. npoorg. Khim., 2, 1993 (1957).
function of molality and extrapolating to infinite dilution. It was not possible to use Ostwald’s dilution lawlo in this manner because for weak acids ( K I ca. lo-’) the appropriate extrapolation introduces considerable error into the value of K1. Instead, equation (3) was employed KI’ = (mHzs(Y2)/(1-
(Y)
=
mHp8(Ya
(3)
where the degree of dissociation, Q = A/A’, is the ratio of the equivalent conductance to the equivalent conductance the weak electrolyte would have if it were completely ionized a t some definite concentration. I n the solutions studied, mn+ = mHs- = (A/A‘)mH,s. A method of determining A‘ from equivalent conductances of strong electrolytes only was used by MacInnes and Shedlovsky” in determining the ionization constants of acetic acid. This method assumes only that Kohlrausch’s law of independent ion migration holds a t low concentrations and that the strong electrolytes are completely ionized. With these assumptions, A’ can be obtained from the following relation in which the equivalent conductances of the strong electrolytes are taken not a t infinite dilution, but a t the concentration a t which the degree of dissociation is desired A’H~s = AHCI- AXACI -t h a m
(4)
A values were obtained as a function of temperature and concentration from MacInnes12 and reference 4. In the application of conductivity measurements to the study of solutions a t very low concentrations, the accuracy and reliability of the conductivity data can be greatly impaired by the solvent effect. For this work, with water of a specific conmho, any such effect ductance of 0.25 X mas of about the same order of magnitude, or less, than the experimental error, and solvent corrertions mere neglected. Experimental Apparatus.-The experimental apparatus consisted of a conductivity bridge, radiocounting apparatus and a constant temperature water-bath. The conductivity apparatus employed an a x . Wheatstone bridge and an oscilloscope (10) E. A. hloelwyn-IIughes, ”Physical Chemistry,” Pergamon Press, New York, N. Y.,1957, p. 825. (11) D. A. MacInnes and T. Shedlovsky, J . Am. Chem. SOC.,64, 1429 (1932). ( 1 2 ) D. A. MacTnnes, “Principles of Clectrochrmistry,” Reinhold Puhl. Co., New York, N. T.,1930, p. 339.
Feb., 1961
HYDROGEN SULFIDE I N
FIRST IONIZATION COKSTrlR‘T OF
as a null indicating instrument. A simple dip type conductivity cell was used, which was accurate to within 0.5%. A vessel used for these measurements was a 1 l., threeneck, round-bottom flask of Pyrex glass or, alternatively, quarts. The center neck accepted the conductivity cell that had been cast, into a male ground glass joint with was. A manifold of three stopcocks with Teflon barrels led to a manometer, a vacuum line, and the Hz or K2S supplies. The vessel was leak-tested before each run. The radioactive tracer-counting system consist>ed of a shndard proportional end window counting tube for use with planchets, and an RIDL SCAMP amplifier and scaler set-up. Procedure.-The first steps in the experiment were to determine the cell constant of the conductivity cell by the usual standard procedure, and to calibrate the radioactive counting apparatus by counting known concentrations of radioactive sulfur. The radioactive hydrogen sulfide..used was obtained from the Volk Radiochemical Company of Chicago, who prepared it by the method of Bills and Ronziol3 to have a specific activity of appro:timat.ely one millicurie per millimole of gas. It was diluted approximately by a factor of ten with 99.9% purified hydrogen sulfide (Matheson Company, Newark, N. J.). The calibration of the total sulfur concentration in the aqueous solutions ((andin effect the HzSconcentrations) was accomplished by neutralizing 100 ml. of 0.1 N KaOI-I with the radioactive H2S in the presence of Hz. Then 10 iV NaOH was added, and the sample solution finally was diluted to :t volurne of 500 ml. Aliquots taken from the 500 ml. of tagged solution were analyzed volumetrically for sulfur following a method recommended by Kolthoff 14; the solution was found to be 0.0194 molal in sulfur, and was diluted to 0.01422, 0.00916, 0.004467 and 0.002473 molal for use in the counting calibration. The same counting geometry and coricentrat,ion of NaOH as in the calibration procedure mere used in the acltual experimental runs. A (3-14 plastic disk: was employed as a reference standard to ensure that the counting rate always could be referred to the same counter efficiency and geometry. The usual corrections for background and beta decay also were made. When plotted, the calibration curve of counting rate us. sulfur molality was quite linear. In filling the reaction flask, deionized watef with a specific resistance of over four million ohms was distilled directly into the flask under a hydrogen atmosphere. The flask was placed into a water-bath, tested for leaks with hydrogen pressure, a Blight vacuum pulled, and the radioactive hydrogen sulfide introduced to about 150 to 200 mm. (gauge) of mercury pressure. After one hour the resistance of the solution was recorded, 1.75 ml. of solution was withdrawn with a hypodcrmic syringe, 0.25 inl. of 10 N NaOH was then pulled into thc syringe in order to convert the HtS to Na?S, and the sample was counted in a planchet with the proportional counter. A slight vacuum was again pulled and the sequence repeated; this was done four or five times for each run, increasing the concentration of H2S in the solution each time.
265
WATER
7
X
1.2
c3
I
7
--
-
e
4
4
.
1
5 0.6 --
-
ii
0.2---
0
I
-”
n
u -
h
00
“
iio
1
-I-_-
I I
-__-_
-_
-_ __
-_ __
I
0.005 0.010 0.015 Molality of H2S. Fig. 1.-Apparent ionization constant us. molality.
TABLE I
VALUESOF SLOPEAND IKTERCEPTS OF FIG.1 S 5 % confidence Intercept X 107 limits of intercept,
‘ I cmp., OC.
Slope X lo7
Ki
0 25 50
1.oo 8 77 13
0,271 0.87 1.52
70 fl.9 1.1.7 1.4 0
in fact, the Debye-Huckel theory would predict a linear relationship for log (Kl’/Kl) as a function of dji. However, since the range of & was quite small (3 to 6 X 10-3) for this work, it did not appear that a correlation of this nature would be conclusive one way or the other. From the equilibrium data the free energy of ionization a t the standard state of infinite dilution has been calculated by AFo = -RT In K to yield values of 9440, 9610 and 10,000 cal. per gram mole of H2S a t 0, 25 and 50’, respectively. The work of previous investigators is plotted in Results and Discussion Fig. 2 as a function of temperature. The data of The values for Kl’ are plotted vs. the molality of this work were in general agreement with the the H2Sin Fig. :I. A straight line was fit’t,edto the values reported by the other investigators, taking points by the method of least squares. The slopes into account the fact that the ionization constants and intercepts a t each of the three temperatures given by Kubl? and Tumanova and Rlishenkos and the intercept confidence limits are shown in were for high ionic strengths, and considering the Table I. The intercepts represent the true ther- fact that Wright and Masss employed “Ostwald’s modynami c ionization const,ant,s. Constant” a t high concentrations of hydrogen sulThe confidence limit,s in Table I are believed to be fide. Latimcr,15 in evaluating the frec energies of too low to represent properly the error in the values H,S(g), HzS(aq), and HS- from the available data of K1, and should be more nearly the order of 54y0 in 1952, used a value of KI of 1.1 X a t 25’. a t 0 and 2.5’ and 7% a t 50’, based on an estimate In applying the Van’t Hoff equation to determine of the possible experimental error discussed below. the heats of reaction, it can be seen from Fig. 2 There is no particular theoretical reason for fit- that the data from this study have the same genting a straight line to the data plotted in Fig. 1; eral trend as do the data of Wright and Maass, and consequently the heats of reaction for either (13) W.Bilk and A. R. Ronzio, J . Am. Ghem. Soc., 72,5510 (1950). (14)
I. &I. Kolthofi’ and R. Relchrr, “Volrmetrie Analysis.” Vol.
111, lntrrscience l’riblishers, Inc., X e w S o r k , N. P.,1967, 11. 292.
(1 3 W. M. Latimer, “Oxidation Potentials,” 211 ~ d . PrentioeHal , Inc., Gnglenood Cliffs, N. ,J., 1952.
7.6 ,-
I
In the carbon dioxide system, in which the ionization constant has about the same value as this system, I’for the ionization of CO:! gas can be determined from the work of Shedlovsky and McInnes,16 who found no such change as is indicated in Table I1 even though the concentration range covered for COZgas was about the same as used here for H2S gas and the ionic strengths were about the same. Wright and Maass, although working with values
of HzS molalities from 10 to 100 times the concentrations used here, did not find K1 was concentration dependent, nor have other workers who employed relatively high ionic strengths (F 10-1 to 10-2). Acknowledging the anomalous results noted above, what explanation can be offered? Certainly one possibility always present with H2S is that the gas reacted with the vessel containing it and caused the data collected to he erroneous. In this work five hours elapsed between the first admission of hydrogen sulfide and the withdrawal of the last sample of solution. If enough ions were formed (from a source other than the ionization of hydrogen sulfide) to change the conductivity to that of equilibrium conductivity water mho), then an error of 8% in the conductivity could have resulted. The error would become augmented with time and result in an increase in the slopes shown in Fig. 1 since the samples were taken in increasing order of concentration. That the slopes increase with increasing temperature would seem to confirm this view, except for the fact that to test this point several runs were made in a quartz reaction vessel, with results not significantly different from those made in the glass one. Certainly by taking data in the most dilute solutions first, and then in the more concentrated ones, any effect of a reaction, if it did exist, was certainly diminished. Fortunately, even if the values of K1‘ may possibly have been biased by this effect, the extrapolated value of K1 is very near the true value since the values in the most dilute solutions would be the least biased. Assuming that the data are not biased, how can the effect of H2Son the values of K1 be interpreted? r merely represents the sum of all the non-idealities in the solution. With the concentration of H B molecules so low, and with the Hf and HS- concentrations being several orders of magnitude less, it is convenient, but not necessarily particularly informative, to ascribe the effects we have noted to solvation of the H2S molecule (per Wright and Maass), the HS- ion and/or the proton. Since there are no experimental data available on the primary or secondary solvation of H2S and HS-, and since theoretical methods of calculating the solvation number for these components are dubious, this explanation can be only speculative a t this time. Certainly the primary solvation effects for H2S must be different from most other gases which are slightly ionized in water and which can become chemically bound to a molecule of water, as, for example, COZor SO2. Another possible explanation is that the undissociated H2S molecules by themselves, or in conjunction with the water, are partly dimerized or associated in some form. If this were true, the value of m in equation (3) would be in excess of the proper value, and K1 would not change as drastically with m ~ 2 sas shown in Fig. 1. Dimerization is a phenomenon likely to cause Kl’to change approximately linearly with concentration of un-ionized solute, l7 and has been noted for acetic acid a t high concen-
(16) T. Shedlovsky and D. A. McInnes, J . A m . Chem. Soc., 61, 1705 (1933;.
(17) R. A. Robinson and R. H. Stokes, “Electrolytic Solutions,” 1st ed., Butterworth’s Scientific-Publications, London,.l955.
1
6.6
-
I WALKER 8 COMACK
A
AUEREACH
--f
3.0
i
I
3.2
3.4 3.6 I/T x 104. us. log Kl for various investigators.
Fig. 2.-l/T
set of data agree very well. The data of Tumanova and Mishenko have much less slope for the same temperature and consequently their calculated AH values would be lower. In examining Fig. 1, one noticeable feature is the unexpectedly strong dependence of the apparent ionization constant K1’ on the concentration of the H2S. The activity coefficient product r = KI/K1’ can be determined as a function of mean ionic strength as well as the molality of the H2S as in Table 11, and the values of r are considerably lower than would be anticipated for the very low ionic strengths existing in this work. Furthermore, for many weak acids such as water and acetic acid, the activity coefficient product is a linear function of the 4a t low values of 6) but this was not found true for H2Sin this work. TABLE I1 EVALUATION OF THE ACTIVITYCOEFFICIENT PRODGCT OF H2SAS A FUNCTION OF CONCENTRATION -0’-
Molality of HZS
0.001 ,005 ,010 .020
+lean ionic strength P
x
106
0.52 1.16 1.64 2.32
r 0.996 .98 .9G .03
7 - 2 5 O Mean ionic strength P
x
105
0.93 2.08 2.95 4.17
,----50°-----.
r 0.99 .95 .91 .83
Me?” ionic strength
x
106
1.2 2.8 3.9 5.5
r 0.99 .96 .92 .85
Feb., 1961
HEATSO F
COMBUSTION OF hlONOOLEFIX
trations. But in the vicinity of one atmosphere, the solubility of' H2S in water follows Henry's law, and this would seem to be incompatible with the concept of dimerization of part of the H2S. Hence a clearcut explanation of the noted change of the
HYDROCARBOSS
267
apparent ionization constant with H2S concentration is not possible a t this time. Acknowledgment.-This work was supported by the National Science Foundation under grant G5080.
HEATS OF COMBUSTION, ISOI1IERIZATIOS, AND FORMATION OF SELECTED C,, C, A S D C,, MOiYOOLEFIN HYDROCARBONS BY JOHN D. ROCKENFELLER AND FREDERICK D. ROSSINI~ Chemical and Petroleum Research Laboratory, Carnegie Institute of Technology, Pittsburgh IS, Pennsylvania Received Julb 14, 1960
Measurements were made of the heats of combustion, in the liquid state a t 25", of 19 selected monoolefin hydrocarbons, including 10 heptenes, 6 octenes and 3 decenes. From these and appropriate other data wereocalculated values of standard heats of isomerization, formation and hydrogenation, as appropriate, for the liquid state at 25 For most of the compounds, values are also given for the gaseous state. The relation between energy content and molecular structure for these compounds is discussed.
.
I. Introduction Experimental data leading to values of heats of formation have been reported for substantially all of the monoolefin hydrocarbons through the h e x e n e ~ . ~ -However, ~ very few data leading to values of heats of formation have been available for monoolefins above the hexene~.C-~ It has become apparent that new experimental data on selected monoolefins of the C, to Clo range are needed to provide the basis for testing, within the limits of pmsent-day measurements, any theory relating the energy and molecular structure of the monoolefin hydrocarbons. With a proved theory, one would not only arrive a t a better understanding of the relation between energy and structure for these molecules, but one could calculate the heats of format:ion of an untold number of monoolefin hydrocarl3ons without recourse to further experimental measurement. Accordingly, the present investigation was carried out to obtain experimental data on 19 selected monoolefin hydrocarbons, including 10 heptenes, 6 octenes and 3 decenes. This report also presents a discussion of the relation between the energy and structure of these molecules. II. Apparatus and Experimental Procedures The experimentd values of this investigation are based on the absolute joule :is the unit of energy. Conversion to the defined thermochemical calorie is made using the relation 1
-
calorie = 4.184 (exactly) joules. For internal consistency with other investigations from this Laboratory, the molecular weight of carbon dioxide was taken as 44.010 g./mole. In this investigation, the chemical and calorimetric apparatus and procedures were the same as described by Browne and Rossini.10 The rise of temperature in each experiment was near 2O, with the final temperature being near 30°, the temperature of the jacket of the calorimeter. The amount of the reaction in each hydrocarbon combustion experiment was determined from the mass of carbon dioxide formed in the combustion, as previously described.lO The bomb had an initial volume of 380 ml. One ml. of water was placed in the bomb prior to each combustion experiment. The pressure of the oxygen for combustion was made 30 atmospheres (calculated to 25"). With the exception of the two branched decenes, the compounds measured in the present investigation were API Research hydrocarbons, made available through the API Research Project 44 from materials purified by the API Research Project 6. The API Research samples had the values of purity given in Table I. Description of the purification and determination of purity of these samples has already been given."-l6 As a result of the methods of
TABLE I PURITY OF
THE
API RESEARCH HYDROCARBONS MEASURED
Compound
1-Heptene 3-Methyl-cis-3-hexene 3-Methyl-trans-3-hexene 2,4-Dimethyl-l-pentene 4,4-Dimethyl-l-pentene 2,4-Dimethyl-2-pentene 4,4-Dimethyl-cis-2-pentene 4,4-Dimethyl-trans-2-pentene 3-Methyl-2-ethyl-1-butene 2,3,3-Trimethyl-l-butene 1-Octene 2,2-Dimethyl-cis-3-hexene
Purity, mole %
99.84 f 0.10 (99.85 f (99.85 f .lo)" 99.88 f .09 99.85 f .OS 99.95 f .04 99.85 f . l l 99.81 f .03 (99.85 i .lo)" 99.95 f .04 99.77 f . I 3 9 9 . 8 6 f .12 (99.85 zk .lo)" 99.81 f .08 99.95 f .03 99.93 f .05 99.91 f .OT
(1) This investigation was supported in part by a grant from the National Science Foundation. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy i n Chemistry a t the Carnegie Institute of Technology. (2) Univers.ity of Notre Dame, Notre Dame, Indiana. (3) F. D. Rossini, K. S. Piteer, R. L. Arnett, R. M. Braun and G. C. Pimentel, "Selected Values of Physical and Thermodynamic 2,2-Dimethyl-trans-3-hexene Properties of Hydrocarbons and Related Compounds," API Research Project 44, Csrnegie Press, Pittsburgh, Pa., 1953. 2-Methyl-3-ethyl-1-pentene (4) E. J. Prosen and F. D. Rossini, J . Research iVatZ. Bur. Standards, 2,4,4-Trimethyl-l-pentene S6, 269 (1946). 2,4,4-Trimethyl-2-pentcne (5) E. F. Bartolo and F. D. Rossini, THISJ O U R N A64, L , 1685 (1960). 1-Decene (6) F. M. Fraser an
