fluence the distribution of the other between the two solvents. Since all real systems will be nonideal to one degree or another, a decision (based on the relative magnitudes of the two effects) must be made as to whether the graphical method will yield results of the desired degree of accuracy. The relative magnitude of each effect may be rapidly estimated by experimentally checking the solubility profile of a candidate quaternary as described herein, and by checking distribution coefficients in the concentration range of interest for the proposed extraction operations. Literature Cited
Brancker, A. V., Hunter, T. G., Nash, A. W., Znd. Eng. Chem. 33, 880 119411.
Brkke;, A.‘.V., Hunter, T. G., Nash, A. W., J . Phys. Chem. 44, 683 (1940). Cruickshank. A. J. B., Haertsch.. N... Hunter. T. G.. Znd. Ene. Chem. 42, 2154-8 (1950). Francis, A. W., Znd. Eng. Chem. 46, 205 (1954). Francis, A . \V., “Liquid-Liquid Equilibriums,” Interscience, New York, 1963. Hunter, T. G., Znd. Eng. Chem. 34, 963 (1942). Ku, P. L., master’s thesis in chemical engineering, Polytechnic Institute of Brooklyn, 1959. Prince, R. G. H., Chem. Eng. Sci. 3, 175-86 (1954). Pratt, H. R. C., Glover, S. T., Trans. Znst. Chem. Engrs. (London) 54, 54 (1946). Riebling, R. W., “Equilibrium Studies in Quaternary Liquid Systems,” master’s thesis in chemical engineering, Polytechnic Institute of Brooklyn, 1961. Smith, J. D., Znd. Eng. Chem. 36, 68 (1944). Solomko. V. P.. Panasvuk. V. D.. Zelenskava. A. M.. J . Abbl. Chem. USSR (English ;rand.) 35, 602 (1962): ’ Vriens, G. N., Medcalf, E. C., Ind. Eng. Chem. 45, 1098 (1953). Washburn. R., Beguin, A. E., Beckord, 0. C., J . Am. Chem. Sod. 61, 1964 (1939)-
-
EXPERIMENTAL WEIGHT PERCENT PYRIDINE IN WATER LAYERS
Figure tions
5. Effect of pyridine on ethanol concentra-
Conclusions
The use of intersecting planes is an approximation to the actual situation of intersecting curved surfaces. The graphical method of Hunter would be expected to predict actual quaternary solubility and equilibrium data accurately only when the profile of the three-dimensional solubility surface is straight, and when the presence of one solute does not materially in-
RECEIVED for review August 30, 1966 ACCEPTEDMarch 2, 1967
A GENERAL SOLUTION T O THE PROBLEM OF
HYDROGEN SULFIDE ABSORPTION IN ALKALINE SOLUTIONS FRANCESCO G l O l A A N D G l A N N l A S T A R I T A Istituto di Chimica Industriale, University of Naples, N a p l a , h l y A theoretical solution for the case of absorption followed by an instantaneous reversible ionic reaction is presented. The theory is particularly useful for the absorption of HzS in solutions of a salt of a strong base and a weak acid, inasmuch as the main reaction is a proton-transfer reaction and, therefore, it may be assumed instantaneous. The following cases of chemical absorption of HzS are reviewed: in hydroxide solutions, in alkaline buffer solutions, in monoethanolamine solutions, in aqueous solutions of a salt of a strong base and a weak acid-e.g., NaAc and NaaP04, and in inert solutions-e.g., NaCl (inert as far as HzS absorption is concerned). The simultaneous absorption of H2S and COZin hydroxide solutions is also reviewed. Absorption data already published as well as original data are presented and discussed, showing good agreement with theory. HE chemical absorption of H2S in aqueous alkaline soluTtions occurs according to a mechanism that is in some aspects different from that occurring for other similar acid gases. The difference is mainly due to the fact that the hydrogen sulfide is able to transform into the HS- ion by a simple proton-transfer reaction. This allows one to assume that the
370
l&EC FUNDAMENTALS
chemical reaction occurring in the liquid phase can be considered instantaneous with respect to the diffusional processes even for slightly basic solutions. The same assumption is not possible for the chemical absorption of other seemingly similar acid gases, For example, carbon dioxide (Astarita and Gioia, 1964), in order to transform into the HCOa-ion, has to undergo
a structure-rearranging chemical reaction, the rate of which, for low values of the pH of the solution, may be comparable with the rate of diffusional processes. I n this paper the following cases of chemical absorption of H2S are reviewed:
At any point in the liquid, the following conditions need to to be fulfilled:
1. 2. 3. 4. base
where the H + and OH- concentrations are neglected in comparison, respectively, with nx, and x,. nx, represents the total constant concentration of the ion MCpresent in the liquid.
Absorption in hydroxide solutions. Absorption in alkaline buffer solutions. Absorption in monoethanolamine solutions. Absorptic:) in aqueous solutions of a salt of a strong and a weak acid. 5 . Simultaneous absorption of H2S and C 0 2 in hydroxide solutions.
Both theoretical and experimental results obtained in the analysis of Processes 1, 2, 3, and 5 have been published in detail (Astarita and Gioia, 1964, 1965; Astarita et al., 1965). Herein, the general conclusions reached are discussed, and the analysis of Process 4 is reported in some detail. The mathematical solution for this case has actually a more general significance, inasmuch as it holds for most cases of absorption accompanied by an infinitely fast ionic reaction with the limitation of equal diffusivities. As for the case of chemical absorption followed by instantaneous reaction, only the solution for irreversible reactions is available (Kennedy and Danckwerts, 1958; Nijsing, 1957) and some numerical solutions for other cases (Perry and Pigford, 1953).
ELECTRICAL NEUTRALITY
nx
+ s + (n - 1)h = nx,
(3)
BALANCE OF X ATOMS. I t is assumed that all diffusivities are equal; thus, the net transport rate of the X atoms being zero, the sum x h is constant. I n the bulk of the liquid x = x, and h = 0; thus:
+
x+h=xo
(4)
EQUILIBRIUM OF REACTION 2
Kc x = hs
(5)
Subtracting from Equation 3 n times Equation 4 one gets:
s=h
(6)
Substitution of Equations 4 and 6 into 5 yields: s2
= Kc (x,
- s)
and thus: Theory
(7) When hydrogen sulfide is being chemically absorbed, it may be generally assumed that the final sulfur-carrying product is, in ionic terms, the HS- ion. In fact, the pK for the first dissociation is of the order of 7 , while that for the second is of the order of 15. Therefore, even in highly alkaline solutions the concentration of S-2 ions may be neglected. A more detailed discussion on the thermodynamics of such absorption can be found (Astarita and Gioia, 1964). Let us consider the absorption of H2S into an aqueous solution of a salt M,X, where MOH is a strong alkali while H,X is a weak acid. The over-all reaction is:
According to the penetration theory, the concentration profiles for a second-order bimolecular reversible and instantaneous reaction are described, as pointed out by Marrucci (1965), by the following set of simultaneous equations:
or, in ionic terms:
Reaction 2 is a proton-transfer reaction and its rate may be assumed to be infinite as compared to the rate of diffusional processes: Reaction rate constants of the order of 10l1 liters per gram mole per second have been reported (Eigen, 1961). In other words, it may be assumed that Reaction 2 is at equilibrium at any point in the liquid, although concentration gradients may exist due to the finite rate of diffusional processes. The rate at which Reaction 2 takes place is simply equal to the rate at which diffusional processes bring reactants together in excess of the equilibrium concentrations. Let us define the following quantities: c = concentration of' undissociated hydrogen sulfide x = concentration of' the Xfl- ion h = concentration of the H X ( % - l ) - ion; when n = 1, this is not an ion, but an undissociated acid s = concentration of the HS- ion
I
Kcx = sh
with the following initial and boundary conditions:
INITIAL
hs - = KC( X
S u f i e s i and o indicate values at the gas-liquid interface and in the bulk of the 'liquid. VOL. 6
NO. 3
AUGUST 1967
371
Condition 13 derives from the consideration that the flux,
4, of H2S entering into the solution must satisfy both the rela-
Therefore, the increase in the mass transfer rate due to the chemical reaction is given by:
tions:
By obtaining st and so from Equation 7, the value of F may be calculated as an explicit function of known quantities. Two important asymptotic cases are the following:
CASEI. Condition 14 states that the net transport of X atoms at the interface has to be zero:
> 1 (because xo is in any practical case larger than ct), in other words, if Reaction 2 is practically irreversible. The condition K 1 is verified when the first dissociation constant of HzS, K1 (which is 9.1 X 10-8 a t 25' C. and infinite dilution) is much larger than the nth dissociation constant of the H,X acid, K,. In fact, K = K1/Kn. When Equation 26 is fulfilled, Equation 7 gives
>>
As shown by Equations 13 and 14, in this particular case, the nonvolatility of components HS-, HX("-')-, and X n does not correspond to a zero interfacial gradient of the individual concentration, as the reaction is infinitely fast. The solution of the above set of equations and boundary conditions is generally prohibitively difficult, essentially because x , s, and h may not be constant at the interface (see Equation 12). Nevertheless, in the present case, the material balance for equal diffusivities (Equation 4) and the electrical neutrality condition (Equation 3) make the interfacial concentrations time-independent (see Equations 6 and 7). The solution therefore becomes extremely simple. The sum of Equations 8 and 11 gives
or
(27)
si 5 xo
while in the bulk of the liquid, if we assume that so
