Absorption of Carbon Dioxide in Aqueous Alkalies HENRY J. WELGE Agricultural and Mechanical College of Texas, College Station, Texas established. Such is the case for the reaction between carbon dioxide and dissolved alkalies, which has been shown (3,8)to proceed according to the equation,
In the case of absorption of gases in liquids with which they react chemically, the characteristics of the absorption may depend markedly upon the mechanism of the chemical reactions involved and also upon the thickness of the liquid film obtaining under the particular conditions of agitation employed. For the case of the absorption of carbon dioxide in aqueous alkalies, the data on reaction rate and on rate of absorption, obtained independently, are in fair agreement
GO2
+ OH-
+
HCO,
for which the reaction rate expression is d(Coz) -dt
-
k ( C 0 2 ) (OH-)
(2)
Combining Equations 1 and 2,
D d2(C02) = k(CO2) (OH-) ~
.
~~~~~
(3)
dxz
~
TABLE I. DATAOF LEDIGAND WEAVER(25" C.)
ERTAIN apparent discrepancies occur between the experimental results previously obtained for the rate of absorption of carbon dioxide in solutions of varying concentrations of sodium and potassium hydroxides. Some of the results are presented in Figure 1, which shows, first, that for comparable alkali concentrations the absolute values of the rates of solution obtained by Ledig and Weaver (6) are much greater than those obtained by the other investigators. This lack of agreement may be due to the different experimental method of Ledig and Weaver, who measured the rate of decrease of the size of bubbles of carbon dioxide suspended in alkaline solutions; other investigators used cylindrical vessels partly filled with the alkali and stirred from below. However, Figure 1 shows further that the rates of solution obtained by Hitchcock (4) seem to be a straight-line function of the alkali concentration, while the rates of solution obtained by Ledig and Weaver apparently do not. Their data are given in Table I and show that a square-root dependence of rate of solution on alkali concentration gives better correlation. A square-root dependence is rather unusual but could be explained in the following way : The general unidirectional diffusion equation for dissolved carbon dioxide may be written :
C
hlolarity of Base (OH-)
m - 3
0.0 0.2 0.5 1.0 1.5 2.0 2.5 3.0
0.0 0.45 0.71 1 .o 1.225 1.414 1.58 1.73
Rate of S o h . Moles Rate COz/Sec./Sq. Cm. ate x 10' x 107 (OH -) I n N a O H I n K O H NaOH KOH NaOH 6.8 6.8 ... 95.5 19.1 42.5 51.1 76.4 1oi:z 38.2 53.9 61.3 61.3 75.0 61.3 75.0 47.6 71.5 58.4 ... 37.5 75.0 109: 0 54.5 53.0 31.3 78.3 . . . 49.5 l22:7 40.9 Mean 53.1
...
...
...
...
...
lo'
... ...
72.0 75.0
... ...
77.0 70.9 73.7
Assuming further that the concentration of hydroxide ion is so large compared with that of the carbon dioxide that i t remains substantially constant from point to point in the solution, Equation 3 may be integrated once between the limits d (COs)/dx, (COJ, and O,O, giving the result
+
4 B d(Co)
=
4,qmF)(COZ)
(4)
According to the definition of the constant D (Q), the rate of diffusion of carbon dioxide across any plane in the solution perpendicular to the direction of diffusion is given by the equation, (rate of diffusion)
=
d(CO 1 D 2 dx
(5)
whence, substituting for the derivative in Equation 5 from Equation 4, Assuming, first, that the steady state is reached-in other words, that the concentration of free carbon dioxide a t any point in the solution remains constant with respect to timethe right-hand derivative may be taken to represent rate of disappearance of carbon dioxide by reaction with the alkali. I n 1933 the writer suggested (11) the use of a reaction rate expression in connection with Equation 1 to eliminate the time dependence, provided the mechanism of the reaction is
(rate of diffusion) = d D k ( O H - ) (Con)
(6)
Taking the rate of diffusion infinitesimally near the gas-liquid interface as equal to the rate of absorption through the interface, (rate of absorption) = D 970
[d9]i = dDk(OH-)
(CO2)i (7)
JULY, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
Equation 7 explains the approximate square-root dependence of the rate of absorption on alkali concentration, if changes in the solubility of free carbon dioxide, (C02);, with changing alkali concentration are neglected, and also changes in viscosity, which influence D.
Calculation of Reaction Rate Constant As a further test of the correctness of the foregoing a s s u m p tions, the value of the reaction rate constant k may be calculated from the absorption data of Ledig and Weaver (6), and compared with the value '1 obtained by direct measurement (3). Rewriting E q u a tion 7 in the form, 60
I I
(rate of absorption)
m
=
0-DATA OF LEDlG AND WEAVER x - DATA OF HITCHCOCK * - D A T A OF DAVIS AND C R A N D A L L
45% (COJi (8)
and using for the term on the leftE hand side t h e average v a l u e -OX*I I 1.0 2.0 given in the last 8 M O L A R I T Y O F ALKALI line of Table I for sodium hydroxide, FIGURE 1. RATEOF SOLUTION OF CARfor D the value BON DIOXIDE IN SODIUM HYDROXIDE SOLUTIONS given by Arnold ( I ) , and for (COS), that given by Lewis and Randall (7), all in coneistent units of gram molecules, centimeters, and seconds, we have, a t
5
'
25" C.:
53.1 X 10-7 =
41.71 x
10-6
4 5 (3.38 X
10-9
whence fi = 37.0, and k = 1370 seconds-' (moles per liter)-l. If, instead, the average of the data of Table I for potassium hydroxide is used, the value obtained for k is The values obtained by 2450 seconds-' (moles per liter)-'. the direct measurements of Faurholt (3) are A t 0" C.: k = 405 X 2.3 = 932 At 18" C.: k = 1740 X 2.3 = 4002 At 25' C.: k = 7080 (extrapolated)
The two sets of values of the reaction rate constant, k , agree in order of magnitude but differ considerably in absolute value. It is difficult to explain this difference adequately, although it may be due in part to the widely different experimental methods and conditions, such as alkali concentration, employed in the two cases.
Influence of Liquid Film Thickness The different character of the absorption observed by Hitchcock (4) is believed to be due to the greater thickness of the liquid film in his experiments. This film thickness may be estimated from the rate of absorption observed by him for carbon dioxide diffusing into pure water alone, which was 0.04 cc. per sq. cm. per minute, or 26.8 X IO-Smole per sq. cm. per second. When alkali is not present, the mechanism of the absorption is not complicated by an irreversible chemical reaction. I n such a case, again assuming the steady state to be attained, the right-hand derivative in Equation 1 has the value zero, and an integration gives the result,
D-=d ( Cax o2)
971
constant = (rate of solution)
(9)
according to the definition of the constant D (9). When values previously given above are inserted in Equation 9, we have (1.71 X d-( C -o z ) dx
- a(Co,) Ax
d(COz) X -= 26.8 X dx =
15.7 X IO-'gram mol./cc./cm.
and since the variation in the concentration of carbon dioxide, A(C02), is from its saturation value a t 30" C., or about 3.0 X 10-6 gram molecule per cc. (6),to zero, we have
The much higher rate of absorption observed by the experimental method of Ledig and Weaver (6) for carbon dioxide and pure water indicates correspondingly more vigorous agitation in their experiments than in those of Hitchcock (4). A similar calculation based on their data leads to the value 0.001 cm. for the thickness of their liquid films. This considerable difference in film thickness greatly affects the character of the absorption for the following special reason. Integration of Equation 4 between the limits (CO,),, (COZ), and 0, x, leads to the result
from which may be calculated the variation of carbon dioxide concentration with x, the distance from the interface. A plot of the result for the special case of 0.2 M sodium hydroxide, using the value of k previously obtained from the data of Ledig and Weaver (6),is shown in Figure 2. Even with this relatively small concentration of alkali, most of the dissolved carbon dioxide is consumed by the time it has diffused a distance of about 0.001 cm. from the interface. As a result of the consumption of carbon dioxide by the alkali in the liquid film, bicarbonate ions (and carbonate ions) are there produced, set up concentration gradients of their own, and in turn diffuse toward the main body of the solution. When the state of agitation of the absorbing solution is such that the thickness of the liquid film is also about 0.001 cm., these products will attain a concentration a t the interface comparable with that of the carbon dioxide or about 0.03 molar. This concentration will cause them likewise to diffuse into the main body of the alkali solution. This concentration of the products obtained is small, in the experiments of Ledig and Weaver ( 6 ) , compared with the concentration of t h e a l k a l i (0.2 molar) from which they are produced. (C Consequently t h e alkali concentration -0.0015 -0.0010 -0.0005 0 DISTANCE FROM INTERFACE, CM. may be assumed, as above, to be substantially constant FIGURE 2. CONCENTRATION OF DIFFUSING SOLUTES AT VARIOUS DISthroughout the TANCES B R ~ M THE LIQUID-GAS. solution. The apINTERFACE
973
INDUSTRIAL AND ENGINEERING CHEMISTRY
proximate variation in concentration of alkali is also shown in Figure 2. However, when much gentler agitation, thicker liquid films (0.019 cm.), and slower absorption rates are encountered, as in the experiments of Hitchcock (4), the products (bicarbonate ion and carbonate ion) must attain correspondingly higher concentrations near the interface to cause them to diffuse through the liquid film into the main body of the solution. As the concentrations of the products rise, the concentration of the alkali from which they are produced decreases near the interface, to the point where the assumption that i t is constant throughout the liquid film is no longer justified. The rates of absorption of carbon dioxide obtained by Hitchcock ( 4 ) and by Davis and Crandall (2) depend rather on the rate of diffusion of alkali into the liquid film, and hence on the first power of the alkali concentration, as has already been stated by others (IO).
Nomenclature concentration of COZ, moles per cc. or per liter, at a point 5 cm. from interface concentration of COn at liquid-gas interface total differential
VOL. 32, NO. 7
partial differential increment D = diffusion constant, sq. cm. per second k = reaction rate constant In = Napierian logarithm OH-) = concentration of alkali, moles per liter ( t = time, seconds x = distance into liquid from gas-liquid interface, cm. b = A =
Literature Cited (1) Arnold, J. H., J . Am. Chem. Soc., 52, 3937 (1930). (2) Davis, H. S , and Crandall, G. S., I b i d . , 52. 3757 (1930). (3) Faurholt, C. J. chim. phys., 21, 400 (1924). (4) Hitchcock, L E., IND. ENQ.CEIEM., 26, 1158 (1934); 29, 301
(1937).
(5) International Critical Tables, Vol. 111, p. 260, New York, McGraw-Hill Book Co., 1928. (6) Ledig, P. G.,and Weaver, E. R.. J . Am. Chem. SOC.,46, 050 (1924); Ledig, IND.ENQ.CKEM.,16, 1231 (1924). (7) Lewis and Randall, “Thermodynamics”, p. 576, New York, McGraw-Hill Book Co.. 1923. (8) Saal, R.N.J., Rec. k a v . chim., 47, 264 (1928). (9) Sherwood, T. K., “Absorption and Extraction”, pp. 22-4, New York. McGraw-Hill Book Co., 1937. (10)Ibid., pp. 210-12; Hatta, S.,Tech. Rept. TBhoku Imp. Unic., 8 , 1 (1928-29). (11) Welge, H J., unpublished thesis, Mass. Inst. Tech., 1933.
Problems in Lime Burning A NEW X-RAY APPROACH W. F. BRADLEY
G. L. CLARK
Illinois State Geological Survey, Urbana, 111.
University of Illinois, Urbana, Ill.
V. J. AZBE, GED as is the process of manufacturing limes by the thermal decomposition of limestonesand dolomites, it is generally agreed that there are many unsolved problems, both chemical and physical, relating especially to the accurate prediction of practical behavior of products of the kiln, such as limes or finishing hydrates. It has long been known that some limestones will make a good finishing hydrate whereas other limestones with almost the same chemical composition will not; or again two limestones of different chemical composition will often give equally good hydrates. Many attempts have been made to find physical explanations, and the x-ray diffraction method was applied a dozen years ago in one of the early applications to industrial problems. Even earlier, crystal structure analyses had been made for the principal solid materials involved in the topochemical reactions of lime burning: calcium carbonate (calcite and aragonite), dolomite (calcium magnesium carbonate), calcium and magnesium oxides, and the corresponding hydroxides. Table I lists the best data on these crystal structures. The burning of limestone and dolomite may be represented diagrammatically in Figure 1 in terms of the atomic structure of the cleavage plane. The lesser volume associated with a given group of C a + +ions is thus illustrated, as is the environment provided, on the one hand, by the coplanar CO,-groups, and in the other by 0-- ions. I n 1927 Farnsworth (3) made the first attempt t o explain differences in plasticities of limes by means of x-ray analyses. Chemically pure calcium carbonate and calcium hydroxide
A
St. Louis, Mo.
were dissociated to controlled degrees and hydrated, the plasticities being correlated with the dissociation conditions. This present study is being directed a t commercially prepared limes and hydrates with a view toward evaluating the applicability of x-ray diffraction methods to the current problems of industry. Such commercial materials came to hand as powders or polycrystalline aggregates, and are best
TABLE I. CRYSTAL STRUCTURES Structure Calcite, CaCOa Magnesite, hlgc03 Dolomite, C a l k (cod2 Aragonite. CaCOa
*
Space Group
Rhomb Angle, OL
D& = R ~ C101°55’* (46’7‘) Rhombohedral D5d = R3; 103O20’* (48’10’) Rhombohedral Ci, = R3 102’50’* (47’30’) Orthorhombio Vk6 Pcmn ... Rhombohedral
-
...
Cubic Cubic Hexagonal
0,” = Fm3m O E = Fm3m Cjm
...
Hexagonal
Csm
...
...
Unit Cell Constant, a 6.4125*
(6.361) 5.84* (5.61) 6.18* (6 .OO) a = 4.94 b = 7.94 c = 5.72
4.80 4.20 a = 3.58 c = 5.03 a = 3.12 c = 4.73
Based on the conventional rhomb. analogous to th,e unit cell of NaCI. Actually the unit cell contains 2 instead of 4 molecules with a and a shown in brackets.
