INDUSTRIAL AND ENGINEERING CHEMISTRY
728
(4) Briggs, L. H., J . Dairy Sci., 3,61, 70 (1931).
Coe, M. R., and LeClerc, J. A., IND.ESG. CHEM.,26,245 (1934). Davidsohn, J., Chem.-Ztg., 54, 606 (1930). (7) Fellenberg, T. von, M i t t . Lebensm. Hug., 15, 1 9 8 (1924). (8) Greenbank, G.R., and Holm, G. E., IND.ENG.C H m f . , 16, 598 (5) (6)
(1924). (9) Ibid., 17, 625 (1926). (10) Ibid., Anal. Ed., 2, 9 (1930). (11) Issoglio, G., Snn. chim. applicata, 6,1 (1916); Kerr, R. H., and Sorber, D. G., IKD.ENC.CHEV.,15, 383 (1923). (12) Kreis, H., Chem.-Ztg., 26, 1014 (1902). (13) Laug, E. P., IND. EXG.CHExf., Anal. Ed., 6, 111 (1934). (14) Lea, C. H., Dept. Sci. Ind. Research (Brit.), Rept. Food Inaestigation Board, 1929, 30 (1930). (15) Mattill, H. A,, J. Bid. Chem.,90, 1 4 1 (1931). (16) Milas, N. A . , J . Am. Chem. Soc., 52, 739 (1930); Chem. Rez., 10, 295 (1932).
VOL. 27, NO. 6
C., Dryer, C. G., Lowry, C. D., Jr., and Egloff, G., ENQ.CHEM., 26,497 (1934). (18) Newton, R. C., J . Oil Soap, 9,247 (1932). (19) Olcott, H. S., J . Am. Chem. SOC., 56,2492 (1934). (20) Olcott, H. S., and Mattill, H. A , , J . B i d . Chem.. 93, 59, 65 (17) Morrell, J. IND.
(1931). (21) (22)
Olcovich, H. S., and Mattill, H. A . , Ibid., 91, 1 0 5 (1931). Orton, K. J. P., and Bradfield, h. E., J . Chem. Soc., 125, 9 6 0
(1924). (23) Royce, H. D., IND. ESG.CHEM.,Anal. Ed., 5, 244 ~ 1 9 % ) . (24) Stirling, 3. D., Biochem. J., 28, 1048 (1934). (25) Taffel, A., and Revis, C., J . SOC.Chem. Ind., 50, 8iT (1931). (26) Wheeler, D. H., J . Oil Soap, 9, 89 (1932).
(27) Pule, J. A. C., and M'ilson, C. P., Jr., IND.ENG.CHEI., 23, 1254 (1931).
RECEIVED December 2 6 , 1934.
Rate of Absorption of Carbon Dioxide Effect of Concentration and Viscosity
of Normal Carbonate Solutions The initial (steady state) rate of absorption of pure carbon dioxide a t a pressure of one atmosphere is measured for solutions of sodium carbonate up to 4 normal and of potassium carbonate up to 7 normal a t 30' C. An equation of the form,
LAUREN B. HlTCHCOCK . O D HENRY 31. CADOT University of Virginia, Charlottesville, Va.
T
satisfactorily reproduces the experimental results over the entire range, where dV/AdO represents initial current density, ci and cs are interfacial and main-body concentrations, respectively, of the reactants, and z is viscosity. The constants k and b are determined by the experimental data and are approximately 10 per cent higher for the potassium compound. The measurements were made under identical conditions with those employed in determining absorption rates for the analogous hydroxides, permitting for the first time a quantitative comparison of the absorption rates of the two carbonates and the two hydroxides as a continuous function of concentration. The initial (steady state) rate of absorption by pure water is also reported. Apparently discordant results of earlier investigators may be satisfactorily interpreted in the light of the new evidence.
HE initial rate of absorption of pure carbon dioxide gas b y stirred solutions of potassium hydroxide and sodium hydroxide a t 30" C. was studied by Hitchcock (5) as a function of caustic concentration and liquid viscosity. It was found that t h e results could be readily interpreted by means of a diffusional mechanism in which the rate of absorption was directly proportional to the concentrations of the reactants and inversely proportional to a function of the viscosity. I n view of the general industrial use of soda ash solutions as absorbents, it seemed desirable to make a similar study of the behavior of aqueous solutions of sodium and potassium carbonates and compare the rates of absorption into these less reactive media with those obtained for the respective hydroxides under identical absorption conditions. Consideration of the literature furnished a n additional incentive to undert,aking this investigation, for i n >pitc of the large number of experiments bearing directly on t'he subject, the results of different investigators appear to be exceptionally discordant. While it is true that the several conclusions are supported by experiments of a qualitative character for the most part, the disagreement cannot be explained satisfactorily on the basis of experimental error alone. The chief difficulty seemed t o be that no two investigators used the same solute concentrations in the same type of absorption equipment, and no one investigator varied solute concentration over a sufficient range. Ledig and Weaver ( 7 ) found that a bubble of pure carbon dioxide gas rising through a dilute solution of sodium hydroxide at 25" C. was absorbed many times faster than if i t rose through sodium carbonate solution of the same concentration, while Davis and Crandall ( 2 ) reported that pure carbon dioxide gas was absorbed through a horizontal liquid surface b y stirred 0.1 molal sodium carbonate at the same temperature slightly more rapidly than by 0.1 molal
JUNE, 1935
INDUSTRIAL AND ENGINEERING CHEMISTRY
sodium hydroxide. Payne and Dodge ( 8 ) , uciny a countercurrent packed toner, are in qualitative agreement with Ledig aiid TT'eaver. Tilliamson and Mathews ( ' 1 ) find that potas-ium hydroxide absorbs carbon dioxide much more rapidly than does potascium carbonate in both packed tower aiid batch type apparatus. They also state that the rate of absorption iq independent of concentration from 0 to 0.6 N potassium carbonate; Pagne and Dodge find that a sixteen fold variation in Sodium carbonate concentration has no significant effect on the coefficient of absorption. Disagreement on the relative rates of absorption even by pure water and by sodiuin carbonate solutions is striking. The question n-ould seem to be a simple one, but Table I indicates hidden compleuities.
T.4BLE
Rate
Cc./sq.
cm. 3.29 1.0 0.184 0.011 0.0161
I.
H:O Faster than XaKO:
.,.
k'es So So
..
Yes
INITIAL
RATEO F
ABSORPTION O F P U R E
CARBOXDIOXIDEBY WATER Type of Equipment Falling liquid drop Rising gas bubble Stirred liquid batch (400 r. p. m.) Stirred liquid batch (80 r. p. m.) Unstirred liquid batch Packed tower
'Temp. C. 25 25 25
Reference (IO)
30
(7) (8) (5)
25 25
(1) (8)
The initial rate of ab-orption determined in this work, and the one nhich forms the basis of comparison in Table I, is that in comnion use, defined as the rate existing momentarily after concentration gradients have been established through the liquid film. The term "practical initial rate" has been prupo-ed for this value, sometimes described as the steady-state initial rate, as opposed to the true initial rate as measured hy Ledig and Weaver. These investigator* erriployed a teclinic which enabled them to measure the abnormally high rate reached in a fraction of a \econd after carbon dioxide first encouritera fresh solution. Their measurenieiiti: indicate that the practical initial rate is reached in all cahe* within one aecond, and values of the latter rate mag be estimated from their data (cf. Dayis arid Crandall, ?j .
729
tube was negligible. None could be detected in the main apparatus at any time. The alkali carbonates used were Baker's c . P. Analyzed brand. Reboiled distilled water was used in preparing solutions for absorption experiments. Concentrations were determined by pairs of volumetric analyses agreeing within 0.1 per cent. Briefly, t.he experimental procedure reduces to recording (1) zero time when gas is iirst admitted to the absorption tube and (2) the time when a rising mercury column passes each of a series of fixed calibration points in a buret as gas is displaced to the absorption tube. Subtraction of successive time readings and buret readings results in a series of time increments and volume increments yhich may be made as small as desired. Each A V is then plotted at the middle of its A4 with respect to the continuous time axis as abscissa, and a smooth curve drawn t.hrough these points becomes in effect a plot of d V / d 4 vs. a4. If d Z V / d @ were constant, the curve thus obtained would be exact; since d Z V / d 8 * varies gradually, the curve is theoretically an approximation which becomes more exact as smaller increments are measured. Figure 1 shows that, as absorption proceeds, the rate decreases, relatively more rapidly during the first 10 minutes than later during the experiment. The slope of this early portion of the curve is steeper and changes more rapidly in experiments where the solution has a higher initial rate of absorption. I n solutions having a relatively slow rate, the slope is substantially constant. Although the rate measurements begin from 2 to 4 minutes after zero time, one may extrapolate the curve to zero time t o obtain the practical initial rate of absorption. The straighter the line, the more confidence one may place in this extrapolation. Since the carbonate solutions absorb much more slowly than hydroxide solutions in general, the initial rates obtained in this way are correspondingly more accurate.
FIGURE1.
EXPERIMENT.4L POINTS (RIJX OF ABSORPTION OF C.4RBON DIOXIDE BY POT4SSIUM CARBONArE ( I X I T I h L L Y 2.010 iv) CS. TIWEAT 30"
13) FOR R.4TE
c.
Experimental Work Tlie practical initial rate of absorption of carbon dioxide has been determined a t 30" C. for aqueous solutions of sodium carbonate from 0 to 4 normal, and for potassium carbonate from 0 to 7 iiorinal:
AND
ONE ATMOSPHEREOF PURE GAS
Deviations of the points in Figure 1 above arid below the curve do not indicate as great a n experimental error as might be concluded a t first, but are common to rate rneasurements and are due principally in this work to pressure surges. If the pressure is differentially high on one reading, it will be equally low on the next, while the small variation becomes magnified in the process of calculating small increments. Similarly, the observer may record time just before the mercury level reaches a reference mark, or just after. Careful examination of a great mass of data taken on this apparatus by different observers indicates that the variations in a given series of observations neutralize one another. The arerage of two or three apparently scattered points always falls on t h e smooth curve. Adjustment of the automatic control elements of the apparatus will minimize these routine fluctuations but, so far as is known, it is impossible to prevent them entirely in measurements of this type. The original data from JThich Figure 1 was prepared are presented in Table 11. The solution in this case was 2.010 N potassium carbonate; other concentrations were used in similar fachion to determine practical initial rates for both potassium and sodium carbonates as summarized in Table 111. I n addition, the initial rate into pure water a t 30" C . was redetermined, since it appears to be an important refer-
INDUSTRIAL AND ENGINEERITG CHEXIISTRY
730
TABLE11. ABSORPTIOSOF CARBOX DIOXIDEBY POTASSICM C.4RBOiiATE
R u n 13 Initial concn. a s KrCOa Vol. of soln. taken, cc. Temp. ' C. Source( of CO? Source of K2C03 Speed of stirring, r. p. m. Area of interface, s q . cm. Gas Buret point So.
Cc.
.. 8:43 8.41
8.41
8.44
8.38
5
0
Xzn. Charge .i 12-59-54 0 1- 1-21 1.45 3.10 1- 3- 0 1- 4-40 4.i7 1- 6-21 6.45 1- 8-05 8 18 1- 9-47 9.88
8:jl 6.43 8.41 8.41 8.44
1-11-43 1-14-28 1-16-13 1-17-58 1-19-44 1-21-29 1-23-17
8151 8.43 8.41
1-26-13 1-28-01 1-29-48 1-31-36 1-33-12
Charge C 26.32 28.12 29.90 31.70 33.30
2 4
80
20.72
Charge B 12.82 14.57 16.32 18.07 19 83 21.48 23.38
8.38
3
Photochronograph Hr.-mzn -sec.
March 6, 1935 2.010 N 400 30 Liquid Carbonic Co. J. T. Baker Chemical Go.
ir-/>9
&\..
Cc./min. Min.
Temp.
c.
...
...
5 : 107
2.28 3.94 5.61 7.32 9.03
30.01 29.99 29.99
13:io 15.45 17.20 18.95 20.71 22.48
29.95 29.99 30,OO 29.98 29.94 29.95 30.00
5.035 5.003 4.878 4.930
4:a6:!
4,817 4,806
4.778 4,822 4.654
4:728 4.735 4.671 (Sample
,..
30: 05 30.05
...
30.00 2+:2'2 29.97 29.01 29.96 30.80 ... withdrawn)
ence point in establishing the respective curves of initial rate us. concentration. As an indication of the reproducibility of results and the identity of the absorption apparatus, it may be noted that the recent value is 0.041 cc. per sq. cm. per minute, while the value obtained about two years ago was 0.040 cc. per sq. cm. per minute.
YOL. 2 , , h O , 6
where the constants k and a are determined entirely by the data and involve no arbitrary values. The conqtants for absorption by potassium hydroxide differed by about 10 per cent from those for sodium hydroxide. Equation 1 fits the data for rate of absorption by carbonates very well above concentrations of 1.0 normal but fails in t h e dilute solutions. Figure 2 shows that the curves for both carbonates fall off relatively rapidly t o the rate into pure water, as compared with the gradual decrease trom the maximum a t high concentrations While the curve> for the hydroxides are not entirely symmetrical about the maxima, the lack of symmetry is much greater in the ca-e of the carbonates. I n other words, a gir-en increase in concentration of metal carbonate is very much more effective in dilute solution than in concentrated solution, o u t of proportion. it seems, to the viscosity variation, and strongly wggecting the importance of the activity coefficient in this caqe.
TABLE 111. IXITIAL ABSORPTIONR A T E O F CARBOX DIOXIDE BY Two CARBONATE SOLUTIOSS .4T 30" C. UNDER ONE ATMOSPHERE PRESSURE OF PUREGAS ASD COSSTAST STIRRING RATEOF 80 R. P. 1LI. -Sodium
Carbonate-Potassium Carbonate-yo, ac./ NorViayo cc./ min./sq. mality, cosity R u n mih./sq. Normality Viscosity R u n KO. om. cs (6). P No. cm. cs ,,GI, : 1 0.041 0 0,8004 19 0.1507 0.357 0.845 11 0.1510 0.519 0.915 14 0.222 1.041 0.939 0.1818 1.039 1.047 13 0.2509 2.010 1.09:4 7,8 12 0.1650 1.519 1,190 16 0.2620 3.019 1.289 2.080 1,390 15 0.2637 3.732 1.457 5,6 0.1765 9,lO 0.1543 3.110 1.874 5.30 1 932 17 0.228 3,4O 0.1205 4.00 2.454 18 0.1766 6.53 2 445 Incipient crystal formation detected on edges of interface.
TABLEIv. RELATIVERATESO F ABSORPTIONO F -kLK.ILI CARBONATES AND HYDROXIDES AT 30" C. IN Cc. PER SQ. CM. PER MIWTE
-
A t h'ormality of:
Discussion of Results The data of Table I11 are shown in Figure 2. The relat i r e rates of absorption by the carbonates of the two metals are of the same order of magnitude as in the case of the hydroxides, shown in Figure 6 of Hitchcock's paper ( 5 ) . The normal carbonate, while not as reactive as the hydroxide, is definitely a reactive solute and as such should show increasing rate of absorption with increasing concentration. Both potassium and sodium carbonate give initial rates of absorption which increase rapidly from the rate into pure water, rising to a maximum a t 1.5 normal for sodium carbonate and 2.9 normal for potassium carbonate. At the maxima these solutions have viscosities a t 30" C. of 1.19 and 1.24, respect ively The initial rates of absorption by the normal carbonates are found to approach equality with those by the respective hydroxides only a t very low concentrations. Over the concentration covered in this investigation, the hydroxides give from two to twenty times as rapid initial rates of absorption as do the carbonates. A few approximate values of the rates, expressed in cubic centimeters per square centimeter per minute, are given in Table IV, and the ratios of hydroxide rate to carbonate rate are shown for each metal. For purposes of comparison, a portion of the initial rate curve for sodium hydroxide is shown in Figure 2. An equation was developed (5) relating initial rate of absorption to the concentrations of the reactants and to the liquid viscosity. It satisfactorily reproduces experimental results for potassium and sodium hydroxide in the form:
.
NaOH NarCOa OH/COj KO H H2C03 OH/COa
0.1 0 15 0.08 1.9 0.20 0.09 2.2
0.5 0.58 0.155 3.7 0.64 0.175 3.7
1 1.14 0.16 6.3 1.38 0.22 6.3
2 2.17 0.18 12.0 2.57 0.255 10.0
3 2.80 0.175 16.0 3.62 0.263
13.8
4
2.92 0.125 23.8
4.51 0.252 18.0
Walker, Bray, and Johnston ( 9 ) give activity coefficients for aqueous solutions of alkali carbonates for ionic strengths up to 2.5, corresponding to a concentration of approximately 1.G normal. Equation 1 was applied to the data for initial rate of absorption a t the corresponding ionic strength by potassium carbonate, using the activity of the carbonate instead of the concentration. The following empirical equation is obtained : yo =
13.0 (0.025 -I- a s ) &S@
I
(2)
It fits the experimental data perfectly up t o a concentration of 1.0 normal. Beyond that it falls rapidly below the observed results. It is possible that the values of the activity coefficient for the highly concentrated solution: are less certain. Walker, Bray, and Johnston point out that it has been possible to verify the values up to ionic strength.. of 0.2 by electrometric methods. The relatively large increase in rate of absorption a t concentrations below 1.0 normal suggested that the rate might be proportional to a power of the driving force or concentration term, other than the first power. An equation of the form, Yo
=
k
(G
+
CS)*
(3)
J L \ E , 1935
ISDUSTRLIL - W D ESGIIIEERISG CHE5IISTRl
was therefore applied to tlie data of Figure 2 and Table I11 with the following results:
These equations are plotted as solid lines on Figure 2 , with the experinientsl points indicated by circles. The agreelnelit is satisfactory over the entire range. For potassium carbonate the average deviation of the experimental points from Equation 4 is much less than 1 per cent u p to a concentration of 5 normal. For sodium carbonate Equation 5 represents the data v i t h an average deviation of less than 1 per cent. The viscoqity of the liquid used in evaluating these equations was taken from the data of Hitchcock and l\IcIlhenny (6). Crystal formation could be detected solely in the experiments with 4 S sodium carbonate. I n this instance a few small crystals developed during the course of half an hour but only on the n-all of the absorption chamber a t the level of the interface.
Comparison with Earlier Results H a t t a (S), using a n apparatus similar dimensionally to that used in the present work, but with liquid stirred a t 93 r. p. ni. instead of 80 r. p. m., has studied extensively the progress of batch absorptions of carbon dioxide by alkaline solutions. Although the present discussion is limited to practical initial rates of absorption and is not concerned with the decrease in rate shown by a given batch, comparison with Hatta's data is possible a t two points a t 30" C. Extrapolating his experiments Kos. 40 and 41 to zero time, i t is possible t o calculate initial rates as approximately 0.29 cc. per sq. cm. per minute into 0.5 N potassium carbonate and 0.37 cc. per sq. em. per minute into the 2 S solution. K e find corresponding values of 0.175 and 0.255, which are in satisfactory agreement considering differences in apparatus and procedure. I n a more recent paper Elatta and Baba (4) find that the initial rate of absorption into a given potassium Carbonate solution a t 30" C. is higher for the stirred batch-absorption method than in the case of a bubbling method, but that, as the given experiment continues and the concentration of total carbon dioxide in the liquid phase exceeds 65 per cent of the total potassium concentration, the bubbling method gives a higher rate of absorption than the static stirred method. Consideration of the apparent disagreement betn eeii earlier investigators in the light of the new data presented in the foregoing leads to the conclusion that their results are actually in reasonable concordance, allowance being made in certain cases for fundamental differences in the method of gas-liquid interaction due to type of equipment. Thus i t appears in the current work that the rate of absorption by 0.1 molal (0.1 X) sodium hydroxide a t 30" C. is 0.15 cc. per sq. em. per minute; for 0.1 molal (0.2 sodium carbonate the initial rate of absorption is 0.11 cc. per sq. cm. per minute. A small experimental error could readily lead to a reversal of these figures and thus account for the slightly higher rate found b y Davis and Crandall ( 2 ) for sodium carbonate. Their apparatus was very similar t o the one used currently, but, as they made only a few measurements, the discrepancy did not appear. All investigators are therefore in virtual agreement on the relative rates of absorption of the hydroxides and carbonates. With respect to the influence of concentration of carbonate on the rate of absorption, while investigators agree that concentration is an important factor in the case of the hydroxides,
731
several report that the rate of absorption is apparently independent of carbonate concentration. It is clear from Figure 2 that the rate for sodium carbonate varies only a small absolute amount, although the percentage variation with concentration is comparable to that found for sodium hydroxicle. Thus a t 0.5 normal, the carbonate absorbs carbon dioxide a t the rate of 0.155 cc. per sq. em. per minute, a t 1.0 normal the rate is 0.18, passes through a maximum of 0.183 a t 1.5 normal, again reaches 0.18 a t 2.0 normal, and has fallen to only 0.175 at 3 normal. An investigator, particularly if studying these solutions in a countercurrent tower where other variables such as gas and liquid rate are very important, niay well find the concentration to have slight effect. I n some cases concentrations have been coniparetl which correspond t o points respectively on the rising and descending branches. of the curve a t practically the same values of the initial rate of absorption. The disagreement with respect to the rates o f ahorption into pure water and into sodium carbonate solution are someTvhat more puzzling. Apparently the removal of the reaction product from the vicinity of the gas-liquid interface is essential, and in most batch absorption apparatus a relatively large volume of stirred liquid is a t the disposal, so to speak, of only as much gas as can enter through the available liquid surface, ordinarily m a l l in relation to the depth of liquid.
1
I
G:~~yJ$'I;-IJ ____+
04
2
_t___-L--
3
c
14-
NORMAL J T Y
FIGLRE2.
INITIAL RATEO F h B S O R P T I O N O F C 4 R I ) O N DIOXIDE B Y P O T 4 S S I U M CCRBONATE A N D SODIUM C 4 R B O N 4 T E AT 30" 4s .4 FLXCTIOS O F CONCENTRATIOX m D E R O A E 4TIIOSPHERE
c
PRESSURE OF PUREGAS
Liquid is stirred at 80 r. p m.
I n the case of liquid flowing over packing in a countercurrent tower, however, the surface exposed to the gas is very great and the average liquid depth very small. One visualizes the dlfficulty in removing reaction product from one zone to another when the latter zone is nearly nonexistent and also the difficulty in supplying reactive solute froin such a layer. Since sodium bicarbonate is agreed by all investigators definitely to lower the rate of absorption below that obtained for pure water, owing to a combination of salt effect and back pressure of carbon dioxide, one is in effect comparing in a packed tower, not the rate of absorption by sodium carbonate relative to water, but the rate into a
