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The kinetics of lime slaking
HydrometaUurgy, 23 (1990) 377-396 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
377
The K i n e t i c s of L i m e S l a k i n g IAN M. RITCHIE and XU BING-AN
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, W.A. 6150 (Australia) (Received November 21, 1988; revised and accepted April 4, 1989 )
ABSTRACT Ritchie, I.M. and Xu Bing-An, 1990. The kinetics of lime slaking. Hydrometallurgy, 23: 377-396. Although the slaking of lime is a reaction of great antiquity, there have been few fundamental studies of its kinetics and mechanism. In this paper, the kinetics of the reaction are reported for lime samples in two different arrangements: rotating discs and powders. In the former case, the rate was measured by solution analysis; in the latter, by calorimetry. The rate of slaking of a rotating lime disc was approximately constant with time but depended on the disc rotation speed. In the presence of Ca2+ or OH- ions, the slaking rate was reduced. These results were accounted for by assuming that the slow step in the early stages of the slaking reaction was the diffusion of calcium hydroxide away from the reacting surface. Reasonable agreement between the measured slaking rates and those calculated on the assumption of slow calcium hydroxide diffusion was obtained. When powder samples were used, the rates of slaking could be fitted to the equation for a shrinking sphere model. It was shown that the effect of increasing the calcium oxide particle size or increasing either the time or temperature of preparation from calcium carbonate was to decrease the rate. Electron micrographs of the powdered lime before slaking were used to interpret these results. The effect of Ca 2+ or OH- ions on the slaking rate of powder lime samples closely paralleled those of the rotating disc sample suggesting the reaction mechanisms are similar.
INTRODUCTION
Of the heavy industrial chemicals, lime, either as quicklime, CaO, or slaked lime, Ca(OH)2, is second only to sulphuric acid in the amount produced. A detailed discussion of its multitudinous uses is given by Boynton [1 ]. These range from high temperature processes such as steel making to a host of applications at or near ambient temperature. Included in this latter category are a number of hydrometallurgical uses such as control of pH during flotation, coagulation, neutralization of acid solutions, control of pH in cyanide leach liquors and recausticization of Bayer liquors, the latter application being the most important in terms of the amount consumed. Lime is often slaked prior to use, and even when quicklime is added directly to a solution to, for example, remove carbonate from that solution, it seems 0304-386X/90/$03.50
© 1990 Elsevier Science Publishers B.V.
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I.M. R1TCHIE AND XU BING-AN
very likely that partial or complete slaking of the lime will occur first. However, despite the enormous importance of lime slaking, little is known about the reaction kinetics and almost nothing about the reaction mechanism. Most of the work reported to date is in the Eastern European literature. Zozulya et al. [2] found that the rate at which quicklime is hydrated increases with increasing lime surface area and the temperature at which the lime is slaked, and that the higher the temperature at which quicklime is manufactured by decarbonation of calcium carbonate, the less active is the resulting quicklime. These authors concluded that lime hydration is diffusion controlled and depends predominantly on the degree of supersaturation of the liquid phase with calcium hydroxide. Ovechkin et al. [3], using a high calcium lime, found that the rate of lime slaking increased with temperature but observed little effect of grain size. They too concluded that the reaction was diffusion controlled, at least in the final stages of slaking. In this paper, we report the results of a study of the slaking of a relatively high purity calcium oxide in the form of rotating disc and powder samples. The results obtained from the two sorts of samples are to a certain extent complementary. The rotating disc experiments give the most useful mechanistic information [4]. The area of the calcium oxide sample is essentially constant during the experiment and through the medium of the rotation speed, the mass transfer to and from the reacting surface can be varied in a reproducible manner. From a knowledge of the way the rotation speed affects the reaction rate, measured by solution analysis at suitable time intervals, it is possible to establish unequivocally whether the reaction is under chemical control or diffusion control, and if the latter, whether diffusion to or from the surface is the slow step. However, this approach is generally limited to the initial stages of the reaction, or at least until the slaking solution becomes saturated with calcium hydroxide, when it becomes difficult to follow the reaction. On the other hand, the powder samples most closely approximate industrial practice. In addition, the reaction is then easy to follow by the temperature rise of the solution associated with the heat given out during the reaction. Against this must be set the fact that there is almost no way of controlling mass transport to the reacting surface, which itself is contracting and changing shape as the reaction proceeds. EXPERIMENTAL Industrial limes contain sufficient impurities for different lime samples to have different properties. In order to avoid this problem A.R. grade calcium carbonate from UNIVAR was chosen as a standard raw material from which a lime of approximately 99% could be made by calcination CaCO3 ~ CaO + C02
(1)
The dissociation temperature for calcium carbonate is reported to be 890 °C
KINETICS OF LIME SLAKING
379
[5 ], but thermogravimetric analysis showed that the UNIVAR material started to decompose at about 630 ° C, and the reaction was complete by about 870 ° C. Accordingly, the A.R. grade calcium carbonate was calcined in a muffle furnace for 10 h at a temperature of 920 + 5 ° C. The calcium oxide so formed was ground and screened for use in the slaking experiments. The discs of calcium oxide were prepared by pressing the powder in a pellet press used for the preparation of infrared samples, and then heating the compact. The effect of the pressure used in making the disc, and the heating temperature and time were investigated. It was found that the optimum pressure was about 40 MPa for a disc with a diameter of 12.8 mm, and that pressures greater or less than this value result in a disc which is loose or likely to fragment. Although the sintering temperature for calcium oxide is 1650°C [6], it was found that when the disc was heated for 40 hours at 1100 ° C, its mechanical strength improved markedly and the resulting disc, whose diameter had shrunk to 12.45 mm, did not break up when rotated in solution. It was also found that the discs had to be heated on a fire clay surface, since they stuck to porcelain and nickel crucibles. In order to use the discs in a slaking study, they were mounted in a stainless steel holder such that only one face was exposed. The holder was attached to a shaft, coaxial with the disc, which could be rotated in the reactant solution at controlled speeds between 0 and 1500 r.p.m. The amount of calcium hydroxide present in solution after an appropriate reaction time could then be determined by a suitable method of analysis: conductivity for discs slaked in water; pH for discs slaked in calcium nitrate solutions; and atomic absorption analysis for calcium ions when the discs were slaked in sodium hydroxide solutions. The slaking of lime powder samples was followed by measuring the temperature rise of the reacting system in a Guild calorimeter which had been previously calibrated. 200 ml of the reactant liquid was placed in the dewar and an accurately weighed amount of lime ( ~ 0.2 g) was added and the mixture stirred by means of a paddle stirrer rotating at 1470 r.p.m. The sample size was chosen so that the temperature rise was large enough to be measured accurately, but not so large that the heat losses from the system were significant. The temperature rise is proportional to the heat involved in the reaction and so can be used as a measure of the extent of reaction. X-ray diffractometry, and optical and scanning electron microscopy were used to investigate the surface composition and structure of both the disc and powder samples.
38O
I.M. RITCHIE AND XU BING-AN
I Q ~r~
Fig. 1. Scanning electron micrograph of a lime disc: (a) before slaking; (b) after slaking for 18 min at a rotation speed of 800 r.p.m, in water; (c) after slaking for 18 min at a rotation speed of 800 r.p.m, in 0.1 M sodium hydroxide solution. T h e scale bars are 10 llm.
KINETICS OF LIME SLAKING
381
RESULTS AND DISCUSSION
Rotating disc studies Surface composition and structure An X-ray powder diffraction pattern of the surface of a quicklime disc which had been stored in a desiccator for five weeks showed only peaks which could be ascribed to calcium oxide and none to calcium hydroxide. Because X-ray diffraction is not good for detecting small amounts of a second phase, particularly when the second phase may not be very crystalline, this result cannot be regarded as proof of the absence of calcium hydroxide on the disc surface. However, it seems likely that there was very little on the surface since when a disc which was rotating at 800 r.p.m., had been slaked for 18 minutes, additional diffraction lines due to calcium hydroxide could be readily observed. These lines were more pronounced when the slaking reaction was carried out in water than in 0.1 M sodium hydroxide. Similar conclusions were reached using optical and scanning electron microscopy. From the scanning electron micrograph shown in Fig. la, it can be seen that the surface is porous, and consists of particles 2-5 ~m across which have been fused together. Figure lb shows the appearance of a lime disc which has been rotated in water at 800 r.p.m, for 18 min. The surface is covered with a large number of small but rough particles which are believed to be calcium hydroxide. The apparently slower reaction in 0.1 M sodium hydroxide also results in rough textured particles, but these are much bigger and more widely dispersed (Fig. lc). Reaction kinetics (a) Reaction rate. Irrespective of whether the lime slaking reaction was carried out in water or in solutions containing either calcium nitrate or sodium hydroxide, the slaking rate was found to be approximately constant at any given disc rotation speed. This can be seen from the plots of amount of calcium oxide dissolved against time shown in Figs. 2 and 3 for the particular cases of the slaking reaction in water, determined from conductance measurements, and in 0.03 M sodium hydroxide, determined from analysis of the calcium content of the solution by atomic absorption spectrophotometry. It is apparent from Fig. 2 that when the reaction is sufficiently rapid, the rate plots (e.g. at 600 r.p.m. ) show a slight curvature corresponding to a small decrease in reaction rate with time. One possible cause of this slight reduction in rate will be discussed later. In the meantime, it is sufficient to note that the reaction is essentially zero order, and the slope of the lines gives the zero order rate constant, ko.
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I.M. RITCHIE AND XU BING-AN
1.0 oJ
E -6 E "0
o
0.5
"0
o (J
5
10
15
time/rain Fig. 2. T h e a m o u n t of calcium oxide dissolved f r o m a disc r o t a t i n g at various speeds in w a t e r at 25 ° C: • = 100 r.p.m.; • = 200 r.p.m.; O = 400 r.p.m.; [] = 600 r.p.m.
~ o5 {D
0 0
I
I
5
10
15
time/min Fig. 3. T h e a m o u n t of calcium oxide dissolved f r o m a disc r o t a t i n g at v a r i o u s speeds in 0.03 M s o d i u m hydroxide solution at 25 ° C: • = 100 r.p.m.; • = 200 r.p.m.; O = 400 r.p.m.; [] = 600 r.p.m.; • = 800 r.p.m.
(b) Effect of rotation speed. It is clear from both Fig. 2 and Fig. 3 that the dissolution rate is strongly dependent on disc rotation speed indicating that the reaction is largely controlled by either the diffusion of some reactant species to the oxide surface, or the diffusion of some product species away from the oxide surface. Figure 4 shows the dependence of the zero order rate constant, ko, on the square root of the disc rotation speed, o), for different concentrations of sodium hydroxide. It can be seen that at the lowest reaction rates (highest sodium hydroxide concentrations), ko is directly proportional to the square root of the disc rotation speed, indicating that the reaction is under diffusion control. However, at the highest reaction rates (lowest sodium hydroxide concentrations), ko tends to fall off with increasing rotation speed, suggesting that the
KINETICS OF LIME SLAKING
383
10
V
E E
\
0 o
1 5
10
( w / r a d s.1 )1/2
Fig. 4. T h e variation of the zero order rate c o n s t a n t at 25°C with the square root of the disc rotation speed: • =0.1 M sodium hydroxide; • =0.03 M sodium hydroxide; O =0.01 M sodium hydroxide; [] = water.
reaction is going from diffusion to chemical control. In the case of the reaction with water, the rate constant is essentially independent of rotation speed at the highest rotation speeds investigated (1000 r.p.m.), behaviour which is characteristic of chemical control [4]. Similar results were obtained for the reaction of calcium oxide with the solutions containing various concentrations of calcium nitrate i.e. the reaction rate constant became progressively smaller and more directly proportional to the square root of the angular velocity of the disc as the calcium nitrate concentration was increased. A rate constant, k, which is independent of the angular velocity can be defined by the ratio ko/to~. For those systems in which the reaction becomes partly chemically controlled at high rotation speeds, and as a result, ko/to ~ decreases with increasing rotation speed, we define k as being equal to the tangent to the curve as to tends to zero i.e. when the reaction is most likely to be under diffusion control.
(c) Effect of concentration of Ca 2+ or O H - . As noted above, the effect of increasing the concentration of Ca 2+ or O H - ions in the slaking solution is to reduce the slaking rate. This is shown graphically in Fig. 5 in which the logarithm of the slaking rate constant k [moles Ca 2+ dissolving in solution per m 2 of CaO disc per second per (radian per second) i ], is plotted against the logarithm of the concentration, either Ca 2+ or O H - . Provided that neither the Ca 2+ nor the O H - concentration is above 10 -2 M, the rate constant k is essentially that of water, but above this concentration, k decreases and more rapidly so in the presence of O H - t h a n in the presence of Ca 2+.
384
I.M. R I T C H I E A N D X U B I N G - A N
Ig (conch / M )
-,6
-?
o
-2 A
O
~0
-8
e~
Fig. 5. T h e effect of c o n c e n t r a t i o n on the rate constant k for th lime slaking r e a c t i o n at 2 5 C. Experimental points: • = Ca2+; O = O H - . T h e solid lines were calculated using the t h e o r y pres e n t e d o n pp. 9 - 1 1 .
-8
E
_=
K -10 -12
I
3.0 (103k/T)
3.5
Fig. 6. Arrhenius plot for the slaking of lime in water.
(d) Effect of temperature. The effect of temperature on the kinetics of the slaking reaction in water was examined, and the results shown in the Arrhenius plot of Fig. 6 were obtained. The points are a reasonable fit to a straight line, from the slope of which an activation energy of 13.6 + 1.2 kJ m o l - 1 was calculated. This low value is consistent with the effect of disc rotation speed and indicative of diffusion control [ 4 ].
Mechanism of the slaking reaction
(a) General considerations. In a formal sense, the slaking reaction can be considered to proceed in three steps: Step 1, the conversion of calcium oxide to calcium hydroxide
CaO+H~O--~Ca(OH)2
(2)
KINETICS OF LIME SLAKING
385
followed by Step 2, the dissolution of calcium hydroxide to give calcium ions and hydroxide ions in solution Ca (OH)2 -*Ca2+ +2OH-
(3)
and Step 3, the diffusionof the calcium ions and hydroxideions into the bulk of the solution. Because the reaction shows a strong dependenceon disc rotation speed and a low activation energy, it must be diffusion controlled. Step 1 cannot be diffusion controlledbecausethe rate constants are too small for a reactant whose bulk concentration is 56 M. On the other hand, Step 3 couldbe rate controlling and wouldgivea zero order process, as observed. If the diffusionstep governsthe rate of the reaction,the dissolution step will be at equilibrium i.e. there will be a film of solid calcium hydroxide on the reacting lime surface which is in equilibriumwith calciumions and hydroxide ions in solution at the reacting surface. The diffusionof calcium ions and hydroxide ions away from the surface will be describedby the Levich equation [4]. It is convenient to discuss three special cases: the slaking of lime with water; the slaking of lime with a high concentration of calcium ions in solution, and the slaking of lime with a high concentration of hydroxide ions in solution.
(b) The slaking of lime with water. According to the Levich equation, the dissolution rate, S, for a reaction controlled by the rate of diffusion of calcium hydroxide away from a surface at which there is a saturated solution of calcium hydroxide into water is S=0.62 D (Ca(OH)2) 2/3 u -~/~ 0,)1/2 [Ca(OH)2]s
(4)
where D (Ca (OH) e ) is the diffusion coefficient of calcium hydroxide in water, u is the kinematic viscosity of water and [Ca (OH)e ] s is the concentration of a saturated solution of calcium hydroxide at the reacting surface. Since ko = S and k = ko/o) ½, k=0.62 D (Ca(OH)2) 2/3/2 -1/6 [Ca(OH)2]~
(5)
The kinematic viscosity is given in the Handbook of Chemistry and Physics [7], and so k can be estimated provided values for D(Ca(OH)e) and [ Ca (OH) 2]s are known. Hedin [8 ] has reported that the value of the diffusion coefficient for calcium hydroxide depends quite strongly on the concentration, dropping from 17.47× 10-'° m 2 s - ' at 1.07 × 10-'~ M t o 13.85× 10-'° m 2 s -1 at 1.93× 10-2 M, this latter concentration being close to the solubility of a standard solution of calcium hydroxide. In the mechanism suggested here, the calcium hydroxide is assumed to be saturated at the dissolving surface, and so it seems reasonable
386
I.M. RITCHIE AND XU BING-AN
to assume a value of D (Ca ( OH )2 ) = 14 × 10- l o m 2 s - 1 for the purposes of these calculations. By approximating activities with concentrations, [Ca(OH)2] can be estimated from the solubility product, Ks, via [Ca(OH)2] = (K J 4 ) 1/3
(6)
where K s = 6.5 × 10 - 6 M 3 has been calculated from the average of the log Ks values listed in Sillen and Martell [9]. Substituting these numbers into Eqn. 5, we obtain a value of k equal to 9.2 × 10- 5 tool m - 2 s - ~which is in reasonable agreement with the experimental value of (12.0 _+2.5) × 10 -5 mol m - 2 s - ½ considering the approximations made in the calculations.
(c) The slaking of lime in solutions containing calcium nitrate. In solutions containing high concentrations of calcium nitrate, the solution conductivity is high and ionic migration can be neglected. The diffusion of calcium ions and hydroxide ions can be considered as independent processes although neutrality must still be maintained in the solution. In addition, the amount of calcium carried away from the reacting surface as the species CaOH + can be neglected since the surface p H is, as the calculations show, relatively low. The relevant equations for the fluxes, J (mol m -2 s -1 ), of calcium ions and hydroxide ions from the saturated calcium hydroxide surface are [4] J ( C a 2+ ) =0.62 D ( C a 2+ )2/3
v-1/6 0_)1/2 { [ C a 2 + ]s - [ Ca2+ ]b}
J ( O H - ) = O . 6 2 D ( O H - ) 2/~ v-1/6 o) 1/2 { [ 0 H - ] s S = J ( C a 2+ ) = J ( O H -
[OH-]b}
)/2
(7) (8) (9)
where the subscripts s and b denote surface and bulk concentrations respectively, and [ O H - ]b ~ 0 for the calcium nitrate solutions. The surface is still at equilibrium and so K~ = [Ca 2+ ] s [ O H - ] 2
(10)
By combining Eqns. 8-10, it can be shown that D ( O H - )2/3 [ O H - ] s = 2KsD (Ca 2+ )2/3 {Ks - [Ca 2+ ]b [ O H - ] 2 }
(11)
from which [ O H - ]s can be calculated for a range of [ C a 2+ ]b, provided values of Ks, D ( O H - ) and D (Ca z + ) are known. Ks is given earlier and D ( O H - ) has been estimated to be approximately 62 × 10- lO m 2 s - a from the data of Littauer and Tsai [10]. We have been unable to locate a value for the diffusion coefficient of Ca 2+, and have therefore assumed it to be the same as that for Cd 2+ (7.0 × 10- lo m e s - 1 in 1 M KNOa [ 11 ] ) on the grounds that the ionic radii of Ca 2+ and Cd e + are very similar [ 12 ]. Once values of [ O H - ] s as a function of [Ca 2+ ]b have been obtained, the slaking rate can be calculated from Eqns. 8 and 10 for a range of [Ca 2+ ]b. The
387
KINETICS OF LIME SLAKING
results give the upper solid line in Fig. 5. Again, it is clear that, within the limits of experimental error and the assumptions made in the calculations, there is good agreement between experiment and theory.
(d) The slaking of lime in solutions containing sodium hydroxide. This situation is similar to that for the slaking reaction in high concentrations of calcium nitrate. However, in this case, account must also be taken of the species CaOH + which is present in appreciable concentration. Besides Eqs. 7, 8 and 11, the following also apply J ( C a O H +) =0.62 D(CaOH + )2/3u-1/6o) 1/2 { [CaOH + ] s - [C aOH+ ]b}
(12)
S = J ( O H - ) / 2 = J ( C a 2+ ) + J ( C a O H + )/2
(13)
and K1 = [CaOH + ] J [Ca 2+ Is [OH-]8
(14)
where J ( C a O H + ) is the flux of the species CaOH + away from the surface into the bulk solution and K~ = 24.7 M - ' [9] is the stability constant for the formation of CaOH +. In the absence of a published value for the diffusion coefficient of CaOH +, which will be somewhat larger than Ca 2+, we have assumed that it is the same as that for Ag + (i.e. 15.8X10 -1° m 2 s -1 [13] ), whose ion size is also somewhat larger than Ca 2+ [12]. The slaking rate can now be calculated using the procedure set out in (b) above. From Eqns. 7, 8, 10, 12, 13 and 14 we obtain D (OH-)2/3 [OH- 1~ - D (OH-)2/3 [OH- ]~ [OH- ]b =2K~D(Ca 2+)2/3+K~KID(CaOH+) [OH-]~
(15)
from which [OH]~ can be calculated for a range of [OH- ]b using the diffusion coefficients and equilibrium constants listed above and assuming [Ca2+ ]b ~ [CaOH+ ]b ~ 0. The slaking rate can then be calculated from Eqns. 8 and 13. The results of these calculations are shown in the lower solid curve of Fig. 5. While the fit to the experimental results is somewhat worse than the case of lime slaking in calcium nitrate solutions, particularly at high concentrations, it is none-the-less considered to be reasonable, given the fairly crude assumptions which were made. Summarising the results of the calculations in (b), (c) and (d), we may say that the mechanism of rate control via slow diffusion of dissolved calcium hydroxide away from the reacting surface gives a good description of the results in water and in concentrated solutions of calcium nitrate and sodium hydroxide. If this interpretation of the mechanism is correct, the slight curvature of the rate plots seen in Fig. 2 at high rotation speeds over the course of the reaction is probably due to a reduction in the concentration gradient of calcium
388
I.M. RITCHIE AND XU BING-AN
hydroxide between the surface and the bulk of the solution, due to increases in concentration of the latter. On the other hand, the movement towards independence of slaking rate constant ko on disc rotation speed, observed with the fastest of the reactions in water at high rotation speeds (Fig. 5), must be caused by a change in rate determining step, i.e. either the formation of calcium hydroxide, or its dissolution becomes slow compared with the rate at which calcium hydroxide diffuses away from the surface. Of these two possibilities, we favour the second, the slow dissolution of calcium hydroxide, over the first. Were the formation of calcium hydroxide the slow step, the succeeding steps would be fast and so there would be little or no calcium hydroxide present on the surface. However, this is contrary to observation. X-ray measurements show that the amounts of Ca (OH)2, formed on the surface of a CaO disc rotates at 800 rpm in water (i.e. in the non-diffusion controlled region) exceeds that formed on the surface of a CaO disc rotating at the same speed in 0.1 M NaOH (i.e. in the diffusion controlled region).
(e) Effect of temperature. A theoretical estimate of the activation energy for the slaking of lime in water can be made by taking logarithms of Eq. 4 and differentiating E a = d In S/d(1/T) =d In D(Ca(OH)2)2/3/d(1/T) + d l n ~-~/G/d(1/T)+dlnK~/3/d(1/T)
(16)
Literature values for the terms on the right hand side of Eq. 16 can now be introduced. According to Levich [4], activation energies for diffusion are generally of the order of 12 kJ mol - 1, while that for viscosity is about - 16 kJ mo1-1. The enthalpy for the heat of solution of calcium hydroxide is 16.3 kJ mo1-1 [14]. Substituting these numbers, we obtain Ea~ 16 kJ mo1-1 in reasonable agreement with the measured value of 13.6 _+1.2 kJ mol- 1.
Lime powder studies Morphological studies A micrograph of a standard lime sample prepared by heating calcium carbonate at 920°C for 10 h is shown in Fig. 7a. It can be seen that the particles are themselves agglomerates of smaller particles which vary considerably in size, but which average a few ]~m across. If the calcium carbonate is heated at higher temperatures or for longer times, the effect is to increase agglomerate size as shown in Fig. 7b which is a micrograph of lime prepared by heating calcium carbonate at 1080°C for 4 h. When the lime is slaked, the calcium hydroxide particles formed are much smaller than the parent quicklime, having an average cross-section of less than
KINETICSOF LIMESLAKING
389
Fig. 7. Scanning electron micrographs of lime powders: (a) prepared by calcining calcium carbonate for 10 h at 920°C; (b) prepared by calcining calcium carbonate for 4 h at 1080°C; (c) after slaking in water at 25°C. The scale bars are 10 pm.
390
I.M, RITCHIE AND XU BING-AN
1 pm. This is shown in Fig. 7c for the calcium hydroxide which results from slaking the quicklime shown in Fig. 7a in water at room temperature at a 50:1 water-lime ratio. Reaction kinetics (a) Temperature rise measurements. Typical plots showing the increase in solution temperature in the calorimeter as a function of time for different slaking solutions are shown in Fig. 8. It can be seen that the reaction with water is very rapid, essentially reaching completion after 3 min. However, as was found in the rotating disc experiments, the reaction rate decreases as the solution is made more alkaline, and in 4 M sodium hydroxide, takes about 70 min to reach completion. Figure 8 also shows that the final extent of reaction, measured by the maximum rise in temperature, decreases with increasing sodium hydroxide concentration. This can be accounted for in the following way. The slaking reaction is made up of the conversion of calcium oxide to calcium hydroxide (Eq. 2) and the dissolution of calcium hydroxide (Eq. 3). The heat liberated in the first of these reactions (zlH= - 65.2 kJ m o l - 1 [ 14 ] ) is likely to be largely independent of hydroxide concentration, but the extent of the second reaction (zlH= - 1 6 . 3 kJ mol-1 [14] ), and hence the heat given out during it, depends very much on the hydroxide concentration through the common ion effect. Thus a heat of slaking can be estimated by adding the heat liberated in the first step to the heat liberated in the second step multiplied by the amount dissolved, which can be calculated from the solubility product (6.5 X 10-6 M 3 ) assuming all activity coefficients are in unity. Heats calculated in this way are
0,4
~
0,2
~
0
I
0
10
i
20 time / rain
i
30
-
-
"
h
40
Fig. 8. The temperature rise as a function of slaking time when 0.2 g calcium oxide is added to 200 ml: • =water; [] =0.1 M sodium hydroxide; O =1.0 M sodium hydroxide; • =4.0 M sodium hydroxide.
KINETICSOF LIMESLAKING
391
1.4
T-. 1,3 0 0
1.2
1 1.1
I
I
I
-6
-4
-2
0
ig([OH']/M )
Fig. 9. Heat liberated during slaking in solutions containing various concentrations of sodium hydroxide. The solid line was calculated using the method described in the text.
compared with the experimentally measured heats of reaction in Fig. 9. It can be seen that the measured values agree with the calculated values within a few percent, which is within the likely experimental errors and also the assumption of ideal behaviour made in the calculations.
(b) Modelling the reaction rate. At any time t, the extent of reaction is given by x=AT/ATa where AT and AT5 are the temperature increases after time t and at the end of the reaction respectively. If the calcium oxide particles can be assumed to behave as spheres of initial radius ro and if the reaction is zero order, as was found to be the case in the rotating disc studies, the rate law should fit the shrinking sphere equation i.e. 1 - ( 1 - x ) l/3= kot/ro
(17)
When the data given in Fig. 8 are replotted according to this equation, the curves in Fig. 10 are obtained. Apart from an initial region of curvation near the origin, which is also an experimental point, it is clear that the plots for each slaking experiment are a reasonable fit to a straight line with a functional relationship similar to that defined by Eq. 17. However, unlike Eq. 17, the experimental points do not fall on a straight line through the origin. This finding is thought to be due to the fact that the lime particles were not spheres of initial radius ro, but were very heterogeneous lumps, as can be seen from the micrographs shown in Fig. 7a and b for lime which had been calcined at 920 ° C and 1080 °C respectively. The lime agglomerates contain many small particles
392
I.M. RITCHIE AND XU BING-AN
1.0
i
°I
o
0
1
20
3'0
40
time / min
Fig. 10. Temperature rise data plotted according to the shrinking sphere model: [ ] = w a t e r ; • = 0.1 M s o d i u m h y d r o x i d e ; O = 1 M s o d i u m h y d r o x i d e ; • = 4 M s o d i u m hydroxide.
1.o
~
o.5
I
0
0
I
I
5
10
time/rain
Fig. 11. T h e effect of particle size on slaking rate (the data are plotted s p h e r e m o d e l ): • = 19 p m ; O = 77 z m ; • = 153 z m ; [ ] = 303 p m .
according to the shrinking
and protuberances which would presumably react very quickly and so give rise to the initial period of rapid growth shown in Fig. 10. According to Eq. 17, the rate of reaction should be inversely proportional to the particle diameter. This was tested by preparing lime particles of different average diameters by sieving [ 15 ], and measuring the rate of reaction of each size range in water. The results are shown in Fig. 11. It can be seen that, even in these approximately monosized systems, the plots of 1 - (1 - x ) ] / 3 against t do not pass through the origin, suggesting that the particles themselves have reactive areas, as indeed one would expect from an inspection of Fig. 7a and b. The slopes of the lines in Fig. 11 are plotted against the reciprocal of the mesh
KINETICS OF LIME SLAKING
393
0.3
";.E0..~2,0..~1 ~ 0
0
= 20 0 40 10 '
3~
~
5'0
10 -3 m / particle s i z e
Fig. 12. Plot of shrinking sphere rate constant, ks, against reciprocal of average particle size: reading from left to right, the points correspond to average sizes of 303 ]~m, 153/~m, 77 ,urn and 19/lm.
size in Fig. 12. Instead of the straight line plot through the origin expected from Eq. 17, the curve is approximately parabolic in shape indicating that the larger particles are reacting relatively more quickly than the small particles. This phenomenon is easy to understand if reference is made again to the micrographs shown in Fig. 7. It is quite clear that large particles are best considered as assemblages of small particles, not as dense, massive particles. The large particles are therefore very porous, their surface area is correspondingly higher and the reaction rate more rapid. In summary, it seems that the shrinking sphere rate equation is a reasonable description of the slaking reaction, although the lime particles are agglomerates of smaller particles rather than being spherical. We have therefore used the shrinking sphere equation to describe the kinetics of slaking in the sections which follow.
(c) Effect of time and temperature of calcination. The effect of calcination temperature on the slaking reaction was investigated by comparing the slaking of a sample of the standard lime, which had been prepared by heating calcium carbonate at 920 ° C for 10 h, with the slaking of a sample of the same material which had been further heated for an additional 1.5 h at 1020 ° C. The results are shown in Fig. 13. It can be seen that the slaking rate of the lime which has had the additional heating at 1020°C is appreciably slower than that of the original sample prepared by heating at 920 ° C. As noted earlier, the effect of increasing the time or temperature of calcination is to increase the degree of coalescence of the lime particles, thus decreasing the reactant area. T h a t this reduction in reactant area is largely responsible for the decrease in reaction rate was demonstrated by the following experiment. A sample of lime which had been prepared by the additional heat-
394
I.M. RITCHIE AND XU BING-AN
1.0
x
I
0.5
I
i
5
110
time/min
Fig. 13. Effect of calcination temperature on the slaking rate (the data a r e p l o t t e d according to the shrinking sphere model): standard lime prepared by heating at 920°C for 10 h, • = mean diameter 49/~m; O = f u r t h e r heating of the same lime for 1.5 h a t 1020°C; [] =crushing and screening of the lime given additional heating at 1020 ° C.
Ig (concn/M ) -6
-4 I
I
-2 A
0 -
_
m
-4
Fig. 14. The effect of concentration on the shrinking sphere rate constant ks. Experimental points: • =Ca2+; O = O H - .
ing at 1020 o C was ground and screened to obtain material of the same average size (49/tm ) as that used to determine the slaking rate of the material prepared at 920 o C. The results of a slaking rate experiment using this ground material are also shown in Fig. 13. It is apparent that the reaction rates of the two materials (920 °C and ground after heating to 1020 °C ) are now rather similar although the lime prepared at the lower temperature still reacts somewhat faster than that which has had the additional heating to 1020 ° C. Similar results were obtained when the lime was heated for longer periods of time at the usual calcining temperature of 920 o C.
(d) Effect of concentration of calcium nitrate and of sodium hydroxide on the slaking rate. The effect of increasing the concentration of either calcium nitrate or sodium hydroxide in the slaking solution is to decrease the slaking rate progressively as shown in Fig. 14. It can also be seen that the effect on the
KINETICSOF LIMESLAKING
395
slaking rate of sodium hydroxide is more pronounced than calcium nitrate at the same concentration. This was observed earlier when using rotating lime disc samples. Indeed, the variation in slaking rate constants for powder samples as a function of calcium nitrate or sodium hydroxide concentration (Fig. 14) is closely similar in form to the same measurements using rotating disc samples (Fig. 5). We infer from this result that the mechanism deduced for the slaking of rotating lime discs (i.e. that the reaction is controlled by the speed at which calcium hydroxide diffuses away from the solid surface) also applies to the slaking of lime powders. CONCLUSIONS
(1) The slaking rate of pure lime discs in water or in solutions of sodium hydroxide or calcium nitrate is controlled by the rate of diffusion of calcium hydroxide away from the disc surface. (2) The slaking rate of pure lime powders can be described by the shrinking sphere model. (3) The slaking rate of pure lime powders depends on the particle size of the powder and the calcination conditions under which the lime was made from calcium carbonate. High calcination temperatures and long calcination times cause coalescence of the lime particles and a reduction of slaking rate. This reduction in slaking rate is partly due to an increase in the size of the lime particles. (4) The effect of sodium hydroxide and calcium nitrate on the rate of slaking of pure lime powders is similar to that of pure lime discs suggesting that the rate of the powder reaction is also controlled by the diffusion of calcium hydroxide away from the surface. ACKNOWLEDGEMENT
The authors gratefully acknowledge Alcoa of Australia Ltd.'s support of this project, including the award of a research scholarship to Xu Bing-An.
REFERENCES 1 Boynton, R.S, 1980. Chemistry and Technology of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 380. 2 Zozulya, A.F., Zaitsev, I.D., Telitchenko, V.A. and Tkach, V.A., 1980. Study of the kinetics of lime hydration. Deposited Doc., SPSTL 205kph-D80. Chem. Abstr., 97, 59959a: 257 (in Russian ).
396
:/
4 5 6 7 8 9 10 11 12 1:~ 14 15
I.M. RITCHIE AND XU BING-AN
Ovechkin, E.K., Volova, L.M. and Chernaya, A.E., 1972. Reaction rate of lime slaking with preparation of concentrated milk of lime. Issled. Obl. Neorg. Teknol., 267, (Chem. Abstr.), 78, 8353y: 283 (in Russian). Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs. N.J., p. 69. Boynton, R.S., 1980. Chemistry and Technolo~" of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 161. Boynton, R.S., 1980. Chemistry and Technology of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 175. Weast, R.C. (Editor), 1983-1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. F92. Hedin, R., 1962. Processes of diffusion, solution and crystallization in system Ca (OH) 2-H20. Swed. Cem. Cone. Res. Inst. Bull., 33, (Chem. Abstr.), 57: 6689a. Sillen, L.G. and Martell, A.E., 1964. Stability constants of metal ion complexes. Chem. Soc. Spec. Publ., 17, p. 42. Littauer, E.L. and Tsai, K.C., 1979. Observations of the diffusion coefficient of the hydroxyl ion in lithium hydroxide solutions. Electroehim. Acta, 24,351 355. Heyrovsky, J. and Kuta, J., 1966. Principles of Polarography. Czech. Acad. Sci. Publishing House, Academic Press, New York, N.Y., 581 pp. Weast, R.C. (Editor), 1983 1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. F170. Johnston, R.R.M. and Spiro, M., 1967. Diffusion coefficients of the silver ion and the disulfitosilver (I) ion by the rotating disk method. J. Phys. Chem., 71, 3784-3790. Weast, R.C. (Editor), 1983-1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. D57. Tan, Tianen, Mai, Benxi and Ding, Huihua, 1984. The Principles of Chemical Engineering. Chem. Ind. Press., Beijing, 1, pp. 137 153 (in Chinese).
377
The K i n e t i c s of L i m e S l a k i n g IAN M. RITCHIE and XU BING-AN
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, W.A. 6150 (Australia) (Received November 21, 1988; revised and accepted April 4, 1989 )
ABSTRACT Ritchie, I.M. and Xu Bing-An, 1990. The kinetics of lime slaking. Hydrometallurgy, 23: 377-396. Although the slaking of lime is a reaction of great antiquity, there have been few fundamental studies of its kinetics and mechanism. In this paper, the kinetics of the reaction are reported for lime samples in two different arrangements: rotating discs and powders. In the former case, the rate was measured by solution analysis; in the latter, by calorimetry. The rate of slaking of a rotating lime disc was approximately constant with time but depended on the disc rotation speed. In the presence of Ca2+ or OH- ions, the slaking rate was reduced. These results were accounted for by assuming that the slow step in the early stages of the slaking reaction was the diffusion of calcium hydroxide away from the reacting surface. Reasonable agreement between the measured slaking rates and those calculated on the assumption of slow calcium hydroxide diffusion was obtained. When powder samples were used, the rates of slaking could be fitted to the equation for a shrinking sphere model. It was shown that the effect of increasing the calcium oxide particle size or increasing either the time or temperature of preparation from calcium carbonate was to decrease the rate. Electron micrographs of the powdered lime before slaking were used to interpret these results. The effect of Ca 2+ or OH- ions on the slaking rate of powder lime samples closely paralleled those of the rotating disc sample suggesting the reaction mechanisms are similar.
INTRODUCTION
Of the heavy industrial chemicals, lime, either as quicklime, CaO, or slaked lime, Ca(OH)2, is second only to sulphuric acid in the amount produced. A detailed discussion of its multitudinous uses is given by Boynton [1 ]. These range from high temperature processes such as steel making to a host of applications at or near ambient temperature. Included in this latter category are a number of hydrometallurgical uses such as control of pH during flotation, coagulation, neutralization of acid solutions, control of pH in cyanide leach liquors and recausticization of Bayer liquors, the latter application being the most important in terms of the amount consumed. Lime is often slaked prior to use, and even when quicklime is added directly to a solution to, for example, remove carbonate from that solution, it seems 0304-386X/90/$03.50
© 1990 Elsevier Science Publishers B.V.
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I.M. R1TCHIE AND XU BING-AN
very likely that partial or complete slaking of the lime will occur first. However, despite the enormous importance of lime slaking, little is known about the reaction kinetics and almost nothing about the reaction mechanism. Most of the work reported to date is in the Eastern European literature. Zozulya et al. [2] found that the rate at which quicklime is hydrated increases with increasing lime surface area and the temperature at which the lime is slaked, and that the higher the temperature at which quicklime is manufactured by decarbonation of calcium carbonate, the less active is the resulting quicklime. These authors concluded that lime hydration is diffusion controlled and depends predominantly on the degree of supersaturation of the liquid phase with calcium hydroxide. Ovechkin et al. [3], using a high calcium lime, found that the rate of lime slaking increased with temperature but observed little effect of grain size. They too concluded that the reaction was diffusion controlled, at least in the final stages of slaking. In this paper, we report the results of a study of the slaking of a relatively high purity calcium oxide in the form of rotating disc and powder samples. The results obtained from the two sorts of samples are to a certain extent complementary. The rotating disc experiments give the most useful mechanistic information [4]. The area of the calcium oxide sample is essentially constant during the experiment and through the medium of the rotation speed, the mass transfer to and from the reacting surface can be varied in a reproducible manner. From a knowledge of the way the rotation speed affects the reaction rate, measured by solution analysis at suitable time intervals, it is possible to establish unequivocally whether the reaction is under chemical control or diffusion control, and if the latter, whether diffusion to or from the surface is the slow step. However, this approach is generally limited to the initial stages of the reaction, or at least until the slaking solution becomes saturated with calcium hydroxide, when it becomes difficult to follow the reaction. On the other hand, the powder samples most closely approximate industrial practice. In addition, the reaction is then easy to follow by the temperature rise of the solution associated with the heat given out during the reaction. Against this must be set the fact that there is almost no way of controlling mass transport to the reacting surface, which itself is contracting and changing shape as the reaction proceeds. EXPERIMENTAL Industrial limes contain sufficient impurities for different lime samples to have different properties. In order to avoid this problem A.R. grade calcium carbonate from UNIVAR was chosen as a standard raw material from which a lime of approximately 99% could be made by calcination CaCO3 ~ CaO + C02
(1)
The dissociation temperature for calcium carbonate is reported to be 890 °C
KINETICS OF LIME SLAKING
379
[5 ], but thermogravimetric analysis showed that the UNIVAR material started to decompose at about 630 ° C, and the reaction was complete by about 870 ° C. Accordingly, the A.R. grade calcium carbonate was calcined in a muffle furnace for 10 h at a temperature of 920 + 5 ° C. The calcium oxide so formed was ground and screened for use in the slaking experiments. The discs of calcium oxide were prepared by pressing the powder in a pellet press used for the preparation of infrared samples, and then heating the compact. The effect of the pressure used in making the disc, and the heating temperature and time were investigated. It was found that the optimum pressure was about 40 MPa for a disc with a diameter of 12.8 mm, and that pressures greater or less than this value result in a disc which is loose or likely to fragment. Although the sintering temperature for calcium oxide is 1650°C [6], it was found that when the disc was heated for 40 hours at 1100 ° C, its mechanical strength improved markedly and the resulting disc, whose diameter had shrunk to 12.45 mm, did not break up when rotated in solution. It was also found that the discs had to be heated on a fire clay surface, since they stuck to porcelain and nickel crucibles. In order to use the discs in a slaking study, they were mounted in a stainless steel holder such that only one face was exposed. The holder was attached to a shaft, coaxial with the disc, which could be rotated in the reactant solution at controlled speeds between 0 and 1500 r.p.m. The amount of calcium hydroxide present in solution after an appropriate reaction time could then be determined by a suitable method of analysis: conductivity for discs slaked in water; pH for discs slaked in calcium nitrate solutions; and atomic absorption analysis for calcium ions when the discs were slaked in sodium hydroxide solutions. The slaking of lime powder samples was followed by measuring the temperature rise of the reacting system in a Guild calorimeter which had been previously calibrated. 200 ml of the reactant liquid was placed in the dewar and an accurately weighed amount of lime ( ~ 0.2 g) was added and the mixture stirred by means of a paddle stirrer rotating at 1470 r.p.m. The sample size was chosen so that the temperature rise was large enough to be measured accurately, but not so large that the heat losses from the system were significant. The temperature rise is proportional to the heat involved in the reaction and so can be used as a measure of the extent of reaction. X-ray diffractometry, and optical and scanning electron microscopy were used to investigate the surface composition and structure of both the disc and powder samples.
38O
I.M. RITCHIE AND XU BING-AN
I Q ~r~
Fig. 1. Scanning electron micrograph of a lime disc: (a) before slaking; (b) after slaking for 18 min at a rotation speed of 800 r.p.m, in water; (c) after slaking for 18 min at a rotation speed of 800 r.p.m, in 0.1 M sodium hydroxide solution. T h e scale bars are 10 llm.
KINETICS OF LIME SLAKING
381
RESULTS AND DISCUSSION
Rotating disc studies Surface composition and structure An X-ray powder diffraction pattern of the surface of a quicklime disc which had been stored in a desiccator for five weeks showed only peaks which could be ascribed to calcium oxide and none to calcium hydroxide. Because X-ray diffraction is not good for detecting small amounts of a second phase, particularly when the second phase may not be very crystalline, this result cannot be regarded as proof of the absence of calcium hydroxide on the disc surface. However, it seems likely that there was very little on the surface since when a disc which was rotating at 800 r.p.m., had been slaked for 18 minutes, additional diffraction lines due to calcium hydroxide could be readily observed. These lines were more pronounced when the slaking reaction was carried out in water than in 0.1 M sodium hydroxide. Similar conclusions were reached using optical and scanning electron microscopy. From the scanning electron micrograph shown in Fig. la, it can be seen that the surface is porous, and consists of particles 2-5 ~m across which have been fused together. Figure lb shows the appearance of a lime disc which has been rotated in water at 800 r.p.m, for 18 min. The surface is covered with a large number of small but rough particles which are believed to be calcium hydroxide. The apparently slower reaction in 0.1 M sodium hydroxide also results in rough textured particles, but these are much bigger and more widely dispersed (Fig. lc). Reaction kinetics (a) Reaction rate. Irrespective of whether the lime slaking reaction was carried out in water or in solutions containing either calcium nitrate or sodium hydroxide, the slaking rate was found to be approximately constant at any given disc rotation speed. This can be seen from the plots of amount of calcium oxide dissolved against time shown in Figs. 2 and 3 for the particular cases of the slaking reaction in water, determined from conductance measurements, and in 0.03 M sodium hydroxide, determined from analysis of the calcium content of the solution by atomic absorption spectrophotometry. It is apparent from Fig. 2 that when the reaction is sufficiently rapid, the rate plots (e.g. at 600 r.p.m. ) show a slight curvature corresponding to a small decrease in reaction rate with time. One possible cause of this slight reduction in rate will be discussed later. In the meantime, it is sufficient to note that the reaction is essentially zero order, and the slope of the lines gives the zero order rate constant, ko.
382
I.M. RITCHIE AND XU BING-AN
1.0 oJ
E -6 E "0
o
0.5
"0
o (J
5
10
15
time/rain Fig. 2. T h e a m o u n t of calcium oxide dissolved f r o m a disc r o t a t i n g at various speeds in w a t e r at 25 ° C: • = 100 r.p.m.; • = 200 r.p.m.; O = 400 r.p.m.; [] = 600 r.p.m.
~ o5 {D
0 0
I
I
5
10
15
time/min Fig. 3. T h e a m o u n t of calcium oxide dissolved f r o m a disc r o t a t i n g at v a r i o u s speeds in 0.03 M s o d i u m hydroxide solution at 25 ° C: • = 100 r.p.m.; • = 200 r.p.m.; O = 400 r.p.m.; [] = 600 r.p.m.; • = 800 r.p.m.
(b) Effect of rotation speed. It is clear from both Fig. 2 and Fig. 3 that the dissolution rate is strongly dependent on disc rotation speed indicating that the reaction is largely controlled by either the diffusion of some reactant species to the oxide surface, or the diffusion of some product species away from the oxide surface. Figure 4 shows the dependence of the zero order rate constant, ko, on the square root of the disc rotation speed, o), for different concentrations of sodium hydroxide. It can be seen that at the lowest reaction rates (highest sodium hydroxide concentrations), ko is directly proportional to the square root of the disc rotation speed, indicating that the reaction is under diffusion control. However, at the highest reaction rates (lowest sodium hydroxide concentrations), ko tends to fall off with increasing rotation speed, suggesting that the
KINETICS OF LIME SLAKING
383
10
V
E E
\
0 o
1 5
10
( w / r a d s.1 )1/2
Fig. 4. T h e variation of the zero order rate c o n s t a n t at 25°C with the square root of the disc rotation speed: • =0.1 M sodium hydroxide; • =0.03 M sodium hydroxide; O =0.01 M sodium hydroxide; [] = water.
reaction is going from diffusion to chemical control. In the case of the reaction with water, the rate constant is essentially independent of rotation speed at the highest rotation speeds investigated (1000 r.p.m.), behaviour which is characteristic of chemical control [4]. Similar results were obtained for the reaction of calcium oxide with the solutions containing various concentrations of calcium nitrate i.e. the reaction rate constant became progressively smaller and more directly proportional to the square root of the angular velocity of the disc as the calcium nitrate concentration was increased. A rate constant, k, which is independent of the angular velocity can be defined by the ratio ko/to~. For those systems in which the reaction becomes partly chemically controlled at high rotation speeds, and as a result, ko/to ~ decreases with increasing rotation speed, we define k as being equal to the tangent to the curve as to tends to zero i.e. when the reaction is most likely to be under diffusion control.
(c) Effect of concentration of Ca 2+ or O H - . As noted above, the effect of increasing the concentration of Ca 2+ or O H - ions in the slaking solution is to reduce the slaking rate. This is shown graphically in Fig. 5 in which the logarithm of the slaking rate constant k [moles Ca 2+ dissolving in solution per m 2 of CaO disc per second per (radian per second) i ], is plotted against the logarithm of the concentration, either Ca 2+ or O H - . Provided that neither the Ca 2+ nor the O H - concentration is above 10 -2 M, the rate constant k is essentially that of water, but above this concentration, k decreases and more rapidly so in the presence of O H - t h a n in the presence of Ca 2+.
384
I.M. R I T C H I E A N D X U B I N G - A N
Ig (conch / M )
-,6
-?
o
-2 A
O
~0
-8
e~
Fig. 5. T h e effect of c o n c e n t r a t i o n on the rate constant k for th lime slaking r e a c t i o n at 2 5 C. Experimental points: • = Ca2+; O = O H - . T h e solid lines were calculated using the t h e o r y pres e n t e d o n pp. 9 - 1 1 .
-8
E
_=
K -10 -12
I
3.0 (103k/T)
3.5
Fig. 6. Arrhenius plot for the slaking of lime in water.
(d) Effect of temperature. The effect of temperature on the kinetics of the slaking reaction in water was examined, and the results shown in the Arrhenius plot of Fig. 6 were obtained. The points are a reasonable fit to a straight line, from the slope of which an activation energy of 13.6 + 1.2 kJ m o l - 1 was calculated. This low value is consistent with the effect of disc rotation speed and indicative of diffusion control [ 4 ].
Mechanism of the slaking reaction
(a) General considerations. In a formal sense, the slaking reaction can be considered to proceed in three steps: Step 1, the conversion of calcium oxide to calcium hydroxide
CaO+H~O--~Ca(OH)2
(2)
KINETICS OF LIME SLAKING
385
followed by Step 2, the dissolution of calcium hydroxide to give calcium ions and hydroxide ions in solution Ca (OH)2 -*Ca2+ +2OH-
(3)
and Step 3, the diffusionof the calcium ions and hydroxideions into the bulk of the solution. Because the reaction shows a strong dependenceon disc rotation speed and a low activation energy, it must be diffusion controlled. Step 1 cannot be diffusion controlledbecausethe rate constants are too small for a reactant whose bulk concentration is 56 M. On the other hand, Step 3 couldbe rate controlling and wouldgivea zero order process, as observed. If the diffusionstep governsthe rate of the reaction,the dissolution step will be at equilibrium i.e. there will be a film of solid calcium hydroxide on the reacting lime surface which is in equilibriumwith calciumions and hydroxide ions in solution at the reacting surface. The diffusionof calcium ions and hydroxide ions away from the surface will be describedby the Levich equation [4]. It is convenient to discuss three special cases: the slaking of lime with water; the slaking of lime with a high concentration of calcium ions in solution, and the slaking of lime with a high concentration of hydroxide ions in solution.
(b) The slaking of lime with water. According to the Levich equation, the dissolution rate, S, for a reaction controlled by the rate of diffusion of calcium hydroxide away from a surface at which there is a saturated solution of calcium hydroxide into water is S=0.62 D (Ca(OH)2) 2/3 u -~/~ 0,)1/2 [Ca(OH)2]s
(4)
where D (Ca (OH) e ) is the diffusion coefficient of calcium hydroxide in water, u is the kinematic viscosity of water and [Ca (OH)e ] s is the concentration of a saturated solution of calcium hydroxide at the reacting surface. Since ko = S and k = ko/o) ½, k=0.62 D (Ca(OH)2) 2/3/2 -1/6 [Ca(OH)2]~
(5)
The kinematic viscosity is given in the Handbook of Chemistry and Physics [7], and so k can be estimated provided values for D(Ca(OH)e) and [ Ca (OH) 2]s are known. Hedin [8 ] has reported that the value of the diffusion coefficient for calcium hydroxide depends quite strongly on the concentration, dropping from 17.47× 10-'° m 2 s - ' at 1.07 × 10-'~ M t o 13.85× 10-'° m 2 s -1 at 1.93× 10-2 M, this latter concentration being close to the solubility of a standard solution of calcium hydroxide. In the mechanism suggested here, the calcium hydroxide is assumed to be saturated at the dissolving surface, and so it seems reasonable
386
I.M. RITCHIE AND XU BING-AN
to assume a value of D (Ca ( OH )2 ) = 14 × 10- l o m 2 s - 1 for the purposes of these calculations. By approximating activities with concentrations, [Ca(OH)2] can be estimated from the solubility product, Ks, via [Ca(OH)2] = (K J 4 ) 1/3
(6)
where K s = 6.5 × 10 - 6 M 3 has been calculated from the average of the log Ks values listed in Sillen and Martell [9]. Substituting these numbers into Eqn. 5, we obtain a value of k equal to 9.2 × 10- 5 tool m - 2 s - ~which is in reasonable agreement with the experimental value of (12.0 _+2.5) × 10 -5 mol m - 2 s - ½ considering the approximations made in the calculations.
(c) The slaking of lime in solutions containing calcium nitrate. In solutions containing high concentrations of calcium nitrate, the solution conductivity is high and ionic migration can be neglected. The diffusion of calcium ions and hydroxide ions can be considered as independent processes although neutrality must still be maintained in the solution. In addition, the amount of calcium carried away from the reacting surface as the species CaOH + can be neglected since the surface p H is, as the calculations show, relatively low. The relevant equations for the fluxes, J (mol m -2 s -1 ), of calcium ions and hydroxide ions from the saturated calcium hydroxide surface are [4] J ( C a 2+ ) =0.62 D ( C a 2+ )2/3
v-1/6 0_)1/2 { [ C a 2 + ]s - [ Ca2+ ]b}
J ( O H - ) = O . 6 2 D ( O H - ) 2/~ v-1/6 o) 1/2 { [ 0 H - ] s S = J ( C a 2+ ) = J ( O H -
[OH-]b}
)/2
(7) (8) (9)
where the subscripts s and b denote surface and bulk concentrations respectively, and [ O H - ]b ~ 0 for the calcium nitrate solutions. The surface is still at equilibrium and so K~ = [Ca 2+ ] s [ O H - ] 2
(10)
By combining Eqns. 8-10, it can be shown that D ( O H - )2/3 [ O H - ] s = 2KsD (Ca 2+ )2/3 {Ks - [Ca 2+ ]b [ O H - ] 2 }
(11)
from which [ O H - ]s can be calculated for a range of [ C a 2+ ]b, provided values of Ks, D ( O H - ) and D (Ca z + ) are known. Ks is given earlier and D ( O H - ) has been estimated to be approximately 62 × 10- lO m 2 s - a from the data of Littauer and Tsai [10]. We have been unable to locate a value for the diffusion coefficient of Ca 2+, and have therefore assumed it to be the same as that for Cd 2+ (7.0 × 10- lo m e s - 1 in 1 M KNOa [ 11 ] ) on the grounds that the ionic radii of Ca 2+ and Cd e + are very similar [ 12 ]. Once values of [ O H - ] s as a function of [Ca 2+ ]b have been obtained, the slaking rate can be calculated from Eqns. 8 and 10 for a range of [Ca 2+ ]b. The
387
KINETICS OF LIME SLAKING
results give the upper solid line in Fig. 5. Again, it is clear that, within the limits of experimental error and the assumptions made in the calculations, there is good agreement between experiment and theory.
(d) The slaking of lime in solutions containing sodium hydroxide. This situation is similar to that for the slaking reaction in high concentrations of calcium nitrate. However, in this case, account must also be taken of the species CaOH + which is present in appreciable concentration. Besides Eqs. 7, 8 and 11, the following also apply J ( C a O H +) =0.62 D(CaOH + )2/3u-1/6o) 1/2 { [CaOH + ] s - [C aOH+ ]b}
(12)
S = J ( O H - ) / 2 = J ( C a 2+ ) + J ( C a O H + )/2
(13)
and K1 = [CaOH + ] J [Ca 2+ Is [OH-]8
(14)
where J ( C a O H + ) is the flux of the species CaOH + away from the surface into the bulk solution and K~ = 24.7 M - ' [9] is the stability constant for the formation of CaOH +. In the absence of a published value for the diffusion coefficient of CaOH +, which will be somewhat larger than Ca 2+, we have assumed that it is the same as that for Ag + (i.e. 15.8X10 -1° m 2 s -1 [13] ), whose ion size is also somewhat larger than Ca 2+ [12]. The slaking rate can now be calculated using the procedure set out in (b) above. From Eqns. 7, 8, 10, 12, 13 and 14 we obtain D (OH-)2/3 [OH- 1~ - D (OH-)2/3 [OH- ]~ [OH- ]b =2K~D(Ca 2+)2/3+K~KID(CaOH+) [OH-]~
(15)
from which [OH]~ can be calculated for a range of [OH- ]b using the diffusion coefficients and equilibrium constants listed above and assuming [Ca2+ ]b ~ [CaOH+ ]b ~ 0. The slaking rate can then be calculated from Eqns. 8 and 13. The results of these calculations are shown in the lower solid curve of Fig. 5. While the fit to the experimental results is somewhat worse than the case of lime slaking in calcium nitrate solutions, particularly at high concentrations, it is none-the-less considered to be reasonable, given the fairly crude assumptions which were made. Summarising the results of the calculations in (b), (c) and (d), we may say that the mechanism of rate control via slow diffusion of dissolved calcium hydroxide away from the reacting surface gives a good description of the results in water and in concentrated solutions of calcium nitrate and sodium hydroxide. If this interpretation of the mechanism is correct, the slight curvature of the rate plots seen in Fig. 2 at high rotation speeds over the course of the reaction is probably due to a reduction in the concentration gradient of calcium
388
I.M. RITCHIE AND XU BING-AN
hydroxide between the surface and the bulk of the solution, due to increases in concentration of the latter. On the other hand, the movement towards independence of slaking rate constant ko on disc rotation speed, observed with the fastest of the reactions in water at high rotation speeds (Fig. 5), must be caused by a change in rate determining step, i.e. either the formation of calcium hydroxide, or its dissolution becomes slow compared with the rate at which calcium hydroxide diffuses away from the surface. Of these two possibilities, we favour the second, the slow dissolution of calcium hydroxide, over the first. Were the formation of calcium hydroxide the slow step, the succeeding steps would be fast and so there would be little or no calcium hydroxide present on the surface. However, this is contrary to observation. X-ray measurements show that the amounts of Ca (OH)2, formed on the surface of a CaO disc rotates at 800 rpm in water (i.e. in the non-diffusion controlled region) exceeds that formed on the surface of a CaO disc rotating at the same speed in 0.1 M NaOH (i.e. in the diffusion controlled region).
(e) Effect of temperature. A theoretical estimate of the activation energy for the slaking of lime in water can be made by taking logarithms of Eq. 4 and differentiating E a = d In S/d(1/T) =d In D(Ca(OH)2)2/3/d(1/T) + d l n ~-~/G/d(1/T)+dlnK~/3/d(1/T)
(16)
Literature values for the terms on the right hand side of Eq. 16 can now be introduced. According to Levich [4], activation energies for diffusion are generally of the order of 12 kJ mol - 1, while that for viscosity is about - 16 kJ mo1-1. The enthalpy for the heat of solution of calcium hydroxide is 16.3 kJ mo1-1 [14]. Substituting these numbers, we obtain Ea~ 16 kJ mo1-1 in reasonable agreement with the measured value of 13.6 _+1.2 kJ mol- 1.
Lime powder studies Morphological studies A micrograph of a standard lime sample prepared by heating calcium carbonate at 920°C for 10 h is shown in Fig. 7a. It can be seen that the particles are themselves agglomerates of smaller particles which vary considerably in size, but which average a few ]~m across. If the calcium carbonate is heated at higher temperatures or for longer times, the effect is to increase agglomerate size as shown in Fig. 7b which is a micrograph of lime prepared by heating calcium carbonate at 1080°C for 4 h. When the lime is slaked, the calcium hydroxide particles formed are much smaller than the parent quicklime, having an average cross-section of less than
KINETICSOF LIMESLAKING
389
Fig. 7. Scanning electron micrographs of lime powders: (a) prepared by calcining calcium carbonate for 10 h at 920°C; (b) prepared by calcining calcium carbonate for 4 h at 1080°C; (c) after slaking in water at 25°C. The scale bars are 10 pm.
390
I.M, RITCHIE AND XU BING-AN
1 pm. This is shown in Fig. 7c for the calcium hydroxide which results from slaking the quicklime shown in Fig. 7a in water at room temperature at a 50:1 water-lime ratio. Reaction kinetics (a) Temperature rise measurements. Typical plots showing the increase in solution temperature in the calorimeter as a function of time for different slaking solutions are shown in Fig. 8. It can be seen that the reaction with water is very rapid, essentially reaching completion after 3 min. However, as was found in the rotating disc experiments, the reaction rate decreases as the solution is made more alkaline, and in 4 M sodium hydroxide, takes about 70 min to reach completion. Figure 8 also shows that the final extent of reaction, measured by the maximum rise in temperature, decreases with increasing sodium hydroxide concentration. This can be accounted for in the following way. The slaking reaction is made up of the conversion of calcium oxide to calcium hydroxide (Eq. 2) and the dissolution of calcium hydroxide (Eq. 3). The heat liberated in the first of these reactions (zlH= - 65.2 kJ m o l - 1 [ 14 ] ) is likely to be largely independent of hydroxide concentration, but the extent of the second reaction (zlH= - 1 6 . 3 kJ mol-1 [14] ), and hence the heat given out during it, depends very much on the hydroxide concentration through the common ion effect. Thus a heat of slaking can be estimated by adding the heat liberated in the first step to the heat liberated in the second step multiplied by the amount dissolved, which can be calculated from the solubility product (6.5 X 10-6 M 3 ) assuming all activity coefficients are in unity. Heats calculated in this way are
0,4
~
0,2
~
0
I
0
10
i
20 time / rain
i
30
-
-
"
h
40
Fig. 8. The temperature rise as a function of slaking time when 0.2 g calcium oxide is added to 200 ml: • =water; [] =0.1 M sodium hydroxide; O =1.0 M sodium hydroxide; • =4.0 M sodium hydroxide.
KINETICSOF LIMESLAKING
391
1.4
T-. 1,3 0 0
1.2
1 1.1
I
I
I
-6
-4
-2
0
ig([OH']/M )
Fig. 9. Heat liberated during slaking in solutions containing various concentrations of sodium hydroxide. The solid line was calculated using the method described in the text.
compared with the experimentally measured heats of reaction in Fig. 9. It can be seen that the measured values agree with the calculated values within a few percent, which is within the likely experimental errors and also the assumption of ideal behaviour made in the calculations.
(b) Modelling the reaction rate. At any time t, the extent of reaction is given by x=AT/ATa where AT and AT5 are the temperature increases after time t and at the end of the reaction respectively. If the calcium oxide particles can be assumed to behave as spheres of initial radius ro and if the reaction is zero order, as was found to be the case in the rotating disc studies, the rate law should fit the shrinking sphere equation i.e. 1 - ( 1 - x ) l/3= kot/ro
(17)
When the data given in Fig. 8 are replotted according to this equation, the curves in Fig. 10 are obtained. Apart from an initial region of curvation near the origin, which is also an experimental point, it is clear that the plots for each slaking experiment are a reasonable fit to a straight line with a functional relationship similar to that defined by Eq. 17. However, unlike Eq. 17, the experimental points do not fall on a straight line through the origin. This finding is thought to be due to the fact that the lime particles were not spheres of initial radius ro, but were very heterogeneous lumps, as can be seen from the micrographs shown in Fig. 7a and b for lime which had been calcined at 920 ° C and 1080 °C respectively. The lime agglomerates contain many small particles
392
I.M. RITCHIE AND XU BING-AN
1.0
i
°I
o
0
1
20
3'0
40
time / min
Fig. 10. Temperature rise data plotted according to the shrinking sphere model: [ ] = w a t e r ; • = 0.1 M s o d i u m h y d r o x i d e ; O = 1 M s o d i u m h y d r o x i d e ; • = 4 M s o d i u m hydroxide.
1.o
~
o.5
I
0
0
I
I
5
10
time/rain
Fig. 11. T h e effect of particle size on slaking rate (the data are plotted s p h e r e m o d e l ): • = 19 p m ; O = 77 z m ; • = 153 z m ; [ ] = 303 p m .
according to the shrinking
and protuberances which would presumably react very quickly and so give rise to the initial period of rapid growth shown in Fig. 10. According to Eq. 17, the rate of reaction should be inversely proportional to the particle diameter. This was tested by preparing lime particles of different average diameters by sieving [ 15 ], and measuring the rate of reaction of each size range in water. The results are shown in Fig. 11. It can be seen that, even in these approximately monosized systems, the plots of 1 - (1 - x ) ] / 3 against t do not pass through the origin, suggesting that the particles themselves have reactive areas, as indeed one would expect from an inspection of Fig. 7a and b. The slopes of the lines in Fig. 11 are plotted against the reciprocal of the mesh
KINETICS OF LIME SLAKING
393
0.3
";.E0..~2,0..~1 ~ 0
0
= 20 0 40 10 '
3~
~
5'0
10 -3 m / particle s i z e
Fig. 12. Plot of shrinking sphere rate constant, ks, against reciprocal of average particle size: reading from left to right, the points correspond to average sizes of 303 ]~m, 153/~m, 77 ,urn and 19/lm.
size in Fig. 12. Instead of the straight line plot through the origin expected from Eq. 17, the curve is approximately parabolic in shape indicating that the larger particles are reacting relatively more quickly than the small particles. This phenomenon is easy to understand if reference is made again to the micrographs shown in Fig. 7. It is quite clear that large particles are best considered as assemblages of small particles, not as dense, massive particles. The large particles are therefore very porous, their surface area is correspondingly higher and the reaction rate more rapid. In summary, it seems that the shrinking sphere rate equation is a reasonable description of the slaking reaction, although the lime particles are agglomerates of smaller particles rather than being spherical. We have therefore used the shrinking sphere equation to describe the kinetics of slaking in the sections which follow.
(c) Effect of time and temperature of calcination. The effect of calcination temperature on the slaking reaction was investigated by comparing the slaking of a sample of the standard lime, which had been prepared by heating calcium carbonate at 920 ° C for 10 h, with the slaking of a sample of the same material which had been further heated for an additional 1.5 h at 1020 ° C. The results are shown in Fig. 13. It can be seen that the slaking rate of the lime which has had the additional heating at 1020°C is appreciably slower than that of the original sample prepared by heating at 920 ° C. As noted earlier, the effect of increasing the time or temperature of calcination is to increase the degree of coalescence of the lime particles, thus decreasing the reactant area. T h a t this reduction in reactant area is largely responsible for the decrease in reaction rate was demonstrated by the following experiment. A sample of lime which had been prepared by the additional heat-
394
I.M. RITCHIE AND XU BING-AN
1.0
x
I
0.5
I
i
5
110
time/min
Fig. 13. Effect of calcination temperature on the slaking rate (the data a r e p l o t t e d according to the shrinking sphere model): standard lime prepared by heating at 920°C for 10 h, • = mean diameter 49/~m; O = f u r t h e r heating of the same lime for 1.5 h a t 1020°C; [] =crushing and screening of the lime given additional heating at 1020 ° C.
Ig (concn/M ) -6
-4 I
I
-2 A
0 -
_
m
-4
Fig. 14. The effect of concentration on the shrinking sphere rate constant ks. Experimental points: • =Ca2+; O = O H - .
ing at 1020 o C was ground and screened to obtain material of the same average size (49/tm ) as that used to determine the slaking rate of the material prepared at 920 o C. The results of a slaking rate experiment using this ground material are also shown in Fig. 13. It is apparent that the reaction rates of the two materials (920 °C and ground after heating to 1020 °C ) are now rather similar although the lime prepared at the lower temperature still reacts somewhat faster than that which has had the additional heating to 1020 ° C. Similar results were obtained when the lime was heated for longer periods of time at the usual calcining temperature of 920 o C.
(d) Effect of concentration of calcium nitrate and of sodium hydroxide on the slaking rate. The effect of increasing the concentration of either calcium nitrate or sodium hydroxide in the slaking solution is to decrease the slaking rate progressively as shown in Fig. 14. It can also be seen that the effect on the
KINETICSOF LIMESLAKING
395
slaking rate of sodium hydroxide is more pronounced than calcium nitrate at the same concentration. This was observed earlier when using rotating lime disc samples. Indeed, the variation in slaking rate constants for powder samples as a function of calcium nitrate or sodium hydroxide concentration (Fig. 14) is closely similar in form to the same measurements using rotating disc samples (Fig. 5). We infer from this result that the mechanism deduced for the slaking of rotating lime discs (i.e. that the reaction is controlled by the speed at which calcium hydroxide diffuses away from the solid surface) also applies to the slaking of lime powders. CONCLUSIONS
(1) The slaking rate of pure lime discs in water or in solutions of sodium hydroxide or calcium nitrate is controlled by the rate of diffusion of calcium hydroxide away from the disc surface. (2) The slaking rate of pure lime powders can be described by the shrinking sphere model. (3) The slaking rate of pure lime powders depends on the particle size of the powder and the calcination conditions under which the lime was made from calcium carbonate. High calcination temperatures and long calcination times cause coalescence of the lime particles and a reduction of slaking rate. This reduction in slaking rate is partly due to an increase in the size of the lime particles. (4) The effect of sodium hydroxide and calcium nitrate on the rate of slaking of pure lime powders is similar to that of pure lime discs suggesting that the rate of the powder reaction is also controlled by the diffusion of calcium hydroxide away from the surface. ACKNOWLEDGEMENT
The authors gratefully acknowledge Alcoa of Australia Ltd.'s support of this project, including the award of a research scholarship to Xu Bing-An.
REFERENCES 1 Boynton, R.S, 1980. Chemistry and Technology of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 380. 2 Zozulya, A.F., Zaitsev, I.D., Telitchenko, V.A. and Tkach, V.A., 1980. Study of the kinetics of lime hydration. Deposited Doc., SPSTL 205kph-D80. Chem. Abstr., 97, 59959a: 257 (in Russian ).
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Ovechkin, E.K., Volova, L.M. and Chernaya, A.E., 1972. Reaction rate of lime slaking with preparation of concentrated milk of lime. Issled. Obl. Neorg. Teknol., 267, (Chem. Abstr.), 78, 8353y: 283 (in Russian). Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs. N.J., p. 69. Boynton, R.S., 1980. Chemistry and Technolo~" of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 161. Boynton, R.S., 1980. Chemistry and Technology of Lime and Limestone. Wiley, New York, N.Y., 2nd ed., p. 175. Weast, R.C. (Editor), 1983-1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. F92. Hedin, R., 1962. Processes of diffusion, solution and crystallization in system Ca (OH) 2-H20. Swed. Cem. Cone. Res. Inst. Bull., 33, (Chem. Abstr.), 57: 6689a. Sillen, L.G. and Martell, A.E., 1964. Stability constants of metal ion complexes. Chem. Soc. Spec. Publ., 17, p. 42. Littauer, E.L. and Tsai, K.C., 1979. Observations of the diffusion coefficient of the hydroxyl ion in lithium hydroxide solutions. Electroehim. Acta, 24,351 355. Heyrovsky, J. and Kuta, J., 1966. Principles of Polarography. Czech. Acad. Sci. Publishing House, Academic Press, New York, N.Y., 581 pp. Weast, R.C. (Editor), 1983 1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. F170. Johnston, R.R.M. and Spiro, M., 1967. Diffusion coefficients of the silver ion and the disulfitosilver (I) ion by the rotating disk method. J. Phys. Chem., 71, 3784-3790. Weast, R.C. (Editor), 1983-1984. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 64th ed., p. D57. Tan, Tianen, Mai, Benxi and Ding, Huihua, 1984. The Principles of Chemical Engineering. Chem. Ind. Press., Beijing, 1, pp. 137 153 (in Chinese).