January, 1926
INDUSTRIAL A N D ENGINEERING CHEMISTRY
19
The Rate of Solution and Availability of Commercial Limes',' By R. T. Haslam, F. W. Adams, and R. H. Kean MASSACHU~BTTS fNSTITUTB
OF ~ C € Z N O L O C Y ,CAMBRIDGs, M A S S .
N ORDER to standardize and improve the quality of commercial limes, it is essential that there be a clear
I
the area through which the diffusion takes place-i. e., surface exposed. The basic equation for the rate of solution of a solid in a liquid then becomes
understanding of the chemical reactions of lime, together -Vdc = DA E )( with a knowledge of the properties of the lime influencing (2) de 6 these reactions. One of the more important of these properThe constancy of the diffusion coefficient, D, was estabties is the value of the lime as an alkali. This is largely determined by two factors, its ultimate solubility and its rate lished by Noyes and Whitney14studying the rates of solution of solution (which is analogous to its availability). The re- of benzoic acid and lead chloride in water at 25' C. They sults of a study of the first of these factors were reported by used a relatively large cylindrical area of solid in a constant' Haslam, Whitman, and Cochraneain a paper dealing with the small volume of solution maintaining- a constant rate of stirring. The values of their saturated solubility of lime constant check closely for in various solvents. The any one run in which the present paper is a discussion The availability of a commercial lime in general desame cylinder was used, but of the second factor, the pends on the rate of solution. The rate of solution vary as much as twofold berate at which lime goes into depends on the fineness of the lime and is directly protween cylinders. Since they solution-that is, becomes portional to the area and to the ultimate solubility of made no area measurements available. the lime. their coefficients represent Noyes a n d W h i t n e y 4 If the lime reacts with an acid that forms a soluble the product DA/6. postulated, as a result of lime salt, the rate of solution is increased, the increase Bruner and Tollocskoa detheir work with benzoic acid over the rate in water being directly proportional to termined the constants for and lead chloride in water, the concentration of acid. If the lime reacts with an benzoic acid, benzylic acid, that the rate of solution of excess of acid that forms an insoluble salt, the parphenylpropionic acid, aceta solid is controlled by the ticles of lime are crusted over with this insoluble coatanilide, and gypsum, using a rate of diffusion of matter ing, so that the rate of solution is actually decreased. plane surface of solid cethrough a liquid film on the Whenever the lime reacts with a salt with the producmented to a paddle suesurface of the solid. Thus, tion of an insoluble salt, the rate of solution decreases pended in a beaker of soluwhen a solid is placed in still further. tion. The surface area excontact with a liquid a satuThese facts show conclusively that for an availability posed was measured in every rated solution is immeditest for lime to be of any great value the test must be case and the coefficient calately formed at the interbased on the particular process in which the lime is to culated as D/6. I n their face. From this boundary be used. computations no allowance the solute diffuses through was made for the chaneine the film of liquid surroundvolume of solution d u i t i ing the solid and into the main body of the liquid in which i t is uniformly distributed the removal of samples for titration. I n addition, the saturated solubility values which they used do not agree with the by convection currents. Fick'sb law of diffusion states that the amount of a sub- most reliable figures available. They conclude from their exstance diffusing in a given time is directly proportional to periments that the rate of solution is not affectedby the surface the area through which diffusion is taking place and to the condition of the solid, but is proportional to the area of the film. Brunner? substantiated this conclusion with benzoic acid. concentration gradient-i. e. , change of concentration with He recognized that a direct comparison of diffusion coeffidistance. This is expressed mathematically: cients obtained by various investigators cannot be made beE = - D A Bdc (1) cause differences in stirring mechanisms affect the thickness e where w is the weight of substance diffusing in the time of the film to unknown degrees. A calculation of the film 9, D is the diffusion constant, A the area through which thickness in his experiments, using rate of solution data and diffusion is taking place, and dc/dl is the concentration gra- the specific diffusivity obtained from electrolytic measurements, gives 0.02 mm. at a stirrer speed of 150 r. p. m. dient in the direction of diffusion. The amount of solute diffusing in a given time is equal Effect of Particle Size to the rate of solution of the solid, or Vdclde, where V is the I n this present work on the rate of solution of lime, screened total volume of solution and c is the concentration of the soparticles of commercial high-calcium and high-magnesium lution a t any time, 8. The concentration gradient through lime were used. Figure 1 shows the effect of particle size s - c the film is evidently 6 - 1 where s is the saturated soh- upon the rate of solution of a high-calcium lime in water. On account of the porosity of the lime, a saturated solution bility, c is the concentration in the main body of the sohtion, and 6 is the thickness of film. A , as above, represents of calcium hydroxide in water penetrates into the particle through the pores. This solution reacts with the calcium 1 Received July 18, 1925. oxide forming calcium hydroxide and liberating heat, causing 1 This work was aided and encouraged by the National Lime Association. a swelling within the particle and its consequent rupture. * Proc. Nal. Lime Assoc., 1914. 4
6
2. physik. Chem., 13, 689 (1897). Pogg. Ann., 94, 59 (1855).
'2.Physik. Chcm., 81,283 (1900). Ibid., 47, 56 (1904).
Vol. 18, KO.1
INDUSTRIAL AND ENGINEERING CHEMISTRY
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This causes an increase in the area of the solid and a more rapid rate of solution. Hence the calculation of values of D/6 after 2 or 3 minutes is prevented. However, values of a constant, K , for the initial rate of solution may be computed by using the integrated form of Equation 2 simplified as follows:
from pure calcite, determined the solubility of calcium hydroxide in water as 1.55 grams per liter at 25°C. Thedifference between these two values-O.22 gram Ca(OH)2per literis accounted for as soluble alkali-i. e., sodium, potassium,
where K = rate of solution constant c = alkalinity of solution as grams Ca(OH), per liter s = saturated alkalinity of solution as grams Ca(OH), per liter 0 = time in minutes W , = weight of lime used in run in grams x, = average diameter of particles in centimeters
This calculation is facilitated by plotting on semi-logarithmic paper the percentage unsaturation against the time. (Figure 2) The slope of the tangent to the curve at the start gives the value of the initial K. (Table I) With the smaller sizes of initial particle the experimental curve departs less from the tangent because the per cent increase in area due to hydration is less.
NOTE -ZERO TM'C FOR l i
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Table I-Rate of Solution of High-Calcium Lime in Water Weight of lime sample, 5.0 grams Volume of water, 1000 cc. Diameter of particle Curve Cm. K I 0.1026 0.00198 I1 0.0786 0.00191 I11 0.0503 0.00211 IV 0.0356 0.00172 V 0.0252 0.00186 VI 0.0178 0.00184 VI1 0.0126 0.00196 VI11 0.0089 0.00208 Average 0.00193 Average deviation of data from mean, 5 per cent
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Figure 2
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40
or lithium present in the lime as alkali. Referring to Figure 4,Curve I, in which 0.5 gram of sample was dissolved in a liter of water, the amount of calcium hydroxide present from a gravimetric analysis is 0.643 gram. Since the weight of sample is only one-tenth of that used in the runs plotted on Figure 1, the soluble alkali is one-tenth of the former value, or 0.022 gram Ca(OH)* per liter. Therefore, the ultimate alkali concentration as calcium hydroxide in Figure 4 should be the sum of 0.643 and 0.022, which is 0.665 gram per liter. The actual value obtained (see Curve I) is 0.660, which checks within the precision of the analysis of the quicklime. The presence of sodium as alkali in the lime was proved by acidifying the aqueous solution with hydrochloric acid and evaporating to dryness. The calcium chloride was dissolved in an absolute alcohol-ether mixture leaving cubical crystals of sodium chloride.
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6
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Figure 1
The increase in rate of solution is proportional to the increase in area. Thus, halving the diameter of the particles doubles the area exposed and doubles the rate of solution. This is more clearly demonstrated by Figure 3. The points show the rate of solution for various sized particles, while the relation between the diameter of particle and the area of a definite weight of particles is represented by the full line. Owing to the higher solubility of smaller particles in their solution, the maximum concentration of solution is greater with the smaller sizes. The maximum alkali concentration of 0.1026-cm. diameter particles (14/20 mesh) is 1.77 grams Ca(0H)z per liter; this maximum for 0.0089-cm. diameter particles (150/200 mesh) is 1.86 grams Ca(OH)2 per liter. The alkali concentration decreases after reaching this maximum, on account of crystal growth. As the crystal size increases the solubility is decreased, causing a further precipitation of calcium hydroxide. This continues until equilibrium is attained. Thus, after 20 minutes both of these sizes have the same alkali strength-i. e., 1.77 grams Ca(OH)2 per liter. The solubility of calcium hydroxide in water obtained as a result of these runs is 1.77 grams per liter. Haslam, Calingaert, and Taylor,*working with calcium oxide, obtained 8
J. A m . Chem. Soc., 46, 308 (1924).
D w ? y r e r e/
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a t e m a 7 a6
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Figure 3
Effect of Different Solvents
The series of runs to determine the effect of different solvents on the rate of solution of lime were all made with 0.5 gram of lime in a liter of solution at 25" C., first high-calcium and then high-magnesium lime being dissolved in each solvent. Since in these runs the weight of lime was one-tenth of that used in the particle size runs, it would be expected that
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1926
the rate of solution of the high-calcium lime in the water would be one-tenth of the previous rate. The values of the rate-of-solution constant for these runs (Table 11) check those obtained for the 5.0-gram runs (Table I), confirming this presumption. of Solution of Limes in Water a n d i n 2 Per c e n t Sugar S o h tion Weight of lime sample 0.5 gram Volume of solution, 1600 cc. Diameter of particles, 0.0503 cm.
Table 11-Rate
LIMB
SOLUTION Water 2 per cent sugar Water 2 per cent sugar
High High High High
K 0.00197 0.00197 0.00201 0.00201
Ca Ca Mg Mg
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solvents. It is seen that the twofold increase in ultimate solubility produces a corresponding twofold increase in the initial rate of solution. This is true of both the high-calcium and high-magnesium limes. Effect of Chemical Reaction of Solvent
When the solvent enters into chemical reaction with the quicklime (otherwise than in a hydration), the rate of solution is influenced by factors which obscure the effect of ultimate solubility. For example, with an acid there is chemical neutralization of the alkali in the lime, which, being a very rapid reaction, tends t o increase the rate of solution. If the 0.1
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0.4
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20
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25
35
40
45
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25
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Figure 4
Figure 5
Furthermore, it was found that the high-magnesium lime had the same initial rate of solution as the high-calcium lime. This is also shown in Figure 4 by the fact that both lines coincide a t the beginning. They diverge later because the solubility of the high-magnesium lime is equal only to its calcium oxide content, in this case approximately 55 per cent. Since the rate of solution depends upon the saturated solubility, as well as upon the area exposed, it follows that an increase in the ultimate solubility should produce a proportional increase in the rate of solution. Figure 5 shows the rate of solution of high-calcium and high-magnesium lime in a 2 per cent sugar solution. It should be noted that again they both have the same initial rates of solution. However, the slope of the curve is steeper than the corresponding curve for water, indicating an increased rate of solution in sugar. This is quantitatively illustrated as follows: The ultimate
salt formed by this neutralization is soluble, the rate of solution is increased. However, if the product is insoluble, the lime particles may be crusted over with this insoluble coating, very markedly decreasing their active area so that the rate of solution is actually decreased. When lime is treated with an acid solution, neutralization will proceed until all of the lime, or all of the acid, is used up. With an excess of acid, the reaction is complete when the neutralization of all the calcium and magnesium in the lime has been effected. When lime is treated with insufficient acid to neutralize the calcium completely, additional lime beyond the:amount combined with the acid will dissolve until the solution becomes saturated with calcium hydroxide. Magnesium oxide in a lime will be attacked simultaneously with the calcium oxide. When the acid becomes exhausted, calcium oxide will continue to dissolve, forming calcium hy-
0
0
1
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ULTIMATE S,XUBlLlTY Cf w H & GRAMS IO 2 0 30
PER
U,TER
I
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Figure b
Figure 7
solubility of calcium oxide in a 2 per cent sugar solution is 2.13 times that in water. Figure 6 shows the ultimate solubility of lime in water and in a 2 per cent sugar solution plotted against the initial rate of solution of lime in these two
droxide, which will precipitate the magnesium as magnesium hydroxide until all the magnesium is removed from the solution. Magnesium will remain in solution only when acid is present in excess of the amount necessary to neutralize
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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lime. As with the calcium lime, the final solubilities of the magnesium lime in water and in a deficiency of acid are the same. Also, after the acid is exhausted the rate of solution follows the water curve, as illustrated for the high-calcium lime. In an excess of acid the increase in the maximum solubility attained is more marked than with a high-calcium lime, owing to the larger amount of magnesium present. The effect of acid concentration on the rate of solution of a high-magnes i u m lime i s 0.8 similar to that of a high-calcium o,, lime-i. e., the rate of solution o . ~ of the lime is directly p r o p o r tional to the acid concentration, as shown in Figure 0 . 4 8. F i g u r e 11 0.1 shows the rate of s o l u t i o n of a o,i h i g h-c a 1 c i u m l i m e i n oxalic acid, the retarding influence of TIME -MINUTES an insoluble pre5 IO "3 25 XI 35 Figure 10 cipitate of calcium oxalate on the surface of the particles being plainly evident. Using a deficiency of acid, the curve is only slightly higher than that obtained with water, which means that the advantages of acid concentration in hastening the rate of solution are nearly counterbalanced by the crusting effect of the insoluble calcium oxalate. A comparison with the curve for water shows that after the acid is exhausted, at 0.33 gram per liter, the rate of solution follows the rate of solution for water. The curve for a n excess of oxalic acid illustrates more markedly the slowing up of the rate of solution by the formation of a n insoluble crust on the particles of lime. I n this case the rate of solution up to the point a t which all the calcium is
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.
