INDUSTRIAL AiVD ENGINEERING CHEMISTRY
March, 1928
of growing time, and considerable human labor to gum-tree plantations in tropical countries. Before that time has really arrived, lacquers using cellulose from comparatively cheap and quickly replaceable sources appear and, quite contrary to the natural products, the greater their production the lower the cost will fall. Eventually, when the problem of feeding the human race becomes more pressing (as it most surely will) any chemical substitution which frees land and labor for foodstuffs will be a capital economic consideration. The Goal-Lower
Prices
So throughout the chemical industries we see the natural tendency to employ in chemical production the cheapest,
253
most available, more abundant, most easily replaceable raw materials. bIuch of our industrial technical advance is based on discoveries that enable us to wrest necessary elements from the commonest sources and by recombining them to increase their form utility. The immediate incentive is, as it has always been, the gain of the individual. Chemical production is made more profitable. Yields are increased; wastes are utilized; costs are lowered. The margin of profit is increased. But always the tendency is towards lower prices; and success in chemical production is to be won only by chemical vision, supported by chemical control of plant operations, and led by chemical research to improved processes and new products.
Computation Methods in Countercurrent Absorption Systems' W. K. Lewis and W. H. McAdams D E P A R T M E N T OF
CHEMICAL ENGINEERING, MASSACHUSETTS INSTITUTE
OF T E C H N O L O G Y , C A M B R I D G E ,
MASS.
The research work of recent years on the interaction to be absorbed, which disURING the last decbetween gases and liquid solvents has thrown a flood solves as' solute in the liquid ade a great deal of of light on the mechanism of such reactions and has a b s o r b e n t . The exit gas work has been done apparently resulted in substantially universal accarries only t h e r e s i d u a l in studying the mechanism ceptance of the so-called two-film theory of diffusion. solute not dissolved in the of a b s o r p t i o n of gases by However, these research results have rendered obsolete absorbent liquid flowing from liquids. The r e s u l t s w e r e the methods of computation hitherto accepted as the bottom. It is advisable well summarized in the Abstandard in the design of commercial absorption units, to express the concentrations sorption Symposium held a t except for certain special cases. This article presents of material being absorbedthe Ithaca Meeting of the i. e., of solute-as parts of AMERICAN CHEMICAL SOCIETY graphical methods of design, based on present-day theories, which are generally applicable. Furthersolute per part of solute-free in September, 1924.2 It is more, these methods are advantageous in that they gas for the gas phase and now generally agreed that the lessen the labor of computation and make possible p a r t s of solute per part of controlling factor in rate of a clear visualization of the operating conditions in the solute-free absorbent for the absorption is diffusion of the unit and the influence of various important factors liquid phase. One may use absorbed material through upon them. any suitable units. two films in series-namely, the films of gas and of liquid Operating Equation on the two- sides of the interface between the phases. Sometimes the problem is simplified by the fact that the Call the pounds of incoming, solute-free gas per unit time, diffusional resistance of one of these films is negligible com- G, and the pounds of liquid absorbent, L. The concentration pared with that of the other, but often both films are im- of solute in the liquid, expressed as pounds per pound of portant. The work cited above has made clear the methods absorbent liquid, is 5 . This has the value x1 a t the bottom of computation for those cases in which during the process of the tower in the effluent liquid and xo a t the top of the of absorption the changes in concentration in the gaseous tower in the incoming liquid. y is the concentration of and liquid phases are small, but in commercial practice solute in the gas, expressed as pounds of solute per pound this situation is seldom met. Thus, in continuous counter- of solute-free gas. Its value is y1 in the incoming gas and current absorption concentrations are normally very low yo in the outgoing. Consider any section in the middle of a t one end of the absorption unit and high a t the other. the tower, taken a t right angles to its axis. At this section Since rate of absorption is profoundly influenced by both the concentrations are x and y , the numerical values of these concentrations and concentration differences, computation quantities differing, of course, with the point a t which the methods become correspondingly involved. The problem section is taken. Consider a second section a t a differential becomes even more difficult where the equilibria are com- distance dl below the first, a t which point the corresponding plicated. The purpose of this article is to outline simple, concentrations are x dx and y d y . Since equality of exact, graphical methods of solution for this general case of input and output demands that any solute removed from steady, countercurrent operation of absorption and desorp- the gas in this section be taken up by the liquid, it follows tion units. that Gdy = Ldx. Furthermore, since continuity of operation is assumed, L and G are constants for any fixed conditions Countercurrent Absorption Unit of operation. It is therefore possible to integrate this equaFigure 1 represents a countercurrent absorption unit. tion directly, obtaining Gy = Lx constant. This equality The incoming gas is indicated entering a t the bottom and may also be written leaving a t the top and the liquid absorbent is flowing in the G(Y - YO) = L ( X - X O ) (1) opposite direction. The entering gas carries the material Inspection of this equation shows that in any such con1 Received September 27, 1927. * I n d . E n i . Chem., 16, 1215 (1924). tinuous, countercurrent system y must be linear in x. Be-
D
+
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
254
cause this relation mas derived solely from an equality of input and output, it must hold whatever the character of the equilibria between the phases, the type of apparatus, the intimacy of contact, the relative velocities of flow, or any other similar relationshim however imDortant from other points bf view. It does, however, postulate steady rates of flow of both gas and liquid. It also neglects any solubility of the gas or volatility of the absorbing liquid. This equation reminds one strongly of the similar relationships existing in rectifying columns and now so generally used in their design.3 Since this expression gives the relation which must exist between the composition of liquid and vapor phases a t any point in a t steady, countercurrent absorption operation, it may be called the operating equation and the line corresponding to it the operating line. Drying of Air by Sulfuric Acid
As a specific case consider the drying of air by sulfuric acid. The equilibrium relationship between air and sulfuric acid is given by the curve OABC in Figure 2.4 Obviously, sulfuric acid Figure 1-Countercan absorb water only- from air concurrent Absorption taining more than corresponds to this Unit equilibrium-i. e., any air being dried by sulfuric must correspond to points to the left of this curve. Furthermore, if one assume air entering such a system with a moisture content y1 = 0.016 (Figure 2) being treated with sulfuric acid with an initial moisture content 20 = 0.60, the moisture in the air being ultimately reduced to yo = 0.006 and the water content of the acid rising to x1 = 1.4, it follows from the preceding paragraphs that the concentrations of moisture in both the air and the acid throughout the apparatus must be represented by the line EF. Such a line must always lie to the left of the equilibrium curve and, furthermore, it can never cross that curve although, theoretically at least, it can touch it. However, if it touches the equilibrium curve, tangentially or otherwise, at that point, gas and liquid are a t equilibrium or only differentially separated from it, so that transfer of solute from gas to liquid in the neighborhood of that point is indefinitely slow, requiring, therefore, indefinitely large surface of contact, which is equivalent to a negligible capacity for any apparatus of finite size. Inspection of equation (1) shows that the slope of the line EF is the ratio of liquid absorbent to gas treated-in this case 0.0125 pound of sulfuric acid per pound of bone-dry air. Since in general it is desirable to use as little absorbent as practicable, it is important to keep this slope low. Assume, for example, that it is required to dry air down to a moisture content yo = 0.006 with acid entering the system with a concentration .TO = 0.6. This corresponds to point F on Figure 2. The flattest line which can be drawn through F and reach the high water content y1 = 0.016 without crossing the equilibrium curve is obviously the line F H , tangent to the equilibrium curve a t J . The slope of this = 0.006 pound of sulfuric line, (0.016-0.006)/(2.26-0.6) acid per pound of bone-dry air, therefore represents the smallest ratio of acid to air which it is theoretically possible to employ in drying air of high moisture content y1 to the
Vol. 20, No. 3
low moisture content yo by the use of acid with initial water content of 20. Furthermore, since in such a system one would of necessity approach equilibrium in the middle of the absorber, it follows that the air-treating capacity of the absorber would be negligibly small or else the size of the absorber infinitely great. It is, however, interesting to note that in such a case the air is not, and can never be, in equilibrium with the absorbent at either its entrance or exit. If the initial air to be treated contains less moisture than corresponds to point J, it becomes possible to draw flatter lines-i. e., to use less acid per pound of air-and still stay on the left of the equilibrium curve. This diagram therefore makes it possible for one to determine directly the theoretically minimum amount of liquid absorbent necessary for any particular case. It is obvious that the amount actually employed will exceed this minimum by a margin sufficient to furnish reasonable capacity. Absorption Rate
The instantaneous rate of transfer of material from the one phase to the other is proportional to the surface of contact between the phases and to the concentration gradient through each of the two surface films on the two sides of the interface, the two phases being a t equilibrium a t the iriterface itself. It therefore follows that in Figure 2 the equilibrium curve OABC represents the interfacial conditions; i. e., a t each point in the apparatus the concentrations there existing at the interface must fall somewhere on this curve. Calling ke and k~ the individual or film coefficients of the gas and liquid films, respectively, A the area of cross section of the apparatus, a the interfacial surface of contact between the gas and the liquid per unit volume of the apparatus (obviously 8, the total interfacial surface, equals aAl), and xs and ye the liquid and gaseous concentrations at equilibrium and therefore also a t the interface, the rate of transfer of material can be expressed as follows:
i L
8 4
McCabe and Thiele, I n d . Eng. Chcm., 17, 605 (1925). Based on data by Wilson, Ibid., 13, 326 (1921).
de
=
Ldx = kLaA(x, - x)dl = Gdy = kGaA ( y
- yJdl
(2)
Obviously, the numerical values of the absorption coefficients k~ and ks will depend on the materials treated, the type of apparatus, and the units employed.
s
Ig 5p
.nu
9
0.000
INDUSTRIAL AND ENG 'NEERING CHEMISTRY
March, 1928
gradient through the gas film is negligible, or that the gas concentration a t the interface is essentially identical with the concentration in the bulk of the gas y. It therefore follows that the interfacial conditions are represented by point B in Figure 2, a t which the concentration in the gas film a t the interface is equal to that in the main body of the gas, rrhile the concentration in the liquid film a t the interface has the value xc. Therefore, the driving force causing diffusion in equation (2) is numerically equal to xt - x corresponding to the length of the line PB. Rew-iting equation (2) in the form - dx -
kLaAdl --
(24 L it is seen that, granting a knowledge of the constants h a , A , and L, one can calculate the length, 1, of absorber necessary by evaluating the integral, dx/(Xe - x). ( A , the cross section of the apparatus, is determined by the gas handled per unit time and by the gas velocity to be employed.) This may be done by plotting the reciprocal of ( r e- x) vs. 2 . In this way it is possible to determine the volume of absorber necessary for any desired operation, once the constants of the equipment are known for the case in question. GAS-FILMCONTROLLIKG-Assume, on the other hand, that this is a case in which the resistance of the gas film is considerable and that of the liquid film negligible. Since the concentration in the liquid film will be substantially equal to that in the main body of the liquid x, it follows that the interfacial conditions will correspond to the point A (Figure 2 ) . Furthermore, the driving force causing diffusion through the gas film is y - ye, corresponding to the line PA in Figure 2. It is obvious that equation (2) can be graphically integrated for this case by a method entirely analogous to that given above-i. e., by plotting l/(y ye) vs. y, the area under the curve being equal to kcaAl/G. GEXERALC.4SE-In those important cases in which both gas and liquid film resistances must be taken into account, the graphical method of computation is of especial value. It is clear from inspection of equation (2) that kL/ko = (y - y.)/(.ce - x) = AY/AX. Granting that the ratio of the liquid and gas-film coefficients is known, by drawing through point P a line PD (Figure Z), the slope of which equals k&o, it will be clear that the intersection D of this line with the equilibrium curve OABC is the only point on the equilibrium curve which can possibly fulfil this last relationship. Therefore, for such a case the concentration gradient, y - ye, through the gas fdm is equal to the line Dill or PiV, and the gradient, xc - x, through the liquid fdm is equal to the line D N or P M . I n such a case the area curve is obtained by using these lines instead of one of the lines PA or PB, as before. From inspection it is obvious that PN is always less than PA, and PM less than PB; i. e., the areas under the reciprocal curves are always greater. In other words, the rate of transfer through two films in series is less than if one film alone were present. The preceding discussion has been based on the assumption that the driving forces Ay and 'Ax are proportional to the differences in potential Ap and Ac. It can readily be shown that where concentrations are low this is substantially true, but where concentrations are high it is not true. I n the latter case the diagram of Figure 2 should be constructed, not in terms of y and x, but in terms of partial pressures and concentrations p and c, or of whatever units of concentration must be chosen such that differences in concentrations expressed in these units are proportional to diffusion rates. On this diagram of p vs. c, the equilibrium curve should be drawn. The actual curve, corresponding to the line FE, can be drawn by computation, most conveniently by constructing first an auxiliary x - y diagram and transferring X I - x
255
the corresponding points from this diagram to the p - c plane. The FE line will not be straight in the p - c plane. If the equilibrium between phases corresponds to Henry's law, a t least in the form y = kx, the equilibrium curve becomes a straight line. Since the operating line is also straight, study of the diagram will show that, if the ratio of gas-film to liquid-film resistance remains constant, the ratio of the driving forces through the two fdms will also remain constant. Consequently, the true driving force through either film is proportional to what would be the driving force through that film were the resistance of the other negligible. That is, it is allowable in such a case to assume a single film resistance; for, while the coefficient thus computed will differ from the true one, it will be constant for these operating conditions and can be employed without hesitation. Further study will also make it clear that the average driving force will be the logarithmic mean of the driving forces a t the two ends of the unit. If the gas being treated in a countercurrent absorption system contains a component which it is not desired to dissolve, but which is appreciably soluble in the solvent employed, one should use an absorption column designed to give the most efficient possible countercurrent contact between absorbent and gas and strictly limit the amount of absorbent used per unit of gas treated to the lowest posqible quantity adequate to dissolve the desired constituents. Unfortunately, the gas treated is often subject to variations both in composition and quantity. Whenever the solubility of the constituent to be absorbed follows Henry's law, the minimum adequate ratio of absorbent to gas treated is independent of the composition. Thus, assume a certain composition and a corresponding ratio of absorbent to gas; if, now, one double the concentration of the desired constituent in the entering gas, since its solubility in the absorbing medium is proportional to its concentration, the absorbing capacity of the menstruum is doubled. Therefore, there need be no increase in the quantity of the absorbing medium per unit quantity of gas treated in order to dissolve the increased amount of the solute. This can be summarized in the following rule: For a given material to be dissolved from a gas in a given absorbing liquid in which the solubility of the material follows Henry's law, the minimum adequate quantity of absorbent per unit quantity of gas treated is independent of the concentration of the material absorbed.
From the above it follows that, to get best results, the ratio of absorbent to gas treated should be kept constant. Materials Obeying Raoult's Law I n the case of a volatile liquid dissolved in an essentially non-volatile liquid, in the presence of a substantially insoluble gas, the partial pressure of the dissolved vapor following Raoult's law, the equilibrium relationships are greatly simplified. Although the following discussion will be general, it will perhaps be clearer to illustrate by the case of benzene vapor dissolved from an inert gas, such as flue gas, by absorbent oil, the oil being later dehuded by distillation with steam. It is assumed that both the absorption and stripping are conducted by countercurrent flow, under steady conditions of operation. Call x the mols of benzene per mol of oil, in the liquid phase, and y the mols of benzene per mol of gas (flue gas or steam as the case may be), L the mols of absorbent oil, and G the mols of gas employed per unit time. Hence, as before, L(XO - X ) G (YO - Y) (3) represents the actual operating conditions in the unit. Granting constancy of temperature in the tower, calling P
INDUSTRIAL AND ENGINEERING CHEMISTRY
256
the pressure of pure benzene at this temperature and T the total pressure on the unit, the partial pressure, p , of benzene over the liquid is given by the expression, p = Px/(l x), while the partial pressure of benzene in the gas is p , = ~ y / ( l +y). At equilibrium these two are equal1. e.,
+
=
Px a-(P-?r)x
(4)
Vol. 20, No. 3
the equiIibrium curve a t a point A , cutting the horizontal axis at point C, corresponding to the best possible stripping compatible with the assumption made. The equation of this line can be calculated from its slope, d.i - G
&-I= whence,
[T
-
(P - T)x~]’ PiT
IT - (P - iT)xol2 (Yo - Y) xg - x = This equation represents a rectangular hyperbola with axes PiT parallel to the major axes. Hence at the bottom of the apparatus, where y = 0, SPECIALCASES-(I) P > ir. When stripping a volatile In - (P - T ) X ” ] 2 component from a non-volatile absorbent by steam, it is x = xg - yo PiT advantageous to have the temperature as high and the This value of z represents the lowest attainable concentration pressure as low as possible. Generally, therefore, the operating conditions are such that P > ir. I n this case of the stripped oil compatible with steam saturation a t inspection of the equilibrium, equation (4), shows that y the top. becomes infinite when the denominator on the right-hand If xo = xo. inspection of the diagram makes it clear that side is zero, when x. = T/(P- T),where xa is the asymptotic it is impossible to strip a t all and a t the same time have concentration above which the dissolved constituent cannot the vapors leaving the still at equilibrium with the absorber exist in the absorbent liquid. If the absorbent enters the stock entering it. This is true because, under these constripping column richer than this, the excess of dissolved ditions, the partial pressure of the entering absorber stock is vapor boils out spontaneously, reducing the concentration equal to the total pressure on the still, so that the presence to the asymptotic value. The equilibrium curve is repre- of any steam whatever would lessen the partial pressure sented by Figure 3. of the solute and therefore destroy the equilibrium. If, as is usually the case, a large fraction but not all of the If, in this figure, xo represents the concen- benzene in the feed is to be removed, then x1 is small but STRIPPING I tration of the incoming finite. The minimum steam consumption would then I rich absorber stock, in- correspond to equilibrium a t some value of 1: intermediate spection will make it between xo and XI, the operating line being tangent to the clear that, if one wishes equilibrium curve a t I to s e c u r e c o m p l e t e 4 stripping-i. e., to have I the operating line go Obviously this value of x is independent of ro and depends through the origin-the 0 steepest line which can only on xl,T , and P. Since the values of y1, xt,and xo are 0 rbe drawn is one tan- known, yo is computed by proportion: Flgure 3 gent to the equilibrium Yo = Y t (xo - xd/(xt - XI) curve at the origin, cutting the vertical line through xo (11) P < T. Absorption should take place at the highest a t the point B, this point corresponding to the highest practicable total pressure and the lowest possible temperapossible degree of saturation of the steam leaving the strip- ture-i. e., at high values of T and low of P. I n other ping column under these conditions. Inspection of the words, the conditions of equilibrium, equation (4),shows that its slope is given by this case (P < n) are ----------%>p r.- P ----. the expression *E.~WION those normally existing in absorption processes but not in stripping. I n s p e c t i o n of the Therefore, for complete stripping the operating line has for its slope the value of this expression at x = 0 ; i. e., equilibrium e q u a t i on b dy/dx = P/Tor dx/dy = ir/P = G/L, where G/L is the rnols makes it clear that it of steam required per mol of oil. Furthermore, it is ob- c o r r e s p o n d s t o t h e 2vious in this case that the equation of the operating line curve of Figure 4, beFigure 4 is y = (P/n)xand that the steam consumption is propor- ing asymptotic to the tional to the total pressure on the system and inversely horizontal line, y = P/(n- P). It is obvious that if one desires to denude the gas comproportional to the pressure of the pure solute a t the operating temperature. I n other words, the lower the total pressure pletely, the operating line must go through the origin and the less the steam consumption necessary for complete cannot possibly have a slope less than that corresponding stripping, and also the lower the volatility of the absorbed to tangency there. Since‘at x = 0, dy/dx = P/T,the component the greater the steam necessary to do the work. corresponding operating line is y = PX/Tand the amount Inspection, both of the diagram and of these equations, of absorbent required per mol of inert gas treated, L/G = shows that the steam consumption for complete stripping P/n. It will be noted that the absorbent required for a is independent of the initial concentration of the rich ab- given amount of gas is proportional to the volatility of the sorber stock. From this it follows that if one is stripping solute absorbed and inversely proportional to the total from the oil a mixture of a number of dissolved components, pressure of the system. Here, too, the absorbent needed since the more volatile strip out first, the steam necessary is independent of the initial concentration in the other phase it is obvious for complete stripping is that computed for the least volatile at the other end of the unit. Since y = Px/T, that z0 = ry0/P= the maximum saturation of oil compatible component, just as though the others were not present. with complete denuding of the gas treated. If one wishes to saturate the steam leaving the stripperTo saturate oil up to equilibrium with the gas entering i. e., to bring it into equilibrium with the incoming rich stock-the steepest operating line attainable is a tangent to the absorber,
I
t
J
1
INDUSTRIAL AXD EhTGINEERING CHEMISTRY
March, 1928 y1 = yo
-
[n
+
Pnxn (R
- P)XOl*
This gives the lowest value to which the concentration of solute vapor in the exit gas can be reduced if the oil is brought up to equilibrium with the entering gas. (111) P = r . For this case a t equilibrium y = 2, and it is therefore theoretically possible to have eauilibrium a t all points in the system, provided the capacity of the e q u i p ment is s u f f i c i e n t t o 0 carry out the absorpztion under a negligible Figure 5 driving force. The conditions for the three cases are given in Figure 5, the upper curve corresponding to stripping, the lower to ‘absorption, and the straight line between them to the special
257
case of P = T. It is worth noting that in both stripping and absorption one normally operates on the unfavorable side of the equilibrium curve-i. e., it is theoretically impossible to secure equilibrium a t both ends of the operating line. Were one absorbing under conditions corresponding to the upper curve or stripping under those of the lower, the reverse would be true. However, this disadvantage is more apparent than real, because the height of the equilibrium curve corresponding to stripping conditions, secured by raising the temperature and lowering the pressure, far more than comDensates for its unfavorable shaDe. I , and the same is true of the advantages gained by lowering the equilibrium curve for absorption, through decreased temperature and increased pressure. While for many cases of absorption Raoult’s law does not apply, there are important instances, notably the absorption of hydrocarbons in oil, where it is a satisfactory approximation. Furthermore, even in those cases where the deviations are too wide to justify its quantitative use, it none the less gives a clear visualization of the qualitative effects of various factors upon operating results.
Molybdenum Tannage’ Joseph G. Niedercorn A. F. G4LLUN & SONS CO., MILWAUKEE, W1S.
H E analogy between the compounds of chromium and those of molybdenum seemingly becomes more firmly established as the true character of molybdenum is better understood. This consideration gives rise to the conception that salts of tervalent molybdenum should form, with hide substance, unhydrolyzable compounds very similar to those formed in chrome tannage. There are two sulfates of tervalent molybdenum, the purplered and the green. The green sulfate has been assigned the ; ~ constitution J of the red salt the formula M O ~ O ( S O ~ ) ~ is as yet undetermined. Both salts are best obtained by the electrolytic reduction of a solution of molybdic anhydride in sulfuric acid, using a diaphragm cell and smooth platinum electrodes.4 In hydrochloric acid solution molybdic acid is reduced as follows:6
T
Movr+ colorless
MoV+ emerald-green
MolI1+ purple-red
MolI1 olive-green
In sulfuric acid solution the emerald-green salt was not obtained unless the solution was more strongly acid than was desirable for tanning purposes, inasmuch as it would become loaded with sodium sulfate in adjusting the acidity; instead, molybdenum blue, MoaOa(?), was formed as intermediate product. I n solutions nearly neutral the reduction did not proceed beyond molybdenum blue; in strongly acid solution it sometimes stopped a t the red stage. No vivid green solutions, such as those that appear in the reduction of molybdenum salts with zinc in an atmosphere of hydrogen, were obtained. An attempt was made to determine the acidity of the solutions potentiometrically, but this method proved unPresented before the Division of Leather and Geldtin Chemistry a t the 74th Meeting of the American Chemical Society, Detroit, Mich., September 5 to 10, 1927. * Wardlaw, Nicholls, and Sylvester, J . Chem. SOL. (London), 126, 1910 (1924). * Chilesotti, Gal?. chim. h l . , 2, 33 (1903). Wardlaw, Law, and Sylvester, J . Chem. SOL. (London), 123, 969 (1923). Chilesotti, Z . Elekfrochem., 12, 173 (1906).
certain because of the oxidation-reduction potentials which made the hydrogen-ion concentration seem much greater than it really was, especially in the case of the red solution.jj6 According to Chilesotti,’ platinum black exerts a catalytic influence upon molybdenum solutions, causing them to be reduced in the presence of hydrogen and then causing them to be oxidized. Because of the strong reducing action of Note-Oxidation with the evolution of hydrogen takes place immediately upon the reduction of all the metal to what is apparently the tervalent state, and occurs even in an atmosphere of hydrogen.
the solution, indicators could not be effectively used, and therefore the acidities were controlled very inaccurately with the hydrogen electrode, making no allowance for oxidation-reduction potentials. Apparent acidities could be duplicated without difficulty. The green solution turned red upon standing, even if kept in a tightly stoppered bottle; it had no sharp precipitation point, but noticeable amounts of hydroxide appeared a t p H 3 and kept increasing. At pH 9 complete precipitation had not taken place. The solution tanned calfskin well a t apparent pH 2 to 2.5. Probably because of the greater oxidation-reduction potential, the red solution showed a greater acidity than the green (the opposite is true of the corresponding chromium salts), and precipitated sharply a t p H 2.5. It tanned very rapidly a t p H 1-1.5, but a t p H 2 it no longer penetrated into the skin. Both salts yielded a dark brown leather that could be boiled without altering its condition. However, upon standing in the air it gradually lost this property; even then no hydroxide was removed by boiling-the skin merely shrank and hardened. Experimental
A solution was made up by dissolving 40 grams of molybdic anhydride in 54 cc. of boiling sulfuric acid (sp. gr. 1.84) 6 Clark, “The Determination of Hydrogen Ions,” p. 242, Williams & Wilkins Co., Baltimore, Md , 1922. ’ 2 . Elekfrochem., 12, 146 (1906).
