April, 1932
INDUSTRIAL AND ENGINEERING CHEMISTRY
AAcr,NOWLEDGNEXT The authors wish to acknowledge their indebtedness to the Heckscher Foundation of Cornel1 University for financial aid without which this work would have been impossible, and to the A. H. Thomas Company for their generous cooperation. ~
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455
LITERATURE CITED (1) Summer J. B., J. B i d . Chem., 69,436 (1926).
!i; ~~~~~~; 5: i:;zt:, 673q)~~D,~ B,,2~ ( B&,,L, ~ ~ ~ ~ ~ j , sumner, J. B,, and ~ d them., , 76, 149 ( 1 9 ~ ) . (4)
J.
(6) Sumner, J. B., and Holloway, R G., Ihid., 79, g@(12928). RECXIVED January 30, 1932. -_.__
Application of Duhring’s Relatio Solubilities
4
R. L. HARRIS,University of Delaware, Newark, Del.
I
N 1878 Duhring announced It has been found that Duhring’s relation f Kl’ = any function of M where (I and K = constants an by can be used to predict the solubilities of nonT = temperature the use of which the vapor M s o l u b i l i t y in moles Per hydrated, inorganic salts in water at various pressure of a substance can be 1000 grams of water temperatures. Results are obtained of a n accalculated with reasonable accuracy often as good as the data themselves and Temperature may Or may not be curacy. iilthough the rule has absolute* Then, if for two salt been expressed mathematically rarely poorer than 5 per cent, even though but solutions the solubility he chosen byDuhringand Others (3’ / “ i l o ) , two points f a r apart on fhe solubility curve haw the same, the calculation is generally made been de termined experimentally . graphically. If the t e m p e r a f(Md = f(Md, and CI + tures a t which one substance exK I T I = CA KL7’2 erts certain vapor pressures be plotted against the temperatures a t which a reference substance exerts the same vapor or the graph of TI vs. Tzwill be a straight line. Many attempts have been made to formulate the equation pressures, the points are found to lie nearly upon a straight line. for the variation of the solubility of electrolytes with temTherefore, if the vapor pressure of a substance be known a t two points, a straight line may be drawn in accordance with perature, but the problem is complicated by the ionization Duhring’s relation, the complete vapor-pressure data for a of the electrolyte and by the possible hydration of the ions. reference substance having been taken from the literature. Some have introduced correction factors to allow for these From this Diihring line the entire vapor-pressure curve of effects, but equations so modified are usually made so involved that they have lost their practical utility. The ideal the substance in question may easily be calculated. Duhring’s relation has been used in recent years by a solubility equation is derived in the same way as is the number of investigators. Badger and McCabe ( 1 ) and Clausius-Clapeyron equation, and is generally deduced for Walker, Lewis, and McAdams ( 1 1 ) call attention to its use organic solutions on the assumption that Raoult’s law a p in evaporator design and in determining the latent heat plies. Such is the case for solutions of naphthalene in orof vaporization of solutions and pure liquids (9). It has also ganic solvents, and Hildebrand1 (5) has shown that in been used in finding the boiling point us. composition curves these instances the graph of os. log ilr, (where T is of solutions of organic solvents, and the vapor pressure the absolute temperature and N z is the mole fraction of curves of solutions of electrolytes in water (2). Aside from solute) are .straight lines. However, Hildebrand further its use in predicting vapor-pressure data, Duhring’s rela- shows (6) that, in the case of solutions of electrolytes in tion has been applied by Porter (12) to the estimation of water, the simple relation no longer obtains, and the modified the change in viscosity of liquids with changing tempera- equation, which is even then admittedly not exact, becomes ture. too unwieldly to be of value in predicting solubilities. Duhring’s relation, however, can be easily applied, and results THEORETICAL DISCUSSION are obtained which are within the accuracy ordinarily reAlthough White (13) has since shown it to be compatible quired in engineering calculations. Another relation which has been of service in predicting with the integrated form of the Clausius-Clapeyron equation, Diihring’s relation was first discovered as a n empirical vapor pressures is that of White (13): The graph of 1 us. 1 T2 rule suggested by the close similarity of vapor-pressure curves. But it has been shown by Hildebrand (4) and others that the where TI and Tz are absolute temperatures a t which two ideal case of solution is quite analogous to that of vaporiza- substances have equal vapor pressures, is a straight line. tion. It would therefore seem plausible that Duhring’s re- Obviously in the case of ideal solubility above referred to, lation should apply to solubility curves in general. More- where over, the solubility curves of salts in water, especially of salts = log .V? + ( ‘ T of the same chemical nature, are similar in shape; so for this reason also Duhring’s relation should be expected to White’s rule will apply exactly. This relation has, therefore, more theoretical justification than Duhring’s as yet apply. Mathematically speaking, for the relation to apply to enjoys, but the actual results of its application are somesolubility curves, it is necessary only that they be of the times hardly as accurate. Almost no deviation from the form: rule was noted when the nitrates of caesium, rubidium, lead,
+
-3
I N D U S T R I A L ,4N D E X G I S E E R I1v G C H E M I S T R Y
456
and silver and when caesium chloride were plotted against potassium nitrate according to the inverted-temperature rule, but in several other cases the results were poor. It may be that the method tends to accentuate minor deviations. At any rate the plotting is slightly more troublesome and apt to be less accurate than when Duhring's relation is used.
METHODOF APPLYING IIUHRIXG'SRELATIOX I n Figure 1 are plotted the Duhring lines of several salts, using potassium nitrate as a reference substance. I n order to
[email protected] up .the illustration, the temperatures a t which a salt &d certain solubilities were plotted against the temperatures at which potassium nitrate had the same solubilities. The Diihring lines shown are representative of a considerable number plotted using potassium nitrate as a base. Data were taken from the International Critical Tables and were expressed in moles per 1000 grams of water. The advantage of the method lies in the fact that determinations of the solubility a t two or three temperatures suffice to fix the Duhring line. The solubility a t other temperatures can be predicted as follows: Take, for example, the problem of calculating the solubility of silver nitrate a t 20" C. From the Diihring line for silver nitrate (line I in the figure), the solubility at 20" C. is equal to that of potassium nitrate a t 64.7" C. From a curve for the solubility of potassium nitrate this solubility is 12.15 moles per 1000 grams of water. This, then, is the solubility of silver nitrate a t 20" C. The value given in the International Critical Tables is 12.30 * 2 per cent. The accuracy of plotting was within 1 per cent. Table I shows the results of calculation from a few Duhring lines. TABLE I. TEMP.
c. - 15
-5 0 5 10 15 20 25 30 40 50 60 70
SOLUBILITIES CALCUL.4TED FROM
... ...
5:60d
6.65 7.80 9.20 10.75 12.30 14.00 15.95 19.506 23.6d~8
7.93 9.19 10.61 12.15 13.82 15.62 19.50
... ...
...
so
90 100 110 a
d e
iZ%.
... ...
5.55
6.20 6.56 6.92 7.32 7.75 8.54 9.43 10.29 11.19 12.17 13.20
6.22 6.58 6.97 7.38 7.78 8.63 9.43 10.34 11.20 12.15 13.2 14.2d
...
...
b &l%.
C
...
5.53
...
...
used to plot calcium and strontium oxalates against barium oxalate, and in this case it worked very well. From the Duhring lines in the figure and from a number of others investigated, it appears to make little difference whether or not the unknown salt is chemically similar to the reference substance used. It would seem that the factors in the function of solubility which change, whether because of temperature or concentration, change in the same way for all solutions of nonhydrated salts of comparable orders of solubility and are, to some extent a t least, independent of the chemical nature of the salt in question. The case of solutions of hydrated salts is somewhat more complex. A few hydrated systems such as the strontium nitrates shown in Figure 1 and the zinc sulfates, form families of straight lines intersecting a t the transition points. It is much more usual, however, for the Diihring line of a particular hydrate to continue straight for a while and then, as the point of transition into the next hydrate is approached,
DUHRING LINES
(Data from International Critical Tables) SOLUBILITY ---. 7 AgNOs NHdCI CSKOS Calcd. Obsd.a Calcd. 0bsd.b Calcd. 0bsd.c Moles per 100 grams of water 4.60d ... ... 6.66
Vol. 24, No. 4
... ... ... ... ... ... ... . I .
2.52 3.34 4.37 5.53 6.98 8.57 10.29
...
... ... ,..
... ...
... i : 86d
2.61 3.50 4.52 5.64 6.92 8.40 1LO.10 12.m
,+3%.
Points used in determining Duhring lines. .4ccurate to only 10 per cent.
As would be expected, the rule is not exact in its application. The function of M referred to above, though it may be the same in form for all solutions, no doubt includes some factors which are different for different solutions under various conditions. The only reason Duhring's relation applies so well is that these factors are nearly alike and vary in much the same way with nearly all salt solutions of the same order of concentration. Obviously two salts with solubilities of different orders cannot be plotted against each other by Duhring's method. It has been found, however, that, in the range of slightly soluble salts where concentrations are low in any case, salts of different solubilities may be quite satisfactorily plotted against each other by multiplying the data for one salt by a constant to make the range of solubilities overlap. Solubilities thus calculated are then divided by this constant. The foregoing scheme has been
FIGURE1. D ~ ~ H R ILINES N G OF VARIOUS SALTS
to curve sharply. Indeed there may be no straight portion. These results are what we should expect, for the theory already advanced (8) is that solution of the hydrates is accompanied, near the transition points a t least, by concurrent dissociation of the hydrated molecule. Under these conditions Diihring's relation could not be expected to apply. Poor results also were obtained when organic salts, such as calcium propionate, were plotted against potassium nitrate. Aside from the fact that the calcium propionate contains one molecule of water of hydration, the salts are so dissimilar that poor results would be expected. The case is interesting, however, for calcium propionate exhibits decreasing solubility. Few nonhydrated inorganic salts show this phenomenon. Anhydrous sodium sulfate decreases in solubility to a minimum, then it increases very slowly. The Duhring line is straight to the point of minimum solubility; then it changes direction sharply, giving another straight line which is vertical because further variation in temperature produces only a slight change in solubility. Strictly speaking, since the sodium sulfate solubility curve includes a hydrate, Duhring's relation should not be applied. But with it, as with several other hydrated systems, straight lines are obtained for the anhydrous salt. One exception to the applicability of Duhring's relation has been found. I n the case of thallium nitrate the Duhring line exhibits pronounced curvature. Other thallium compounds, as the hydroxide, follow the rule well, but the nitrate seems to be a real exception. KO explanation has as yet been found for the behavior of this salt. It appears to be anomalous. KO other exception has been noted when
April, 1932
I N D U S T R I h L -4N D E N G I N E E R I N G C H E h l I S T R Y
457
inorganic nonhydrated salts were plotted against potassium nitrate, although a considerable number of cases have been investigated. The exception cautions us, however, to determine an unknown Duhring line a t three points, in order to prove the line to be substantially itraight before it is used in the prediction of solubilities.
( 2 ) Baker and Waite, Chem. M e f . Eng., 25, 1137 (1921). (3) Dodge, J. ISD. EXG.CHEM.,14, 569 (1922).
ACKSOWLEDGIIEST licknowledginelit is made t o A. 8. Ea5tman of the University of Delaware for assistance in the preparation of this paper.
(9) Lewis, TV. K . , and Weber, H. C., J. I s n . ESG. (‘HEu., 14, 4hG
LITERATURE CITED (1) Badger and .McCabe, “Elements of Chemical Engineering,” pp. 176-8, McGraw-Hill, 1931.
(4) Hildebrand, “Solubility,” pp. 35-7, Chemical Catalog, 1924. (5) Hildebrand, Ibid., p. 155. ( 6 ) Hildebrand, Ibid.,pp. 165 and 166. ( i )Leslie and Carr, ISD.ESG.C H E x , 17, 810 (1926). (8) Lewis, G. N., and Randall, M., “Thermodynamics,” p. 217,
McGraw-Hill. 1923. (1922). \----,
(10) Schulta, I b i d . , 21, 557 (1929).
(11) Walker, Lewis, and hlcAdams, “Principles of Chemical Engineering,” 2nd ed., pp. 439-33, McGraG-Hill, 1927. (12) Walker, Lewis, and Mcbdanis, Ibid., pp. SO and 81. (13) White, IND.ESG. CHEM.,22, 230 (1930). RECEIVED August 6, 1931. The author’s present address ie Washington University, St. Louis, M o .
Vitamins in Canned Foods XII. Supplementary Nature of Grapefruit and Prunes W. H. EDDYAND CELIAZALLGURIK,Teachers College, Columbia University, Xew York, N. Y., AND E. F. KOHMAN, Research Laboratories, National Canners Association, Washington, D. C.
A
I’PAREXTLY the earliest work on the vitaminic properties of prunes was that by Hess and IJnger ( 2 ) . They studied only the dehydrated fruit and came to the conclusion that it possessed practically no value as a preventive against scurvy. Eckman (1) studied a number of dried fruits, including prunes, to determine their antiscorbutic properties, and concluded t h a t peaches were the only dried fruit fed in moderate amounts that would sustain life for several months when they supplied the only antiscorbutic. Even with peaches, scurvy was not prevented but only delayed. Osborne and Mendel (6) found dried prunes to hare appreciable vitamin B, being considerably richer in this factor than apples or pears. Morgan and Field (4) demonstrated that sulfuring prior to the drying process caused the vitamin A content, in dried fruits t o be retained in substantially greater amounts than if the sulfuring were omitted. It may be inserted here that sulfuring prior t o dehydration of prunes is not commercially practiced. Morgan, Field, and h-ichols (5) found sulfuring to have even more marked effects in retaining the vitamin C potency of dehydrated prunes. As fresh prunes are in season for only a short period, they froze fresh prunes to insure a supply for the feeding period. They report protective doses varying from 12 to 20 grams of frozen prunes from different seasons, but growth was subnormal. Apparently, no one has studied the vitamin content of canned prunes. MacLeod and Booher (3)report some data on the vitamin C content of both raw and canned grapefruit. They found that standard guinea pigs were protected against scurvy in dosages of approximately 2.0 grams, either of juice alone or combined juice and pulp. While somewhat more canned grapefruit was necessary, the larger dose was approximately accounted for by the extent to which grapefruit is diluted in canning by the added sirup. Osborne and Rfendel(6) state that the vitamin B content of the fresh juice of grapefruit is about comparable t o that of milk, but that no more than traces, if any, of vitamin A are present.
TYPESOF FRUITUSED During the past year, the present authors have made a comprehensive study of both canned fresh prunes and canned fresh grapefruit. These experiments were planned t o determine the effect on vitamin content, if any, of variations employed in the canning of each fruit, as well as to make a general survey of the vitamin content of these canned fruits. Both French and Italian prunes were included in the studies. The French prune is a high-sugar low-acid prune and comprises the great bulk of dried prunes on the market. Italian pruner are relatively high in acid and low in sugar, as compared with the French variety. While the French prunes of this country are grown largely in California, the Italian prunes are grown mostly in Oregon and Washington. French prunes are not commercially canned in the fresh stat(.. While formerly practically all the Italian prunes were dehydrated or dried also, within recent years canning of the fresh prunes has grown to a considerable proportion. The high-acid and color content of the Italian prunes makes them particularly suitable for canning in the fresh state. The color of the sirup of these prunes when canned is a deep rich reddish purple. The following lots of canned prunes were -tudied: LOTSY, CAXXED FRESH FRESCH PRUSI.,S.The fruit for this lot was shaken from the tree onto canvas at the time and as is customary in harvesting for drying or dehydration. If a comparison with canned fresh Italian prune- is desired, this lot should be compared with lot 2 below. LOT 1, CANNED FRESH (SEMIRIPE) I T A L I a N PRUNES. A portion of the prunes on a few trees were picked by hand on September 2 when well colored, but when the sugar had not yet developed to a marked extent in them. LOT 2, CANNEDFRESHITALIAX PRUSES.Two weeks after lot 1 was picked and canned, the prunes were all harvested for canning, as they had then reached the normal stage for harvesting. While the color was not much greater than that of the prunes picked 2 weeks earlier, the sugar had developed t o its full extent. This lot of prunes was subjected t o a vacuum of 27 to 28 inches under sirup, and the vacuum was released while the prunes were still under the sirup. In this way any air within the prunes-particularly, that surrounding the pits-would be removed. LOT 3, CANNED FRESHITALIAN PRUNES.Fruit from the
