FRXCTIOKAL CRUSTALLIZATIOS
BY C. A. SOCH
I t is often desired to separate a mixture of tm-o salts getting both pure. By fractional crystallization from a solution at constarit temperature it is rarely possible to effect a complete separation. Let us suppose the simplest case, in which the salts form no compounds and no solid solutions. For each temperature there will be a definite concentration for the solution in equilibrium with the two salts as solid phases. If the original solution or mixture contained relatively more of either salt than the monovariant system that excess can be recovered. Since the relative proportions of the two salts in the saturated solution usually varies with the temperature it is possible, by repeated crystallization at two different temperatures, to obtain a complete separation. Theoretically this mould require an infinite number of operations and it becomes desirable to have some definite statement of the general conditions governing such conditions that one may be able to form some idea of the least number of operations in which a given percentage separation can be obtained. Since working at high temperatures presents certain experimental difficulties it is also important to be able to estimate how much one is losing in efficiency by working at 50°,let us say, instead of at 100'. T h e present paper is intended to fill some of these gaps in our knowledge of this subject. I t was also deemed advisable to study the effect of partial precipitation with alcohol since it would certainly be possible to change the relative concentrations of the two salts in this way and there are no data illustrating this point. Ordinary ninety-five percent alcohol was treated with anhydrous copper sulfate until a test portion did not color the salt even after standing some time. T h e alcohol was then filtered
from the copper sulfate and distilled from metallic sodiiiiii, taking precautions to prevent absorption of moisture from the atmosphere. T h e distilled product was preserved in a glassstoppered bottle. T h e salts used, potassium chlorid, potassium nitrate, sodium chlorid and sodium nitrate, were freed from their impurities-KC1 and NaCl from sulfates, K K 0 3 and Kayo3 from chlorids-by repeated crystallization. ,4fter each crystallization the mother-liquor was decanted and tlie crystals sucked dry with the water-pump. T h e ordinary distilled water of the laboratory was used both i n this work and in the solubility determinations. In each case, after purification, tlie salt was dried thoroughly i n a n air bath, pulverized and put in a glass-stoppered bottle. Soliibility determinations were made at 2 j c and at 80' i n pure water and at 2 j " in forty percent aqueous alcohol. T h e salt pairs were potassium chlorid and potassium nitrate, potassium chlorid and sodium chlorid, potassiuiii nitrate and sodiuiii chlorid, sodium nitrate and sodium clilorid. Potassium nitrate and sodium nitrate were not taken owing to the difficult!- in analyzing the solutions while potassium chlorid and sodium nitrate are the instable pair. Bottles of about 30 cc with rubber stoppers were used for holding the solutions. Both bottles and stoppers were always cleaned carefully and dried. In all measurements an excess of each salt was lveighed out roughl). into the several bottles and then the desired amount of solvent added, twenty cubic centimeters with forty percent alcohol and fifteen with prire water. T h e forty percent alcohol was made by veighing out carefully the required amount of absolute alcohol and water. T h e two were mixed thoroughly and distributed at once among the several bottles, which were immediately closed tightly with rubber stoppers. T o ensure complete satriration the bottles were first 5115pended for three hours in water kept just above thirty degrees. This bath was allowed to cool slovly and when it reached 2 8 O the bottles were transferred to a constant temperature bath and there kept at z j 0 for about twentj--four hours. T h e bottles were shaken vigorously at intervals. T h e water i n the bath
\vas kept stirred up by a JTitt stirrer rim bj- a Kaabe turbine. One bottle at a time \vas taken froiii the bath aiid since the temperature of the room \vas bnt little below that of the bath no precaution was taken to prevent precipitation be\-ond that of pipetting off the solutions as rapidly as possible. TI-eiglied amounts of the solutions were evaporated to drj-ness according to the method described by TreI-or1. Each residue was dissolved i n water and made up to one hundred cubic centimeters. Tlie total amount of clilorid was determined by titration \vi th a clecinoriiial solution of silver nitrate iising potassium bichromate as a n indicator. In each titration 2 0 cc of the IOO cc solution were used. T h e amounts of the nitrates are equal to the differences between the residues and the total chlorids. In tlie determinations at 80’ it was not found necessarj- to keep tlie solutions in tlie bath more than eight hours. S o pipette was used and tlie solutions were transferred directly to tared bottles warmed to So ’. Before neighing, these el-aporating tubes were allom-ed to cool. Tlie residues were dissolved in n a t e r and made 1112 to five hundred cubic ceiitiiiieters of which tvient-yfive u-ere taken for titration. Tlie results obtained are gix-en iii Tables 1-111. I n Table I, under tlie heading alcohol”, are gir-en the grams of salt in one hundred grams of aqneous alcohol ; under water are the grams of salt in one hundred grams of water. Since the aqueous alcohol was sixty percent water b!. wt:iglit, these values are ten-sixths of the values given under alcohol”. Beloxv the coiicentrations of the salt pairs are given tlie ratios of these concentrations. T o save space the data in Tables I1 and 111 are arranged horizontall\- instead of yerticalli-. Tlie coiiceiitrations are grams of salts per liundreci gi-ams of water. T h e values are tlie mean of two independent determinations and the probable error is about one percent. T h e values at 80” agree only fairly wit11 those of GtarcI’ ; the data for sodium and potassium clilorids accord well with tlie results of Precht aiid U-ittgen3. T h e displacement of the equilibriulii ‘(
‘ Zeit. phj-s. Chem. 7, 46s i 1891) . -1ii1i.
Chini. Phys. i;) 3, z;j
’ Ber. chetn. Ges. Berlin. 14,
i 1S94) 1667 ( ISSI
c. A. Soch
46
by addition of alcohol is in no case as large as the change produced by difference of temperature.
TABLE I -4queous alcohol at 2 j O Alcohol
____-
KC1
I 0.06
37.97 16.93
I i
1
Ratio iiaC1 KC1 Ratio
0.87
TABLE I1 ITater at 25" KC1
KC1
[
KITO,
KITO,
~
Ratio
KNO,
Ratio
KSO,
i
~ _ _ - _ _ _ - _ _ _ _ ~ _ _--I
NaCl
9aC1
Ratio
I
Ratio __-
Fmciioiznl Cy3/stn1ZizniZbz
47
pass from the temperature T to TI,subtracting or adding enough water to keep the second salt from dissolving or precipitating, the concentration of the second salt has thus been changed from B to BI, the absolute amount in solution being the same. Since the amount of the first salt is still A grams some must precipitate and equilibrium will be reached when the amount in S O ~ U tion is By grams. Since B = Al/xby definition, the final amount of the first salt in solution will be Y grams. If we bring the systeni back to the temperature T adding or subtracting enough water to keep the first salt from precipitating or dissolving, we shall have a solution supersaturated with respect to the second salt and, by the same process of reasoning, we find that the amount of the second salt left in solution will be B-f’ X
grams. ITe have now come back to the original position except that the total amount of solution is less than before and we have certain amounts of the two salts in the pure state. Since tht. only change in the solution is a decrease in the absolute mass of the phase, it is clear that repeating the double operation will give a similar result. This can be put in a general forin. If we start at the temperature T with a solution saturated with respect to both salts and pass to the temperature Tiallowing only one salt to crystallize and pass back to the temperature T allowing only the other salt to separate, the total amounts of the two salts remaining in solution after 71 cycles will be A
(a-) ’I
and B
(-5) ’‘
where we define the double operation as a cycle. In deducing this formula it is not assumed that TIis higher than ‘ I ’ nor \-ice\-ersa. I t is assumed, however, that x y. If we make the contrary assumption that x- y the general form of the eqnation remains the same but we shall have for the amounts left in solution after 7~ cycles
B(5)’.
If we let X = the ratio of x and 1'where X is aln-ays less than unity we may write for the amounts in grams left in solution : AX" and BX"
and for the anionnts in grains obtained piireAl(r
-~X I )
and B ( I - X " ) .
(1)
Expression I is the theoretical statement of tlie results to be obtained by fractional crystallization at tm-o temperatures. Practically tlie yield would alwaJ-s fall short of the value calculatecl from the formula, on-ing to the impossibility of getting rid of all the mother-liquor witlioiit washing with pure water and thus dissolving some of the salt. Allnothersource of error lies in the fact that one would alwaj-s stop a little short of the point a t which the solutioii is saturated with respect to both salts. T h e formula is of 1-alue in two n-aj-s. A comparison of the actual with the theoretical yield shows the degree of accuracy with which the separation is being effected. If we desire a given percentage separation we can deduce froin the formnla the miniilium number of cycles necessary to effect this and we shall a t least know that more will be needed, how many more depending on the accuracy of the work. T o take a practical example it follon-s from 111~7data for S a c 1 and KC1 at z j o and 80' that 1-ery nearly half the total salts are obtained pure at each cycle. Five cycles would therefore give nearlj, ninety-seven percent separation. Tl-itli sodium chlorid and sodium nitrate on the other hand, three cj-cles would g i l e over ninety-eiglit and onehalf percent separation, assuming absolute accuracy of work. It shoulcl be noticed that if, as is usually the case, water is distilled off on passing to the higher temperature) water must be added when coming back to the lower temperature. Knowing the total amounts of the two salts in solation at any time and the solubilities at the two temperatures it is a simple matter to figure out the amount of water to be added or subtracted each time. T h e progress of fractional crystallization at two temperatures is one .vc-liicli should alwa>-s be checked quantitativel?- at each step and the saving in time vi11 compensate a hundred-fold for the extra trouble involved.
If we add alcohol to a solution satorated with respect to two salts, there will be a change in the relatix-e concentrations of the tn-o salts aiid also in the absolute concentrations. 11-e have therefore to consider the precipitated mixture of salts and the amounts remaining dissolved in the aqueous alcohol. TTe d l suppose that the aqueous alcohol is then evaporated. T h e two mixtures of the two salts can each be treated with water. If carried out properly the result will be two aqaeous solutions saturated with respect to tlie tn-o salts, cr>-stals of one of the salts remaining pure at the bottom of one solution aiid crystals of tlie other salt at tlie bottom of the other solution. T h e crystals can be separated by filtration, the solutions mixed and the round is complete. 1Te will therefore define as a cj-cle, tlie partial precipitation by alcohol, distillation of the aqueous alcohol, and treating tlie residues with water. Let and B be the amounts of the two salts in any given quantity of pure water, -aI and RI tlie amounts in the same quantity of mater to n-hich a definite anionnt of alcohol has been added. If A/B = ;lr, L I J B I and -4,'L41= z it can be shown that the amounts left in solution after 72 cycles d l be - j j 1 ,
or
Letting P = the term inside the bracket we have for the amounts left in solution after 7 t cycles : .IY" and BY"
and for the anionnts obtained pure A ( I - Y") and B ( I - Y") (11) Expressions I and I1 have the same form, differing only by the difference between X and Y. Xt the first glance it is clear that the difference between -2- and y,must be very much greater than the difference between x and y for the second expression to compare favorably in results with the first, even supposing that the
two cycles involved the same amount of work. For KC1 and NaCl it was found that nearly one-half the total amount of salt was purified at each cycle when crystallizing between 2 5 " and 80". For the same salts at 2 j " and using forty percent alcohol, a little more than one-thirteenth can be purified per cycle. With sodium chlorid and sodium nitrate the difference is even greater, the rate being about three-fourths per cycle for the two temperatures and one-fourteenth for the alcohol method. I t seems probable that precipitation with alcohol could be employed profitably in very few cases, possibly when potassium iodid was one of the salts. Covnell University
