FRACTIONAL PRECIPITATION FROM SOLUTIOK BY PHILIP BLACKMAN
If a substance be dissolved in a liquid and another used t o precipitate it, then more of the substance by weight can be precipitated from the solution by using the other liquid in portions than by employing it all in one precipitating operation. Let W = the weight of the dissolved substance, v1,v2 = the volumes of the precipitate and of the solvent respectively, s = the coefficient of solubility of the substance in the solvent, p = the coefficient of precipitability of the solute by the precipitant (i. e., the quantity precipitable by unit volume of the precipitating liquid). I. If the operation of precipitation be performed by using the total volume, vl, of the precipitating liquid, then, if w be the weight of the solute precipitated, W - w is the weight of the solute remaining, and
Hence :
11. If the precipitating process be carried out in 9% operations, employing each time the volume z , i v of the precipitant, then the successive weights, wl, w,,w 3 .. . . . . . .ut,, of the solute precipitated will be : w1 = vlp (W-Zu1) /?Z.V,S, w 2= ~ l p ( n r - ~ ~ l - ~ Z G ' 2 ) / n . v , s , w 3= vlp (W-W1-W2-W3) /n.v2s, . . - . . . . . . . . . .. . . . . . . *
w, = 7j p(q.-W
--.W
_-&3-.
. ....
. . . . -Wn) /?Z.V*S.
Fractiortal Precipitation jrowt Solution
437
Thus the total weight precipitated in the n operations
Consequently p (?”, a, + WZ + +. . . . . . . . . .) + w,I -+ . . . . . . . . . . ) + c1
(w,
zi’,
W$
T2S
Therefore :
+ w,-k + . . . . . . . . . .+
w,
‘io3
-”
we
= the total weight precipitated
Equation ( 2 ) , it will be observed, exceeds Equation the quantity
(I)
by
which proves the above statement. The preceding algebraic method of procedure (compare ‘‘ Solution : Fractional Extraction ” by the author in the Cheniical Xews, 93, 7 2 (1906)) is especially interesting in view of Ostwald’s statement in his The Scientific Foundations of Analytical Chemistry ” (English Translation, I 908 Edition, page 18) t o the effect that the solution of the problem requires the aid of the calculus. Hackitej Tecliiiical Imfztutc,
Lowdon, S.E . , Evglavd.
