PRECIPITATION O F SALTS
BY H. A . BATHRICK
It has been shown that the experiments of Gkrardin' and of Bodlander' on the precipitation of salts from aqueous solution by alcohol can be represented by an equation of the form (x+A)y"=C. where x and y denote respectively the quantities of alcohol and of salt in a constant quantity of water'. Though the agreement between the values calculated from the formulas and those found by direct measurement was satisfactory on the whole, there were discrepancies ; especially in the solutions rich in alcohol. At the request of Mr. Bancroft I have made some measurements of the solubilities of several salts in aqueous alcohol of different strengths. As it is not easy to determine the amount of alcohol in the saturated solution directly I have avoided this by using aqueous alcohols of known percentage compositions Py weight and working in closed vessels4. I n this way all that was necessary for a complete analysis was to evaporate a weighed quantity of the solution to dryness and weigh the residue. The chief errors of this method are that the aqueous alcohol may change in composition by absorbing moisture or by dissolving solid matter from the glass bottles in which the mixtures are kept and that some of the liquid may evaporate before the solutions become saturated. T h e first difficulty is obviated by using bottles which have been thoroughly treated with steam ; by making up relatively small quantities of each mixture so that it may not stand in the bottles very long ; and by keeping the bottles carefully stoppered except when in use. I n spite of these precautions --
'Ann. chim. phys. (4)5, 129 (1865). ?Zeit. phys. Chem. 7,308 (1891). ' 3Bancroft. Jour. Phys. Chem. I , 33 (1896). 4Cf. Nicol. Phil: Mag. ( 5 ) 31, 374 (1891).
N.A. Bathrick there are one or two cases where the large error shows that a change in the solution has taken place. I t was not thought worth while to repeat these isolated experiments in order to get more accurate results. I t must not be thought that this conclusion was drawn because the results did not agree with those calculated from the formula. That is, of course, not permissible. T h e conclusion was based on the fact that one or two observations when plotted did not lie on the empirical curve drawn through the points determined. It would have been a good plan to have tested the aqueous alcohol occasionally with the refractometer but this was not done. T h e second difficulty is not a serious one and can be eliminated by repeating the experiment. T h e mixtures of aqueous alcohol were put in carefully stoppered flasks together with a large excess of solid salt and the whole left twenty-four hours in an Ostwald thermostat. A t t h e end of this time the solutions were analyzed by evaporation. Except in the case of ammonium chlorid, this determination is accurate to within one per cent. The values for the amount of salt in a gram of solution are probably accurate to within two milligrams. T h e values for salt in a hundred grams of water have, in addition, the error due to the composition of the aqueous alcohol, in most cases a very small one. I have made determinations at 30' and at 40Owith aqueous alcohol and also two series with aqueous acetone at 40'. T h e results are given in Tables I-X. I n the first column are the percentages by weight of water in the aqueous alcohol or aqueous acetone. I n the second and third columns are the values for grams of salt in one gram of solution as calculated and as found. I have thought it bet- . ter to tabulate the results in this form because these are the values given directly by analysis. T h e letters x and y in the formulas denote grams of alcohol and grams of salt in one gram of water, y in all cases referring to the salt. Where two formulas are given in one table, the second refers to the data below the dotted line. T h e agreement is most satisfactory for all strengths of aqueous alcohol. T h e values of the exponential factors are the same that were used in describing the results of Bodlander and of Ggrardin, confirming the assumption that t h h term is independent of the temperature. T h e agreement between the term A in my results and in those of Gerardin is not'very good ; but this is due to experimental
P?*gcipitatz'oii of Salts
I59
error as he makes the solubility of potassium chlorid in pure water both at 30' and 40' about ten milli'grams less per gram of solution than I have found it. I have made measurements of the solubilities in aqueous acetone only with potassium and sodium nitrates because the corresponding chlorids give two liquid phases at 40'. At a lit-
.
0.288 0.261 0.241 0.216 0.178 0 . '45 0. I 23
0.291 0.256
100.00
91.72 83. IO 74.05 65.58 54.13 45.67 34.96 24.39 12.05
0.227 0.212
0.177 0. I45
0.121
1
1
0.092 0.062 0.028
0.088
0.060 0.028
TABLEI1 NaCl at 30'
%H,O
~
1
100.00
94.72 91.72 83. I O 74.05 54.13 45.67 34.96 24-39 12.05
1
y calc. 0.267 0.245
1
y found
I
log c
0.246
0.329-3
0.048 0.029
0.875-2 0.945-2
0.176 0.152
0.052 0.029
H. A. Bathrick
I 60
~_ 100.00 ___ -~ ~ 0.284
94.72
0.280 0.253 0.232 0.199 0.161 0.135
I
0.253 0.232 0.198 0.172 0.135 0.108
I
0.100
0.276-2 0.288-2 0.290-2 0.296-2 0.248-2 6.291-2 0.203-2
- - - - - - - - - - - - - - - - - - - - - - - -. - - - - - - - - -
I
0.064
0.064
0.013 0.005
0.004
0.348-1 0.355-1 0.353-1 0.260-1
TABLEI V KNO, at 30' Zog C=0.780-2 _
_
_
-
~
zag
y calc. 100.00
91.72 83. I O 74.05 65 * 58 54. I 3 45.67 34.96 24.39 12.05
0.315 0.237 0.182 0. I35
0.313 0.244 0.183 0.131
0 . IO2
0. I 0 2
0.067 0.047
0.065 0.043 0.026 0.013 0.004
0.027
0.013 0.004
c
0.776-2 0.798-2 0.786-2 0.758-2 .0.781-2 0.762-2 0.725-2 0.745-2 0.746-2 0.742-2
Prec$itation of Salts
161
.absolute. By changing both A and ?z slightly it might be possible to obtain greater accuracy in the mathematical expression. A t present we are unable to calculate any of the constants in the
TABLEV NaCl at 40’ (X+O.Z)
(x+
3/“5’c,
0.2jf.?’=
C,=0.345-3 log C2=0. 080-1 [OK
c,
y found
y calc. -_
.
~~
0.269 ‘0.248 0.238 0.208
100.00
94.72 92.05 83.18 73.54 64-91 55.46
-- -----
69 0.249 0.239 0.205
- --- - --- -
- - --- - -- ---
0.ogs 0.061 0.038
0.093 0.062 0.038
0.008
0.01 I
~
0,343-3 0.356-3 0.360-3 0.3 18-3 0.349-3 0.345-3 0.323-3
0.151 0.124
- - -- - - - - - - -
c
~~~
0.2
0.151 0.125
45.71 34.75 25.95 10.35
log .
0.040-1 0.097-1 0.098-1 0.311-1
TABLEVI KC1 at 40’ log C,-o.go0-2 log C,= o 4 3 0-1
(x+o.22)y”=C1 ( x 0.22 jy =C,
+
y calc. 0.296 0.267 0.245 0.211
0.178 0.146 0. I 16 0.075 0.04 I 0.015 0.006
~
y found 0.295 0.264 0.250 0.216 0. I79 0,147 0.116 0.076 0.039 0.016 0.005
1
1
(08
c
0.396-2 0 389-2 0.426-2 0.429-2 0.404-2 0.414-2 0.398-2
H. A. Bathrick
I 62
formula and until we can do that, the constants as given in this paper can be considered only as first approximations. This inaccuracy does not interfere in any way with the conclusions drawn in regard to n and A . As long as the equation describing the facts remains of the same general form, the value for A will be a function of the solvent, the salt and the temperature and not of the precipitating agent, provided the concentrations are expressed in grams,
TABLEVI1 KNO, at 40' ( ~ + o . z ) y ~ ~ = log C C=o.opo-~ ~~~
%KO
I
I
y calc.
l
1
,
yfound
100.00
94-72 9p.74 83.04 74.46 65.01 55.99 45.05 34.91 23.55 11.55
dog
c
__
, 0.396 0.340
l
0.034-1 0.0400.055-1
1
0.046- I 0.039-1 0.036-1 0.039-1 0,049-1 0.047-1 0,139-1
0.392 0.340 0.320
0.250
0.245 0.192
0. I94
0.104 0.068 0.041
0.143 0.104 0.067 0.042
0.020
0.020
0.005
0.006
I
TABLEVI11 NaNO, at 40' (x+0.6)yZ-C, dog C=0.820--1
3' calc. 100.00
91.78 82.56 74.01 63.98 57.22 44.74 34.90 23.01
12.81
0.512 0.473 0.427 0.382 0.325 0.286 0.212
0.153 0.086 0.037
I
'
1
y found 0.51 I 0.476 0.423 0.38 I 0.326 0.288 0.213 0.753 0.086 0.040
dog C 0.8 I 6--I
1
%
0.830-1 0.807-1 0.8 18-1 0.822-1 0.827-1 0.824-1 0.820-1
Pvecijifation of Salts
163
T h e value of n will also be independent of the temperature within the present limits. Nicol' has made some measurements on the solubilities of mixed salts using the chlorids and nitrates of sodium and potassium. His experiments were carried out at 20' while my
TABLEI X Acetone : KNO, at 40' log CI=0.96o-z log C,= 0.620-r
(x+o.z)J=C, ( x 0.2 )y= C,
+~
_
_
~
31calc.
~~ ~
~
y found
log I
91.53 83. '9 74.81 65.71 55.89 46. I O
0.403 0.338 0.284 0.236 0.191 0.145 0.106
24.03 12.38
0.067 0.029 0.007
100.00
-.
l
' ~
~
'
0.339 0.280 0.237 0.198 0.145 0.106 ,
1 1
I
0.067 0.029 0.007
c
- -- ..
0.919-2 0.962-2 0.944-2 0.965-2 0.008-1 0.960~2 0.957-2
- --- - - ----
1
0,623-1 0.621-1 0.6 I 7-- I
TABLEX Acetone : NaNO, at 40' 6)y3= C, log C,= 0.830--I (x+o.6)y"=C2 log C2=0.r70
(x
+
0.
.~ -
log
c .
100.00
91.53 83.19 74.81 65.71 55.89 46. I O
0.511 0.47 7 0.440 0.402 0.357 0.306 0.251
0.835-1 0.831-1 0.823-1 0.8 15-1 0.888-1 0.894-1 0.804-1 --
-----
0.169 I
Phil. Mag. (5) 31, 369 (1891).
0.098 0.031
~
0.161 0.173
.
H. A . Bathrick
164
determinations were made at 30' and at 40'. so that the same constants can not be used in the two sets of experiments. By making a suitable correction for the difference in temperature it should be possible to calculate Nicol's data. T h e constant A in my experiments had the value of 0 . 2 for sodium chlorid at 30' and 40'. W e shall not be far wrong if we assume the same value for 20'. The value of the same constant for potassium nitrate was 0.18 at 30' and 0 . 2 0 at 40' so that 0.16 seems a plausible value at 20' and, by the same reasoning, the most probable value of this constant for potassium chlorid is 0.18. With sodium nitrate, the question is a more difficult one as there are measurements only for 40'. Reducing this vaIue in about the same ratio as in the other two cases we have 0.5 as the first approximation. Nicol's experiments have been calb
TABLE XI
TABLE XI1
KC1 at
KNO, at
20'
x=g. k C l y = g . KNO, in IOO g. H,O. (X ~ 6 ) ~y' ( 18)=C, log c,=52.350
+
+
20'
x=g. KC1y=g. KNO, in IOO g. H,O. (x+16) (y+r8)=C2 log c2=7.950 y calc.
0.0
5.6 16.8 19.0
34.5 34.2 33.4 33.3
34.5 34.2 33.4 32.9
0.0
8.3 16.6 24.9 31.1 32.9
y
found
30.6 25.8
31.1 25.7
22.7
22.2 20.2 19. I
20.4
19.1 18.7
19.0
a l a t e d using these values and the results are given in Tables XI-XVI. T h e letters x and y denote grams of the salts in one hundred grams of water instead of one gram as in my own experiments so that the constant A is one hundred times the values first deduced. T h e general equation used has the form ( x + A ) (y+B)"=C as has been already pointed out by Bancroft. T h e agreement between the calculated and the found values is excellent when the common ion is the cation. T h e results of the precipitation of potassium chlorid by sodium chlorid are less satis-
Pveci9itation of Salts
I 65,
factory and it seems almost as if the variations were not due simply to experimental error. I t is unsafe, however to base such a conclusion on the evidence now before us, more especially since the reverse precipitation can be expressed very accurately. Bodlander determined the solubility .of potassium nitrate at 20.5' in solutions containing varying amounts of potassium chlorid and Bancroft has shown that these results can be described by the general formula for this case making use of the constants obtained from the precipitation of the same salts by alcohol. Since the limiting constant A in
TABLE XI11 NaCl at
TABLE XIV NaNO, at
20'
x=g. NaCl J/=g. NaNO, in IOO g. H,O (.x+50)'"( y+ zo)=C, log C,=20.680
I
20'
x=g. NaCl y-g, NaNO, in IOO g. H,O (x$50) (y ~o)'.'= C, log z37
+
c,=$f.
_-
~
~
I y calc.
x
_ __
_
~yfound
-
0.0
14.2 28.3 42.5 54.5
1
36.7 32.2 29.4' 27.4 24.9
35.9 32.8 29.8 26.9 26.0
19.5 26.0
TABLE XV NaCl at
I
61.7 56.7
TABLE
KCl at
20'
x=g. NaClj'=g. KC1 in IOO g. H,O (x4-I@'( y 2 0 ) =C,
+
XVI 20'
x=g. NaClyL-g. KC1 in IOO g. H,O (x+ Is) ( y s 2 0jzs=C2 log C2=5.600 ---_
_
x
35.9 34.4 32.7 31.3 30.7
60.5 54.5
I
_
~
_
1 y calc.
1
_
_
_
I
found
I 0.0
6.5 13.0 19.5 30.7
1
34.7 28.3 24.0 20.8 16.7
34.5 29.7 24.7 20.4 14.0~
~
H. A. Bathrick
I 66
Bodlander's results was not the same as in mine, it has seemed worth while to tabulate this set of experiments using the same constants throughout that were used for the corresponding table in Nicol's experiments. This has been done and the results are given in Table XVII.
TABLFXVII KN0,at 20.5' x=g.KCl y=g. KNO, in roo g. H,o ( x 16) (y 15 )4= C,
+
~.
+
, x
1
0.0
5.4 8.9 1 14.~1 17.7 23.3 1 26.6 I 30.3 '
~~
ycalc. jyfound 31.2 27.7 26.0 24.0 22.7 21.3 20.5 19.9
31.3 27.7 25.6 23.2
.
22. I 21.0
20.5
20.4
As will be seen, this formula describes the facts about as well as the slightly different one used by Bancroft. This brings out very clearly the difficulty in obtaining really accurate values for the so-called liriiiting constants A and B. The experimental error must be reduced far below its present value before one can hope to determine these values inside of ten per cent. I t will be noticed that two sets of equations are necessary to express the results when there are two salts in the solution. This will not surprise any one because one salt is splid phase in the system described by one equation and the other in the system described by the other equation and it has been clearly understood for ten years that the solubility curve has a break when there is a change in the nature of the solid phase in respect to which the solution is saturated. I t is true that this has usually been applied to systems with two components where the .temperature changes ; but 1
u
the two cases are analogous since both are monovariant systems'. There are also needed two equations to express the solubility of a salt in aqueous alcohol of varying strengths. T h e solid phase remains the same, but Bancroft has pointed out that the liquid phase does not and that there must be a sudden change at some point from water as solvent to alcohol as solvent. That this actually takes place can best be seen from a diagram. In Fig. I are the experimental data for the system, sodium chlorid, sodium nitrate and water at z o o , and for the systeiii, sodium chlorid, alcoholand water at 30'. T h e abscissae are the logarithms of the grams of sodium chlorid in one hundred granis of water. T h e ordinates are logarithms of grams of sodium nitrate or grams of alcohol in one hundred granis of water. In order to keep the diagram within reasonable dimensions the scale for the alcohol concentrations is only one-half that of the sodium chlorid and sodium nitrate concentrations. Along AB sodium chlorid is solid phase and along BC sodium nitrate, water being solvent along the whole length of the curve. There is a distinct break at B where the solute changes, in respect to which the solution is saturated. Along the whole of the curve A,B,C, sodium chlorid is solid phase ; but there is a break at B, just as distinctly as at B. Since there is no change in the solid phase, there must be a change in the solvent to account for the break. Along A,B, water is solvent and alcohol along BC. There is still a word to be said about the expression for the precipitation of one salt by another : (x+A),(y+B)"= C. Since two equations are needed, this involves six constants and it niight well be urged that any one could devise two equations each with four constants which would represent ten observations with almost any required degree of accuracy. This is perfectly true ; but the point is whether the equations used come under that head. T h e most conspicuous feature about the constants in a purely empirical formula is that they apply only to the cases for which they are deduced. This is not true here. T h e limiting constant A is the same whether the salt is precipitated by alcohol, by acetone or by another salt having __ _
~
_
_
~
'Prof. Trevor uses the terms nonvariant, monovariant and divariant to denote systems containing 1 z t 2 , I ~ + Iand 11 phases.
168
H. .4. Bathrick
FIG. I.
Prec@itation of Salts
*
169
either the anion or the cation in common with the first. I f we have determined the quantitative relations when the two salts are precipitated by alcohol, only one determination is needed to enable us fo describe the way in which each of the salts will precipitate the other. T h e single determination is, of course, that of the solution saturated in respect to both salts. W e can go further. If the exponential factor proves to be independent of the temperature, only one determination will be necessary in order to predict the mutual solubilities of two salts a t all temperatures provided we have already studied the behavior of those salts in aqueous alcohol at the same temperature. I n one sense the formulas used in the paper are empirical, because we cannot deduce them at present ; but there seems to be no reason to suppose that they are really empirical which would mean that they could never be deduced. T h e exponential factors in the ordinary Mass Law applications would have been empirical if they had been discovered before Dalton’s atomic theory had been promulgated and accepted. T h e results of this investigation are : I. T h e solubilities of salts in aqueous alcohol or acetone can be represented by the equation : (x+ A)y”=C. where J/ refers to the salt, x to the alcohol or acetone. 2. T h e factor 7z is apparently independent of the temperature. 3. T h e term A is a function of the salt, the solvent and the temperature. 4.,It is not a function of x if x be expressed in grams. 4a. If x be expressed in reacting weights, the product of A into the reacting weight is independent of the nature of the substance denoted by x.
Harvard University ;JZI& r , r895.
