INDUSTRIAL A N D ENGINEERING CHEMISTRY
150
Vol. 19, K O . 1
Standardization of Titanous Sulfate Solutions’ By William M . Thornton, Jr., and Arthur E. Wood DEPARTMENT OF CHEMISTRY, THE JOHNSHOPKISS UNIVERSITY, BALTIMORE, MD.
ALTS of trivalent titanium are among the most powerful the substance used. With p-nitroaniline some extraneous reducing agents which have been proposed for analytical oxidation occurred, but by means of a blank experiment i t work, and their use in volumetric analysis is becoming would be possible to determine the extent of such oxidation more general for both organic and inorganic substances of and to correct for it. The values obtained against ferrous many kinds. As a result, a good deal of interest has been ammonium sulfate would then be correct and this salt, if taken in finding simple and accurate methods for standardiz- pure, could be the standard for such analyses as well as for ing solutions of titanous salts. widely different ones. I n other words, an absolute rather Knecht2J in 1903 suggested as a standard a solution of a than an empirical standard may thus be used. ferric salt of known strength, and many other workers have Thornton and Chapman12 used ferrous ammonium sulfate used various ferric compounds. Knecht stated that, al- which had been prepared by dissolving in water and prethough ferric alum might conveniently be used, its purity cipitating with alcohol. A known sample was titrated just couldunot always be relied on. He therefore preferred ferrous to the end point with permanganate which, in turn, had been s t a n d a r d i zed against Buammonium sulfate of known reau of Standards sodium concentration oxidized with oxalate. The solution was nitric acid, or preferably Titanous sulfate and titanous chloride are among the boiled, cooled, and titrated with permanganate.4 Atackj most useful reagents for quantitative analysis by rewith titanous chloride. Anmentions “specially pure” duction. other sample was titrated ferrous ammonium sulfate Some modifications of the apparatus of Thornton with the titanium solution as a standard, but states and Chapman for the storage and use of titanous sulfate without first oxidizing with that it is difficult to obtain are discussed, the degree of stability of the solution permanganate. This gave and keep a reliable supply thus stored is indicated, and the suitability of potasthe data necessary for calof this salt, guaranteed samsium thiocyanate as an indicator is shown. culating the value of the tiples sometimes containing As a means of standardizing the titanous salts a solutanium solution in terms of 1per cent less than the theotion of ferrous ammonium sulfate, previously oxidized either the ferrous ammoretical quantity of iron.6 by potassium permanganate, has been suggested. nium sulfate or the sodium Efforts have been made to As this method has been unfavorably criticized, several oxalate. The first titration find other substances which supposedly high-grade samples of this salt were purw i t h t i t a n i u m gives the might serve as standards for chased in the open market and tested. v a l u e i n terms of ferrous t i t a n o u s salts, either for Uncertainty as to the purity of the ferrous amammonium sulfate. Corg e n e r a l use or for special monium sulfate of commerce led to the examination of r e c t i n g this titer by subpurposes. Thus Rhead’ for other materials. Sibley iron ore, as furnished by the tracting the small quantity copper analysis standardized Bureau of Standards with certified analysis, was found used in the second titration his solution with recrystalto be a satisfactory standard. and its use for this purgives the value in terms of lized copper sulfate. Radlpose is recommended. sodium oxalate. The values berger and Siegmund* for calculated against the two sugar analysis used copper s t a n d a r d s checked very s u l f a t e whose value had been determined electrolytically, AtackIg for the analysis closely. This method can be regarded as strictly accurate, of various substances, standardized against methylene blue, however, only when the ferrous ammonium sulfate is free from which he proposed to evaluate by means of potassium chlo- basic salts. Otherwise the titration showing the quantity of ferric iron present would be too low, as the basic ferric salts rates5 For the analysis of aromatic nitro compounds (and this is do not dissolve in cold dilute sulfuric acid readily and would applicable to other organic compounds which may be an- thus be likely to escape determination, in part a t least. Hendrixson and Verbeck13 found the end point electroalyzed by the same technic )EnglishIoand Callan and Henderfionl1 advised p-nitroaniline as a standard. The method metrically when the titanium solution was titrated against used, however, makes this an empirical standard, and the either permanganate or dichromate, directly or by means of a fact that English found his results to differ slightly from ferric salt solution, but in no case do they give the primary those he obtained when he standardized with ferrous am- standard. Kolthoff and TomicekI4 mentioned as standards monium sulfate should not be construed as an objection to potassium dichromate, potassium ferricyanide, potassium the use of ferrous ammonium sulfate as a standard. The iodate, potassium bromate, and ferric alum. They tried process of standardization differed in technic depending upon all except the halogen salts in their electrometric titrations. Only the ferric alum seems to be generally applicable as a 1 Received June 1, 1926. standard. The other two, being colored solutions, could not * Bey.. 86, 1549 (1903). a J . SOC.Dyers Colou~ists,19, 169 (1903). well be used where the end point is to be determined by a 6 Knecht and Hibbert, “New Reduction Methods in Volumetric color change rather than electrometrically. Moreover, Analysis,” p. 67 (1925). as they showed, the ferric alum, in order to become a satis6 J . SOC.Dyers Colourists. 29, 9 (1913). factory standard, should be dried under definite vapor presa Ibid., 81, 203 (1915).
S
7
J . Chem. SOC.(London),89, 1491 (1906).
* 0csterr.-ungar. 2. Zuckerind. Landw., 42,
AnaZysf, S8, 99 (1913). 10 THISJOURNAL, 12, 994 (1920). 11 J . SOC. Chcm. I n d . , 41, 157 (1922). 9
34 (1913).
J . A m . Chem. SOL., 43, 91 (1921). Ibid., 44, 2382 (1922). 14 Rec. trau. chim., 43, 775 (1924); 2. anorg. allgcm. Chem., 160, 157 (1926). I*
1J
January, 1927
I-VD USTRIAL A N D ENGINEERING CHEMISTRY
sure conditions. Zintl and Rauch15 suggested that dichromate is not satisfactory for electrometric titrations if the titanous chloride is strictly pure but that ferric salts or copper salts are satisfactory. For titrations of bismuth they showed that the titanium solution must be standardized against bismuth. Although Knecht and others have shown that ferrous ammonium sulfate oxidized with permanganate is a satisfactory standard, provided it is pure, Atack has pointed out that its purity cannot be assumed. It seemed worth while, therefore, to test this salt obtained in American markets for its suitability as a primary standard for titanium solutions, and, if it should not prore satisfactory, to try to find some substance which would be. Apparatus
The apparatus (Figure 1) was in general the same as that used by Thornton and Chapman.12 The buret, B , was connected through a side arm to a glass tube leading from the outlet of the stock bottle, S, and having a stopcock, E , at its lower end. Connection with the side arm of the buret was made by a short rubber tube, J , which brought the ends of the two glass tubes together until they touched. The stock bottle was elevated a little more than 4 feet above the work table. Its top was closed with a 2-hole rubher stopper, through which passed two narrow glass tubes, one leading through a 1-hole rubber stopper in the top of the buret, the other to a Kipp generator, by means of which the titanium solution in the system was kept under an atmosphere of hydrogen a t a pressure of about 12 inches. The titanous sulfate, approximately 0.05 X, was charged into the stock bottle until it was almost full, connections were made with buret and Kipp, and the buret was filled. The buret was then emptied and the stock bottle and buret were swept for about an hour with hydrogen to remove air as completely as possible. The solution was then admitted into the buret again. After standing a day or two the sweeping was repeated for about 15 minutes. The apparatus was then ready for use. The Thornton and Chapman apparatus was modified slightly in order to keep the buret more perfectly clean and to keep the 2-way stopcock buret from leaking in either direction when used under a pressure of 4 or 5 feet of water. As the buret cannot be cleaned once the apparatus is assembled, a filter, G, of glass wool was introduced between the Kipp and the stock bottle. It consisted of an enlargement, about 16 em. long and 1.5 em. in diameter in the glass tube connecting the generator and the stock bottle, packed with glass wool. This simple device kept the buret so clean that a perfect meniscus was maintained throughout the period of the experiments. At first no stopcock was used a t E , but the rubber tube, J, was about 10 em. long and the ends of the glass tubes were about 5 cm. apart. A screw clamp controlled the admission of the solution into the buret from the stock bottle. This device was entirely successful in preventing any leakage into the buret, but, owing to an unforeseen difficulty, this part of the apparatus was modified by using an ordinary buret with a side tube sealed in just above the 1-way stopcock (Figure 1). Special care was taken to make sure that the stopcock, E , was tight under the pressure used, which cannot be assumed without careful testing. This change in the apparatus seemed to overcome the difficulty so long as the apparatus was in daily use. After it had stood unused for several days the trouble reappeared but to a somewhat less degree. The trouble referred to was that practically every day the second titration ran higher than the one which preceded Z
anorg. alLgern Chem , 146, 281, 291 (1925)
151
it or the one which followed it if samples of the same size were used for all three. After the first titration that portion of the titanium solution which had stood for some time in contact with the rubber tubing was drawn into the buret and used for the second titration. Until the apparatus was changed, standing overnight was sufficient to cause the second result to be high. Afterward the effect was not noticeable unless the apparatus had been unused for a longer period. I n an attempt to minimize the possibility of oxidation of any of the titanium solution by penetration of the oxygen of the air through the rubber, the tubing was thoroughly coated with Valspar varnish in the second set-up. This could not very well be done in the first set-up because of the screw clamp. This may explain the fact that less trouble was had with the solution after the second set-up. If the trouble was due to a reaction between the rubber and the titanium solution it would seem that the solution in the stock bottle should have shown a greater effect, as it was always in contact with a rubber stopper a t the outlet a t the bottom of the bottle. This solution, however, changed in value only slightly during three months. Great care was taken to tie in all rubber stoppers securely with fine wire and not only to varnish or shellac the rubber stoppers but also to run the film over on to the glass. The rubber tubing a t J was treated in the same way. These
Figure 1
precautions may have contributed to the permanence of the titanium solution. Moreover, before the investigation of various substances as standards had been begun, the inlet tube for carrying carbon dioxide into the titration flask was lengthened so that it dipped deep into the solution being analyzed. The object was to make the preliminary sweeping of the flask with carbon dioxide more rapid and thorough and to add the stirring effect of the stream of gas to the rotary motion of the flask for thorough stirring during the titration process. This shortened the time of preliminary sweeping to 5 minutes with no apparent loss of accuracy.
INDUSTRIAL A N D ENGYlnrEERING CHEMISTRY
152
Indicator
Potassium thiocyanate has been very commonly used by workers using titanium as a volumetric reagent. Some substances, such as dyes, are their own indicators. Xnecht first used potassium thiocyanate as an outside indicator, but soon found that equally accurate results were obtained by adding the indicator to the test solution.16 However, Atack states that both potassium and ammonium thiocyanates of commerce are occasionally unreliable and he prefers methylene blue. Also Stokes and Cain" have shown that thiocyanates sometimes spontaneously decompose and that some of the decomposition products have a bleaching action on ferric thiocyanate, thus seriously interfering with the colorimetric determination of iron. With these criticisms in mind, tests were made to determine the end point electrometrically simultaneously with the color end point and independently of the indicator. The Roberts titration outfit, manufactured by Leeds and Northrup, was used (Figure 2). It consists essentially of a small calomel electrode, with a long capillary outlet tube dipping into the solution to be titrated, a platinum wire for the other electrode, and a simple potentiometer with slide wire and galvanometer. Two dry cells supplied the current. The outlet tube of the calomel cell was flushed frequently. Normal potassium chloride was used. At first the suspicion t h a t t h e thiocyanate did not give the correct end point seemed to be confirmed, but it was later shown t , h a t t h e difference in the electrometric end point when the indicator was present and when it was absent was due to the slowness with which equilibrium was reached in the absence of the t h i o c y a n a t e . When the titration was made without an indicator, but a t 35-45' C. instead of a t room temFigure 2 perature, the electrometric end Doint checked the color end point closely. The thiocyanate seemed to act as a catalyst to hasten the reduction, for the electrometric usually checked the color end point when they were determined simultaneously. The results of this study are shown in Table I. It would seem safe, then, to rely upon the correctness of the end point obtained with potassium thiocyanate. Any unfavorable action of the decomposition products on the ferric thiocyanate is so slight as to be negligible in oxidimetric work.
-7
E-
/@&
Iron Factor of Titanium Solution
The iron factor of the titanium solution was next determined. Solution B consisted of ferric alum (about 25 grams of the crystallized salt per liter) and 50 cc. of sulfuric acid (1:l). Any ferrous iron present was oxidized with 0.05 N permanganate, care being taken not to overstep the end point. About 0.2 cc. per liter was used. The solution was boiled, cooled, and allowed to stand 2 days. No sediment appeared. 16
17
J . SOC.Dyers Colourisfs, 24,68 (1908). J . Am. Chcm. Soc., 29, 409 (1907).
Vol. 19, No. 1
The soIution was thereafter kept in the dark in glass-stoppered bottles. Fifty-cubic centimeter samples were reduced with a Jones reductor, following essentially the method of Lundell,18 except that a shorter column of zinc, about 30 cm., was used. Two samples titrated with standard permanganate gave titers of 45.42 and 45.41 cc. after correcting for temperature, buret calibration, and reductor blank. The permanganate solution, which had been standardized against Bureau of Standards sodium oxalate, had an iron factor of 0.003203 gram per cubic centimeter. Using the titer 45.41, the iron content of the ferric alum solution is 2.909 grams per liter. This was confirmed by a gravimetric determination made by precipitation in platinum and gold with purified ammonia, using the precautions recommended by Allen and J o h n ~ t o n . ' ~ Table I-Electrometric
T i t r a t i o n s w i t h a n d w i t h o u t Indicator
I1
SOLUTION A=
SOLUTION Ba ~~
~
T I T A N O USULFATE S BLECTROMETRiC
KSCX cc. ---
KSCN cc.
cc.
KSCN cc.
23.62 5 1 1 1 1
...
24:07
... 23:65 23.65 23.64 23.65 23.70
...
Averag e / 23.65
23: 66
23.72 23.65 23.66: 23.71
I
...
23.66
ELECTROWETRIC
KSCN cc. cc. -1 1
23: 60
... ...
~
TITANOUS SULFATE
-
23.94 24.03
... ...
... 5 .. ...
26.77 26.79
2i:io
..... .
1 1
Using Not using KSCN KSCN cc. cc.
26.86 26.82 26:io
... 26:88
:
26 85
26:77b 26.768
...
... ...
... ... 24165 24.02 IIAverageI 26.78
I
26.80
26.87
25 cc. of ferric alum solution titrated in each experiment. b Run at 38-45' C. (without KSCN). Titers put in column 3 instead of column 4 because they check the values In columns 2 and 3 and are averaged with them. a
This gives the data for calculating the iron value of the titanium solution. Accepting as the most probable value (Table I) 26.78 cc. of the titanium solution as equivalent to 25 cc. of ferric alum (solution B), the iron factor of the titanous sulfate solution becomes (0'002909 2 5 ) = 0.0027156 gram per cc. 26.78
The permanganate solution was tested for iron and none found. Ferrous Ammonium Sulfate
Several samples of ferrous ammonium sulfate obtained in the open market were tested. All but one of these samples (C) were taken from freshly opened small packages and were used as they came from the bottles, except two lots which were coarsely crystalline. Care was taken to select the better appearing crystals. The procedure in preparing the samples was as follows: The sample was dissolved in 60 cc. of water containing 10 cc. of sulfuric acid ( 1 : l ) . The solution was oxidized with permanganate, care being taken not to overstep the end point, boiled 10 minutes, and cooled. Then 5 cc. of a 10 per cent solution of potassium thiocyanate were added as indicator. The solution was swept with a rapid stream of carbon dioxide for 5 minutes to remove air as completely as possible from the titration flask and titrated with the titanium solution, continuing the flow of carbon dioxide. The titanium was added dropwise, rapidly at first, the last cubic centimeter being added a t the rate of 6 to 8 drops per minute. TOavoid overstepping the end point it is necessary to allow the last two or three drops a minute or more each, as the reaction toward the end requires a little time. 1s
J. Am. Chem. Soc., 4S, 2620 (1923).
19
THISJOURNAL, 2, 196 (1910).
I N D U S T R I A L A N D ESGINEERING CHEMISTRY
January, 1927
Sample C was taken from a freshly opened package of an American made salt which had been on hand for a short time. Some of it was dissolved in water to which a little sulfuric acid had been added, and precipitated by filtering into alcohol. The crystals were dried at room temperature for three or four days, care being taken to exclude dust, and bottled until needed. The sample so treated is designated CC in Table 11. The results of the tests are given in Table 11. of Ferrous A m m o n i u m S u l f a t e
T a b l e 11-Titration BRAND
SAMPLE Gram
TITER cc.
IRON FOUND Gram
IRON CALCD. DIFFERENCES Gram Gram
0.7955 0.7969 0.7683 0.7937 0,7804 0.7975 0.7960 0.7978 0.7963 0.7978 0.7966 0.7961
41.53 41.90 39.90 41.21 41.10 41.97 41.84 41.93 41.56 41.58 41.72 41.65
0.1136 0.1138 0,1084 0.1119 0.1116 0.1140 0.1136 0.1139 0.1129 0.1129 0.1133 0.1132
0.1133 0.1138 0.1094 0.1130 0.1111 0.1136 0.1134 0.1136 0.1134 0.1136 0.1134 0.1134
cc -4
B C
D E
-
+O ,0003
+ O ,0003
-- 00.0011 0010 t
+o
t
0005
+ O . 0004
+o. 0002
+0.0003 -0.0005 0.0007
-0 . 0 0 0 2 -0.0001
Sample CC gives exactly the same analysis as sample C. The results in Table I1 indicate that it is hardly safe to use as a primary standard a sample of ferrous ammonium sulfate taken at random from supposedly pure salts procurable in the open market. If the purity is to be tested the salt becomes a secondary rather than a primary standard and of such it is easy to find several. Ferric alum treated as described earlier in this article is probably as good as anything if a secondary standard is satisfactory.
As we were not seeking a secondary standard, however, we next tried the best brand of ferric oxide available on the market. The manufacturers claim that it is specially prepared by an elaborate process and is practically 100 per cent pure. The samples were thoroughly dried a t 115" C., dissolved in about 10 cc. of concentrated hydrochloric acid, and cooled. Then 10 cc. of sulfuric acid (1:1)were added and the volume was made up to about 75 cc. Next 5 cc. of thiocyanate indicator were added and the sample was titrated with the titanium solution. The results are given in Table 111.
SAMPLE Gram
of Ferric Oxide
IRON T I ~ ( S O ~ ) S FOUND cc. Gram
0.1531 0.1525 0.1527
39.33 39.17 39.20
T a b l e IV-Permanence DATE
0.1067 0.1062 0.1063
series of tests showing the degree of permanence of the titanium solution over a period of 3 months. Sibley Iron Ore
Sibley iron ore, the reliability of which is probably no less than that of most primary standards, was tested next. It was thoroughly dried a t 100' C. A carefully weighed sample (about 1.5 grams) was dissolved in about 10 cc. of concentrated hydrochloric acid, about 3 drops of hydrofluoric acid being added a t the end to dissolve the silica. This solution was transferred to a Pyrex dish, 25 cc. of sulfuric acid (1 :1) were added, and the hydrochloric acid was evaporated off on the steam bath. The residue was taken up with water, heating if necessary, cooled, oxidized with permanganate, and boiled 10 minutes. This, when cool, was transferred to a 500-cc. volumetric flask and made up to the mark. Aliquot parts of 50 cc. were taken a t once. To each of these were added 10 cc. of sulfuric acid (1: 1) and, just before titrating, 5 cc. of thiocyanate indicator. After sweeping with carbon dioxide, the sample was titrated with titanium in an atmosphere of carbon dioxide. The results are given in Table V. T a b l e V-Titration SAMPLE Gram 0.15506 0.15504 0.15500
of S i b l e y I r o n Ore IRON
TITANOUS SULFATE FOUND Cc.
39.34 39.32 39.30 39.29 39.30 39.32
IRON CALCD. DIFFERENCE Gram Gram
Av.. Cc.
Gram
39.33
0.10664
0.10638
39.29
0.10654
0.10636
0.0001S
39.31
0.10651a
0.10633
0.00018
0.00026
-
a In calculating this value a new factor for the titanium solution (1 cc. = 0.0027096 gram iron) was used.
Ferric Oxide
T a b l e 111-Titration
153
IRON CALCD. Gram 0.1071 0.1066 0.1068
DIFFERENCE Gram
-0.0004 -0 . 0 0 0 4 - 0.0005
of T i t a n o u s S u l f a t e S o l u t i o n a TITANOUS SULFATE A v . . Cc cc.
January 2 9
26.77 26.79 2c:is 26.77 26.79 26:iS February 26 26.81 26,80 ?6:81 26,81 March 18 26.82 2i:sz April 29 26.83 26.84 26:84b 25 cc. of ferric alum (solution B) titrated in each experiment. b The difference between the extremes is 0.06 cc., or 0.22 per cent. February 4
(I
For calculating the iron content a new factor (1 cc. = 0.0027118 gram iron) was used for the titanium solution, as it changed a little during the period of about 5 weeks in which it had been in use. Table IV gives the results of a
The foregoing procedure was varied in the following manner: Silica was filtered off from the first sample shown in Table V after the ore had been dissolved (no hydrofluoric acid having been added in this case) and the paper was burned in platinum. Two drops of sulfuric acid (1 :1) and about 5 cc. of hydrofluoric acid were added and evaporated off in a radiatorz0 with every precaution. The residue was fused with potassium pyrosulfate. This was taken up with water and added to the filtrate, which was then evaporated with sulfuric acid. I n the last sample given in Table V the solution in the Pyrex dish was carried down only once to expel the hydrochloric acid instead of three or four times. The results indicate that the preparation of the sample of this particular ore may safely be shortened by not removing the silica, provided i t is dissolved by the use of the three drops of hydrofluoric acid, and by carrying down the evaporation only once to remove the hydrochloric acid. The process was further shortened in the last sample by transferring the solution directly from the Pyrex dish in which it was evaporated to the volumetric flask, water being then added until the flask was about two-thirds full and the permanganate for oxidation of the ferrous iron run into the flask directly, omitting the subsequent boiling. Great care is, of course, necessary not to overstep the end point. With these variations for shortening the process of getting the ore into solution and ready to titrate it is very little trouble to use it as a standard. Summary
With a carefully set up apparatus of proper design it is possible to keep a solution of titanous sulfate for a t least 3 months with very slight change in its iron value. This value should, however, be checked occasionally. Checking may probably be done most easily by keeping on hand a solution 20
Thornton, THISJOURNAL, 8, 418 (1911).
INDUSTRIAL AND ENGINEERING CHEMISTRY
154
of ferric alum, the exact iron value of which need not be known. Apparently the less rubber tubing used between the storage bottle and the buret the better. The cause of the harmful influence of the tubing has not been definitely determined, however. Potassium thiocyanate may be successfully used as an inside indicator, for the determination of iron a t least. From 1 to 10 cc. of a 10 per cent solution may be used, 5 cc. being enough. The end point is a little easier to determine when 5 cc. are used than when only 1 cc. is used. Ferrous ammonium sulfate bought in the open market cannot be relied upon to serve as a satisfactory primary standard
Vol. 19, KO. 1
for titanous sulfate solutions. The same is true of the ferric oxide tested in the experiments here discussed. Sibley iron ore as put out by the Bureau of Standards with analysis appears to be a reliable primary standard for titanous sulfate solutions. It may be prepared for titration without a great expenditure of time or effort. Ferric alum, its oxidation carefully made complete with permanganate, is a very satisfactory secondary standard. Even if another ultimate standard is used, a solution of ferric alum is convenient for occasionally checking the permanence of the titanous solution and quantitatively measuring any changes it may undergo, even though the exact iron value of the ferric alum is not known.
Applicability of the Indirect Method of Analysis to Determination of Sodium and Potassium in Soil Solutions’ By Ray E. Neidig and W. B. Bollen DEPARTMEST O F AGRICULTURAL CHEMISTRY,UNIVERSITYO F IDAHO,A N D AGRICULTURAL EXPERIMENTSTATION,Moscow, IDAHO
I
N THE study of alkali soils at the Idaho Agricultural
Experiment Station numerous determinations of sodium and potassium must be made. The gravimetric methods now in use are so time consuming as to be almost prohibitive where many determinations are required. The necessity for a simple and more rapid method led the writers to investigate the indirect method of calculating the amounts of sodium and potassium from the weights of their mixed chlorides and total chlorine. The indirect method of analysis has long been known, but, as CrookesZhas remarked, i t does not appear to possess the confidence of chemists and is rarely mentioned in published investigations. As to its reliability, Crookes states, “From a long list of analyses it is shown that the indirect method is in all cases equal in accuracy to the ordinary (platinochloride) separation, while in the matter of convenience and economy of time there is no comparison between them.” Earlier work on indirect methods of analysis is reviewed in a recent article by C ~ m e l l a . ~This author also introduces a graphical method based on arithmetical progression, and develops formulas permitting independent calculation of the constituents of a homogeneous binary salt mixture. Comparative data obtained by these and other formulas from several series of analyses made on knowp solutions of potassium chloride and sodium chloride are not concordant. Apparently the discrepancy is due, partly to factors calculated on obsolete atomic weights, and partly to calculation of potassium chloride independently of sodium chloride by the author’s method, or else to errors in transcribing. Independent calculation of the components of mixtures of two, or even more, homogeneous salts is possible with other formulas, and from the standpoint of error distribution this is preferable to the more convenient method of calculating one salt by difference. Development of F o r m u l a
Formulas for a two-salt mixture are readily derived as follows: 1 2
Received August 17,1926. “Select Methods in Chemical Analysis.’’ p. 20, Longmans, Green &
Co., 1886. 8 Ann. ckim. a p p l i c a f a , 15, 123 (1925); C. A . , 19, 3441 (1925).
L e t x = NaCl v = KC1 = (NaC1 KC1) G = total C1 a = 0.6066 = C1 factor of NaCl b = 0.4756 = C1 factor of KC1 Then x + y = s ax by = c From (1) y = s - x Substituting for y in ( 2 ) ,
,:
+
+
+
ax b(s-x) = c 2 l n - h )-, = r- - h s- - - \ -
C-0.4756s - c-0’4756s = 7.6336~- 3.6305s 0.6066-0.4756 0.1310 or NaCl = 7.6336 C1-3.6305 (NaC1 KC1) or Na = 3.0031 C1-1.4283’(NaCl.+ KC1)
c-bs
=
a-b
+
’
I n like manner it can be demonstrated that
+ KC1)-7.6336 C1 + KC1)-4.0030 C1
KC1 = 4.6306 (NaC1 or K = 2.4282 (NaC1
These formulas are essentially the same as those given by Crookes, except that the factors are based on atomic weights from the International Critical Tables. Inspection of the formulas shows that any errors made in the determination of total salts and chlorine are multiplied by the factors given. This may appear to be a serious defect, but granting a refinement of technic commensurate with the gravimetric determination of potassium the final errors in calculated results need not exceed *2 or 3 mg. By using N/35.46 silver nitrate solution, chlorine can be determined to within 0.1 mg., but allowing a range of error of *0.5 mg. for chlorine and * 1mg. for the weight of salts, the errors in calculated amounts of sodium and potassium would not exceed the values shown in Table I. This range of accuracy is satisfactory for our class of soils work, where the error in milligrams rather than in per cent is given first consideration. Errors of analysis in the same direction tend to compensate each other, while opposite deviations rapidly increase the errors in calculated amounts of bases. To insure tolerable errors it is therefore essential to avoid increase in weight of the purified salts by contamination with foreign matter or by incomplete drying. When one salt is absent, or present in very small amount, its calculated value may be negative. A negative value of not over 1 or 2 mg. may be taken as zero, while large negative values indicate a serious error in the analysis.
