ANALYTICAL CHEMISTRY
904 Tahle V. Effect of Omission of Weighting
Spx? SPXY SPY? bZSpr2 SP(U - Yr)z Degrees of freedoni l‘arianoe from regression
F b
Weighting Omitted Included 0.03691 5 4.69943 -0,2280437 - 30.49180 +1.41802 +198.32550 1,40851 197.84389 0.00751 0.481 61 2 2 0.00376 0.24081 822(~’) 383 (++) -6,48841 -8 . 1 7 7 s
EFFECT O F OMISSION OF WEIGHTING
Table V summarizes the values that. would have been obtained without) weighting. Xone of the numbers in this table are of the same order of magnitude until t’he next to last line. ThiP is because the sums of squares and products with weighting had coef?icient,s included n-hich ir-ere of an order of magnitude greater than unity. Omission of weighting has affected the estimate of the slope, b, b y less than 5%, or 1 kcal. in activation energy. If omission of weighting affect? the results by only 5Yo1one might wonder if the extra effort is north the bother. Hoxever, one can never be cert,ain that the results will not be off b y more. Sometimes physically impossible values are obtained. dn outstanding example of this occurred \Then one of the authors \vas fitting some creaming rate data to an exponential equation. This was done by transforming to logarithms of first differeiiws. The data ranged from zero to 151.9. When \r-eighting was neglected the asymptote was l4l.T1a physically impossible re.wlt, ciiice it’ was less than the last experimentally obsewetl value. l!?ie:i weighting was properly included, the asymptote wac: 159.G--a quite satisfactory value. Of much greater iniportance, however, is the eflect of omission of weighting upon the significance test. I n the above example, F
tlecreaced from 822 to 383 with corresponding drop in statistical odds from 800 to 1 down to 360 to 1. The t value in the above test decreased froin 8.35 to 3.82, with corresponding drop in odds from 830 t o 1 down to 50 to 1. I n neither of these cases was statistical significance entirely lost. However, cases may well occur when significance might be con~pletelylost. It might then be thought that, at any rate, the test will be on the conservative side. However, there is no way of knowing that this can be guaranteed. The test could be underconservative a s well as overconservativc. The object of carrying out a modern statistical significance tePt iq to be able to make the statement that the probability is 1e.s than a certain amount, a1that these results could have been obtained by chance alone. If, because of neglect of weighting, onr has to hedge by stating that probabilities are either less than CII greater than CY that these results could have been obtained b>chance alone, then why carry out any test a t all” Such a statement could be made a prtori without doing any work whatever. Therefore the relatively slight additional nuisance introduced by weighting may w l l be considered small cost for the peace of minil attained on knowing that the complicated computation. ai e rigorously correct and not subject to criticism. LITER4TURE CITED
(1) Birge, R. T., Phys. Ret).,40, 207-61 (1932).
(2) Daniel, Cuthbert, 116 Pinehurst d r e . , Yew I’ork 33, S . T., pr:vate communications. (3) Deming, W. E., ”Statistical rldjustrnent of Data,” Sew Torli, John Wiley 8i Sons, 1943. (4) Is-isher, R. rl., “Statistical Methods for Research Workers.” 11th ed., Edinburgh, Oliver and Boyd, 1950. ( 5 ) Villars, D. S., “Statistical Design arid iinalysis of Experiments for Development Research,” Sect. 8; 2 , p. 159 ff., Dubuque, Ion-a, William C. Brown Co., 1951. RECEIVED for review M a y 15, 1953. Accepted January 21, 1954. Presented before the Division of Physical and Inorganic Chemistry at the 123rd Meeting of the AMERICAS CHEMICAL SOCIETY, Los .4ngeles, Calif.
Dete rminat ion of Fluoride Procedure Based upon Diffusion of Hydrogen Fluoride LEON SINGER and W. D. ARMSTRONG Department o f Physiological Chemistry, University o f Minnesota, M i n n e a p o h , M i n n .
A
S.4LTSIB for small amounts of fluoride in many materials require separation of the fluoride from ions whlch interfere n ith fluoride determination by colorimetry (6, 7‘), titration ( I , 10, 12, I S ) , or fluorometry ( 1 1 , 1 4 ) . Isolation of fluoride from metal ions and from nonvolatile anions is usually accomplished bv the TTilIard-Winter procedure (15), or a modification of that procedure, wherein the fluoride is converted to fluosilicic acid and collected as such by steam distillation from QUIfuric or perchloiic acid solution. Conversion of fluoride to hydrogen fluoride by treatment of the .ample with a strong nonvolatile acid follo~r-edb ~collection . of the hydrogen fluoiide by distillation n ould furnish an obviously possible means for separation of fluoride from nonvolatile ions. Heretofore, this procedure has required the use of a platinum still (8, 9) or diffuqion cell ( 4 ) . Polyethylene is stated by Its manufacturers t o he inert to strong solution^ of hvdrofluoric acid u p to 60” C. and a still improvised from polyethylene bottles has been successfully used (3)for purification by distillation of concentrated hydrofluoric acid solutions. These facts suggested that polyethylene could hr used for the construction of a n nppa-
ratus for the quantitative evolution and collection of miall amounts of hydrogen fluoride. Tetrafluoroethylene (Teflon) has properties which probably would be superior to those of polyethylene for this purpose, but cannot easily be obbained in the desired forms because it cannot lie fabricated by injection molding. Through the use of readily nv:iilal)le forms of polyethylene a method for aiialysiG for fluoride h q e d upon diffusion of hydrogen fluoride has been devrloperl and applied to the determination of fluoride in aqueous solutions of ~odiunifluoride and in ached bone. The method has the advaiit:igr of simplicity and economy and a large number of qaniples can he carried forward concurrently by one operator. I t also appears that the new method does not exhibit a significant distillation blank, a factor which is important in the analysis for small amounts of fluoride. APPAR4TC‘S 4ND RE4GEYTS
The diffusion cell is a 2-ounce polyethylene bottle with pi screw cap of the Fame material (Schaar and Co., 754 West Lexing-
V O L U M E 2 6 , NO. 5, M A Y 1 9 5 4 ton St., Chicago, Ill.). The cap is forced nearly flush into a length of '/B-inch internal diameter brass tube and secured in place a i t h cement (Figure 1). I n this way the expansion of the cap as it is tightly screwed into place on the bottle is prevented, giving a closure of the bottle which withstands a t least 40 pounds of gas pressure. When necessary, irregularities in the rim of the bottle neck are removed by gentle abrasion with fine emery cloth. I n practice a bottle and cap are mated before use by inspection and tested for leak by firm compression of the bottle. The receivers for the hydrogen fluoride ( B , Figure 1) are made in large numbers from polyethylene sheets 3/32-in~h thick (American Agile Corp., P. 0. Box 168, Bedford, Ohio). The sheet is srored in rectangles of the indicated length and breadth and a depression approximately 1/32-inchdeep is cut a t the indicated position by use of a '/:-inch 2-fluted end mill in a drill press. After the receiver strips have been separated by a sharp knife or band saw a t the scored marks, transverse corrugations are cut, a3 shown in B in Figure 1, on the floor of the depression, by the use of a rotating rounded-head dental burr. The receiver strips are prepared for use by distributing 2 to 3 drops of alcohol over the roughed area followed by 0.1 ml. of approximately 2% sodiuni hydroxide solution. The alcohol is employed to facilitate spreading of the aqueous hydroxide solution which alone does not wet polyethylene. Finally, the strips are dried overnight in a desiccator charged with phosphorus pentoxide. The receiver strips are prepared as described in order to obtain a large surface area for distribution and retention of the sodium hydroxide used to vollect the hydrogen fluoride. The bottles and caps, prior to first use, and the receiver strips :ire washed, in order, x i t h an alcohol-ether mixture, water, concentrated perchloric acid, water, and redistilled water. The redistilled water used for all purposes in this work was prepared 1)y passing laboratory-distilled water through a n ion exchange column (La Motte Filtr-Ion), following which it was redistilled from borosilicate glass apparatus. The water was collected and stored in polyethylene bottles. A 1-liter Dem-ar type flask is filled to the top with water, which is then frozen. A well about 1.75 inches in diameter and 2 inches in depth is cut into the upper surface of the ice. This flask and it3 contents are kept in a deep-freeze cabinet when not in use. .I2-ml. glass syringe M ith a 3-inch length of narrowbore glass tube sealed to the nub. Hemostat forceps and heavy scissors are used for handling nnd cutting the receiver strips, .ilaboratory-type oven is regulated a t 50" C. Perchloric acid, 70%, is kept a t a temperature considerably helow 0" C. in a deep-freeze cabinet. Reagents and apparatus as required for the determination of fluoride in the solution prepared from the fluoride collected on the receiver strips. I n this work fluoride was titrated with thorium nitrate using the indicator of Bien ( 2 ) and was also deterniined fluorometrically (11).
905 thoroughly to ensure complete solution of the fluoride. A mechanical shaker is convenient for agitation of a large number of tube$. Titrate 1-ml. aliquots of the solution for fluoride by the method of Bien ( 2 ) or use appropriate aliquots for the fluorimetric (11) determination of fluoride. Solutions in the bottles were frozen and cold perchloric acid was employed in order to reduce the chance of loss of hydrogen fluoride before the bottle was capped. This procedure prevented loss of fluoride, added as aqueous sodium fluoride, even when a strong stream of air was blown into the bottle for 30 seconds after addition of the acid. RESULTS AND DISCUSSIOS
The reproducibility and precision of the results when the diffusion procedure was applied to the analysis for fluoride in sodiuni fluoride solutions and bone ash are shown in Table I. These result?, and all others reported in this paper, were obtained by determination of the fluoride content of 1-ml. aliquots from 10
t-$i 0. D.
an
-I2 7 rnm
PROCEDURE
Figure 1. Polyethylene Apparatus for Collection of Hydrogen Fluoride by Diffusion Tiansfer a measured volume, not in excess of 1 ml., of an aqupous solation of the sample to a diffusion bottle and permit the A . Cut-away view of assembled diffusion cell wlution to freeze by placing the bottle in a deep-freeze cabinet. 6. Receiver; right, detail of receiver C. Adapter m a d e from polyethylene tubing In the case of dry powders, cover the sample in the bottle with a 1. Length of brass tubing m a l l amount of Imter and freeze the water. The last point of 2. Polyethylene cap of hottle 4 procedure is employed as a precaution to prevent dislocation of 3. 4cidified sample aample particles onto the sides of the bottle by the disturbed air &-henthe acid is injected. Place the bottle in the ice &-ellin the Dewar flask and inaert through the neck of the bottle the adapter Table I. Analysis arid Recovery of Added Fluoride b?-Diffusion of made of polyethylene tubing shown as C in Hydrogen Fluoride Figure 1. This adapter prevents the neck of the s o . of Ba-1; from being wetted with acid a t the next step Fluoride Diffusion _ _Founii ~ _ by_ _ _ _ i n the procedure. With the svringe add 2 ml. oi Ireiii .\laterial .innlj-zetl Trials Titration" Fluorornet r p cold perchloric acid, remoye the adapter, insert a 1 S a F b (20 y 1: -. s o u g h t i lij 1!4,9S I 0 . 1 2 piepared receiver strip into the bottle as shown i n 1.5 1 9 86 & 0 . 2 8 y Figure 1, and close the bottle by firmly screwing 2 "Fluoride-free hone"c ( c ; F-) 5 0.000 0.0001i 0 0000' the cap into place. Carefully rotate the diffusion ( 2 results zeroi bottle so as to ensure that the bottom and sides of 3 "Fluoride free hone" ' 2 0 y Y 9 99.08 k 2.95 9 7 . 0 6 r 2.28 the bottle to a height of about 1 cm. are wetted ( % recovery nddrd F - I with acid. Place the bottle in the oven heated to 20 0 O i O t j =t 0 00287, 50' C. and allou it to remain for 20 hours. Y 0 0718 f 0 0033 Remove the receiver strip, cut off and discard 5 Boneash t 20 Y F 13 9 8 96 & 2 . 0 3 the lower end of the strip which has been in con(% recovery added F I tact with perchloric acid, and place the upper part 6 Blank(yF-) 4 0 00 0,012 & 0 013 of the strip bearing the collected fluoride in a a Results given a s means i standard deviation of mean. narrow test tube containing a known amount of * #ded to diffusion bottles as 0.2 ml. of aqueous solution. water. Centrifuge the tulle and contents for 5 Fluoride-free bone" prepared by repeated evaporations of H S O t froin bone ash in nunutes to remove air bubbles adhering to the platinum followed b y ignition of residue. d Bovine cortical bone ashed a t 700° C. Sample weights 18.8 t o i4.4 nig. strip lvhich prevent contact between the water snil the
