V O L U M E 24, NO. 10, O C T O B E R 1 9 5 2
1639
dye) gave results which are not significantly different from the true values. The two batches of dextrin, A and B (3 mil. of 2y0 solutions), gave results which differ from the true values by significant amounts but in opposite directions. This is not surprising, as the name “dextrin” covers a number of different types of starch degradation products and different dextrins may well have different properties. Gum arabic (3 ml. of 1% solution) gave results which were significantly high, although the differences were not greater than 2 parts per thousand. I t ir concluded that Polyethylene glyrol 400 is superior to other protective colloids for use with dichlorofluorescein from considerations of both accuracy and convenience. The use of
5 drops of a 50% solution in water containing 0.1% dichlorofluorescein is recommended. LITERATURE CITED
(1) Kolthoff. I. hf., J . Anal. Chem.. 71, 235 (1927). (2) Kolthoff, 1. M., Lauer, IT.31..and Sunder, C. J., .I. Am. Chem. Soc., 5 1 , 3 2 7 3 (1929). (3) Santos-Ruiz, A., and Portillo, R., Anale. soc. espail. fis. qutm. (Madrid),39,91 (1940). (4)Stalser, R. F., Dillon, E. S., and Vosburgh, TV,C., ANAL.CHEW, 2 2 , 9 5 2 (1950). R E C E I V Efor D review J u n e 17, 1961. Accepted August 16, 1962. Presented a t the Pacific S o r t h a e s t Regional Xleeting, Seattle, Wash.. 1951.
Photometric Analysis Error W . 4. E. I\JcBKYDE, D e p a r t m e n t of C h e m i s t r y , University of Toronto, Toronto, Canada
i S AX effort t o show the regions of concentration which may
be
determined 15ith comparatively low relative analysi;: error, Ringborn (a), Alyres( I ) , and others have advocated an unusual method of representing photometric data-namely, a plot of (1-T) against log c. The region of steep slope on such a plot discloses the range of concentrations which may be determined with fair precision. The uriter feels that this type of working curve for transforming instrument leadings to concentrations suffers from certain practical drawbacks and, except for cases of gross deviation from Beer’s law, provides little information that cannot be obtained by other means. I n the first place it is much more difficult t o fit a skew-shaped curve through experimental points without sacrificing some accuracy than to draw a straight or nearly straight line: the Ringbom plot yields a working curve of the former sort whereas the conventional absorbancy-concentration plot is usually nearly a straight line. I t is also more difficult to interpolate concentration values on a logarithmic than on a linear scale. Furthermore, because many chemists routinely work with absorbancies in preference to transmittancies, several commercial in3truments have scales which &her read in, or are proportional to, absorbancies; accordingly it becomes highly artificial to convert these to absorpt,ancies (1- 2’). The purpose of the Ringboni plot is t o reveal regions of concent,ration where the relative analysis error is comparatively small, and yet, when 13eer’s law is strictly obeyed, this error function R i a known funct,ion of concentration. Thus, f o r d In c/dT t o be less than 5, t h e absorbancy must lie between 0.112 a n d 1.105 (transmittancy between 0.772 and 0.0785). There are various absorbing systems known t o analysts for which Beer’s law does not quite hold valid, and the deviation becomes more noticeable the higher the absorbancy. For such cases we may express the relationship h t w e e n absorbancy and concentration as
A
=
abc
+ bf(c)
where j is a correction term which changes in some waj. with c. The symbols here are given in accordance \&h recently adopted .4merican practice (3). By differentiating t o obtain the expression for the error function we have
_-.
0.4343dT -~ ahdc + bdf/dc dc Tlog T abc bj abc bf
+
+
And if bf is small in comparison with abc, this becomes 0.4343dT -~ T log I’ dclc
dl’
-
0.4343 1’ log 2’ (1
&c c (1
also b r small compared H ith a , 30 that the error function does not differ greatly from the value< derived when Beer’s law holds exactly. For systems which fail to conform to the absorption law a t low absorbancies or show gross deviations therefrom, the foregoing derivation is not applicable, and information concerning analysis error is available only from the Ringboni plot. The analyst who is concerned with colorimetric determination of traces of constituents is concerned with the shape of the absorbancy-concentration curve and the error function when concentration is small. A glance a t many of the procedures employed for trace anal?& shows that they nearly all conform t o the absorption law or show only minor deviations in the region of low concentration. I n most of these cases the analjsis error function exceeds 5 for absorbancies less than 0.1 12 or therabouts. For smaller absorbancies, the relative error function hecomes approximately 1 / 1 - T (6). It is sometimes possible to increase the absorbancy to be measured by keeping the volume of the final solution, containing the colored constituent, to a minimum, and occasionally by increasing the depth of the absorbing vessel. The restriction in the latter case is thst, with the sccessories supplied with many commercial instruments for increasing the light path through the absorbing solution, the increase in the value of b is almost offset by dilution of the solution in order to fill the cell. It seems probable that very small amount3 of a substance cannot be determined with great precision in most cases, since the error on a relative basis of any measurement becomes large as the quantity t’obe measured is made small. I t is perhaps relevant to point out, however, that the value of dc/dT varies inversely as T , so that the absolute error in measuring c is actually slightly smaller as T approaches unity. These remarks are intended to offset the impression which appears to have been created that photometric analysis should never be extended to solutions whose absorbancies fall outside the range corresponding to a small error function, An extreme case of this att,itude came to the writer’s attention recently. He was asked to review a manuscript prior t o its publication in which the author, who was intere3ted in trace analyses performed with a spectrophotometer, made the suggestion that precision might be improved by adding to each sample a known amount of the constituent to be determined. The amount of added constituent was to be of such a size as to bring the absorbancy of the final solution into the region of low relative analysis error. A similar proposal has evidently been made before ( 2 , 4 ) . The writer endeavored t,o show by the following argument that this proposal would, if anything, increase the relative analysis error. I n this demonstration the absorption law was assumed to be applicable. Suppose that the original solution concentration was ci, absorbancy A , . Suppose that there is added to this the constituent to be determined until the new concentration is ca =
df /dc +
+ ip)
-7)
0.4343 d d /d T log T
(+)
If the preceding assumption is true, then dfldc will pro!)ably
1640
ANALYTICAL CHEMISTRY
rcl. The correct choice of r will bring A Zinto the range of lower relative analysis error. This will now become
d>/s dT
- 0.4343 TB log Ts
But dca is the error in measurement of this new solution caused by an error d T in measuring the transmittancy of it. But this same absolute error in c, calculated as relative error in ci, will be r times the relative error calculated on cp. Thus, whatever value the function 0.4343/T2 log T , reaches, the error function *d will be r times as great. d Tz
0.4343 r 10 --rA l.rAl
But, since T is always between 0 and 1, T‘ is less than unity for positive values of r. Hence this quantity is greater than the relative analysis error for solutions of concentration ci when measured directly. I t is to be concluded that for solutions of low absorbancy no improvement in the precision of analysis is achieved by enriching the solution with the constituent being determined to the point of obtaining a final absorbancy corresponding to a low analysis error. LITERATURE CITED
Then,
(1) Ayres, G. H., AXAL.CHEM.,21, 652 (1949). (2) LeRoy, G., Ann. faZs. et f r a u d e s , IO, 208 (1917). (3) Mellon, M. G., “.lnalytical Absorption Spectroscopy,” p 101,
0.4343 10- I 1,~ A I
Nevi York, John TTiley B- Sons, 1950. (4) Ibid., p. 110. (5) Ringbom, A., Z. anal. Chein., 332 (1949). (6) Sandell, E. B., “Colorimetric Determination of Traces of Metals.” 2nd ed., p. 64, New Tork, Interscience Publishers, 1950.
-
RECEIVED for review February 14, 1!432.
Accepted J u l y 2. 1952.
Determination of Calcium, Magnesium, and Iron in limestone By Titration with Versenate KUANG LU CHENGI, TOUBY KURTZ, ~ N ROGER D H. BR.AY University of Illinois, Urbana, Ill. YTANDARD methods ( 1 ) of analysis for the major cations in limestone involve time-consuming precipitation and separation of calcium, magnesium, and iron. The procedure described in this paper permits direct determination without separation of these constituents by titrations based on the complexing action of Versenate a t appropriate p H levels. This proposed procedure is rapid and accurate, and lends itself to mass analysis technique. A well-known complexing compound (7), the disodium salt of (ethylenedinitrilo) tetraacetic acid (Versenate), has been applied successfullj7 to m t e r , soil, and plant material analyses (S-5), and recently to limestone analyses ( 2 ) . The application of this reagent to the analysis of limestone provides a simple procedure which is subject to little interference. PROCEDURE
Digestion of Sample. Weigh 1.000 gram of properly prepared sample into a 250-ml. beaker and add, cautiously, 10 ml. of water and 10 ml. of perchloric acid. Heat over a gentle flame on the hot plate until the solution becomes colorless ( a few hours may be required for silicates), and then evaporate the solution to dryness. Cool, and take up the residue by adding 3 ml. of 1 to 1 hydrochloric acid and 10 ml. of water. Filter off the silica, if necessary, and make up to 250 ml. with water. DETERMINATION OF CALCIUM
Reagents. VERSEXATE SOLUTIOK.Dissolve 4 grams of the disodium salt of (ethylenedinitrilo) tetraacetic acid in 1 liter of water. Standardize this solution against a standard calcium solution. STAKDARD CALCIUM SOLUTIOS. Dissolve 2.500 grams of reagent grade calcium carbonate in about 5 m]. of l to l hydrochloric acid and dilute to 1 liter nith water. This solution contains 1 mg. of calcium per milliliter. PoTAssIuar HYDROXIDE, 20% aqueous solution. Mix thoroughly 40 grams of IKDICATOR POWDER. CALCIUM powdered potassium sulfate and 0.2 gram of murexide. Murexide can be obtained from Eastman Kodak Co , or prepared from uric acid (3). Titration. Pipet a IO-ml. aliquot of the solution to be analyzed into a 200-ml. porcelain dish, then add about 20 ml. of water, 1 ml. of potassium hydroxide, and a tiny scoop of calcium indicator powder (20 to 30 mg.). Stir, and titrate with the 1
Present address, Commercial Solvents Corp., Terre Haute, Ind.
standardized Versenate. The end point is reached when the color changes from pink to violet. If overtitrated, the end point may be located conveniently by backtitrating with a calcium solution of the same normality as the Versenate solution. DETERMINATION OF MAGh ESIUM
Reagents. VERSENATE SOLUTION, as described under determination of calcium. BUFFERSOLUTION.Dissolve 60 grams of ammonium chloride in about 200 ml. of water, add 570 ml. of concentrated ammonium hydroxide, and dilute to 1 liter with water. POTASSIUM CYAXIDE, 10% aqueous solution. F241 INDICATOR. Dissolve 0.15 gram of Eriochrome Black T(F241) (also obtainable from Eastman Kodak Co.) and 0.5 gram of sodium borate in 25 ml. of methanol. Titration. Pipet a 10-ml. aliquot of the solution to be analyzed into a 250-ml. beaker, then add about 25 ml. of water, 2 to 3 ml. of buffer solution, a few drops of potassium cyanide solution, and 8 drops of F241 indicator. Stir, and titrate with the Versenate solution. The end point is reached when the color changes from wine red to pure blue. The volume of this titration is for both calcium and magnesium; however, magnesium can be calculated by subtracting the calcium value from the value for both calcium and magnesium. The Versenate solution can be either standardized by a standard magnesium solution (use MgSOa. 7HzO) according to the described procedure or calculated from the molality of the Versenate solution as found with the standard calcium solution. \T7hen difficulty in the F241 end point is encountered because of low magnesium in the sample, 10 to 15 ml. of a 100 p.p.m. standard magnesium solution may be titrated to the end point before the aliquot of the unknown is added. The titration may then be carried out as described above. A back-titration may also be used if the end point is difficult to detect. I n this technique ( 4 ) a definite excess amount of the standard Versenate is added to the aliquot of unknown and is back-titrated by a standard magnesium solution of the same molality. DETERMINATION OF IRON
Reagents. VERSEKSTESOLCTIOX,as described under determination of calcium. SODIUM ACETdTE, 3570 aqueous Solution. Dissolve 2 grams of salicylic acid in 100 nil. of INDICATOR. methanol. STANDARD IRON SOLUTIOX.Dissolve 1.0000 gram of electrolytic iron in 10 ml. of 1 to 1 hydrochloric acid, digest on the steam bath until all iron has been dissolved, and make up to 1 liter with water.
