Direct Titrimetric Determination of Sulfate JAMES S. FRITZ and M A X Q. FREELAND lowa State College, Ames, lowa
is that alizarin, which does not c:rrry :1 ncgaiive charge in solution a t lower pH values, because it is unsulfonated, fails to give an cind point. o - ( 2 - H ~ d r o x y - 3 , 6 - d i s u l f o - l - 1 i a y l l t h \ i ~ acid disodium salt, commonly known :is Thorin, r:in also be used as :in indicator for this titration. I t futictio~i.-in the .same manner as Alizarin Red S. The end point ia marked by a change from \-ellow to pink. Thori11exhibits n sliarper end point than .%harill Red 5,particularly at lo~vcrpH values. Vnder the conditions of this titration it gave the shaq)wt end point I)cta.een an apparent pH of 2 and 3: although the, titration is stoichiometric in the “apparent” pH rang(’ 1.5 to 3.5.
This w o r L was prompted bj the need for a rapid, accurate, and widely applicable titrimetric method for sulfate. The method proposed involves direct titration of sulfate with standard barium solution. Alizarin Red S serves as the indicator, pi\ing a sharp, iivid change from jellow? to pink at the end point. The titration is carried out in 30 to 40y0 alcohol, as no end point is observed in water alone. Equilibrium is quicltlj atlained, permitting a rapid titration. Coprecipitationerrors are greater than for graiinietric sulfate methods, but most of these can be atoided by the preliminary removal of cations with an ionexchange column. The simple titrimetric procedure should be useful in many cases where a rapid approximation of sulfate is required. Jn the absence of interfering anions the ion exchange-titrimetric method is as precise as the gravimetric method and considerabl~faster.
soL\-mrr COMPOSITIOII
B”
C .%USE of t h e , tiiiir-coiisumiiig and tedious naturc: of the gravirneti,ic ,‘ drtcrniination of sulfate, numerous a,tteinpts have been matl(~t-droside solution. o-(2-H~droxy-~,R-tlisulfo-1-11aphthglazo)-benzenearsonicAcid Disodium Salt (Thorin). Prepare a 0.025% solution of the sodium salt in water. PROCEDURE
General Procedure. For macrotitration dissolve a sample containing 2 to 4 millimoles of sulfate in 45 ml. of water, add 40 ml.
1595
of methanol, and adjust the pH to 3.0 to 3.5 with dilute magnesium acetate or perchloric acid. Rapidly add about 90no of the required barium chloride or perchlorat,e, then add 5 drops of Alizarin Red S and tit,rate to t’he first permanent pink. .411ow a time lapse of 3 to 5 seconds between addition of the last few increments of titrant. For t,it.rations on a semimicro scale use a 0.2- to 0.8-millimole sample, 10 ml. of water, 10 ml. of methanol, and 1 drop of indicator. Ion Exchange Procedure. .\gitate the resin (H form) in a beaker and decant the finer particles. Repeat this several times. With the column open pour in 14 ml. of resin, measured wet. Backwash with a slow stream of distilled water for a few minutes, then place the sintered-glass disk, with capillary tube attarhed, on top of the resin column and run 50 ml. of 3 . 5 S hydrochloric acid t,hrough from the bottom at. a flow rate of about 4 ml. per minute, washing it through with distilled n-ater. Continue the washing until only a faint chloride test is obtained. This n-ill require about 150 ml. and 30 minutes. Introduce the 5-ml. sample containing 1 millimole of sulfate by pipet directly onto the resin column and !?ash through with 20 ml. of distilled water in small portions, allon-ing the liquid level to come to rest a t t,he top of the resin column each time before a new rinse is added. Titxate the sulfate in the eluate by the standard macroprocedure. LITERATURE CITED
(1) Johnston, J., andddanis. L. H., J . A m . C h e m . Soc.. 33, 829 (1911). (2) Kolthoff, I. M., and Stenger, V. A,, “Tolumetric Analysis,” 1-01, 11. pp. 30G14, New T o r k , Inter>cience Publishers, 1947. (3) I b i d . , Vol. I,p. 92. (4) Samuelson, O., Snensk Kcm. T i d s k r . , 52, 115 (1940). (5) Schroeder, W. C., IND.Esc,.(:HEY., . ~ s . L L . ED..5, 403 (1933). (6) Willard, H. H., and Furman, N. H., “Elementary Quantitative .halysis,” 3rd ed., p. 171, Sew York, D. Van Xostrand Co., 1940. RECEIVED for reT.iew October 12. 1‘133. .Iccepted .Jiily 14, 1954 Pi,esented before the Division of Analytical Clleuiistry a t the 123th AIeeting of the .‘ivERIcAs C H E M I C A L fiocrsTS. Kansas City. M o . Contribution f r o m the Institute for Atomic Research a n d Department of Chemistry, Iowa State Lahoratory oi t h e College, Ames, Iowa. Work Iierforined in the .IIIICS Atomic Ehergy Commission.
Tables for Evaluating Bateman Equation Coefficients for Radioactivity Calculations F. 1. FLANAGAN and F. E. SENFTLE
U. 5. Geological Survey, Washington 25, D. C. Tables of decay constants and functions thereof are presented to simplify the problem of calculating the constants involved in the Bateman equation. These tables make it possible to calculate any constant involved in any of the four radioactive series b? a maximum of three mathematical operations, either by three divisions or by two multiplications and a division. They are useful and time-saving where a large number of such calculations are involved.
R
ADIOACTIVE equilibrium in the thorium, uranium, or neptunium series can be disturbed by chemical treatment of materials containing some or all of the members of these series. .4~ a result of such a break in the radioactive chain, it is important to know the variation with time of the quantity or activity of a particular decay product. Calculations involving radioactive equilibrium were simplified by Bateman ( 1 ) and his method is standard procedure (Ruther-
ford et al., 5 ) . The solution of the general case of n products is given by 2 V
= S‘ (Cle-X11
+ C?e-X21 . .
,
C,,e-hrd)
where S atoms of a giveii species are formed from S’atoms of a parent species in time t, A is the decay constant, e is the Naperian base, and C, is a constant having the form
c2=
AIA?. . . . (A, - A?) (A, - A?)
An-1
..
(AJt - A ? )
These constants, although simple in themselves, are tedious to calculate, especially where there are a large number of calculations, and where many terms are involved. T o facilitate the evaluation of these Bateman constants a number of tables have been computed. The half-life data are taken from the publications of Way et al. ( 6 ) , Fleming ( 2 ) , Ginnings et al. ( 3 ) , and Hollander et al. (4). Table I shows the half lives and decay constants of the various
