following sequence considered
DO A1
gas phase vi=v
F!
of
processes
is
D1 * A3 F! Ai gas liquid Liquid A?
liquid phase solid interface interface 17) v p = o
2 . 3 = 0 v 4 = 0
The fraction of solute occupying the respective states a t equilibrium is given by R , x2*, x*3, and x4*. These can be obtained from equilibrium measurements. The rate constant between any two states, Ai Ai is given as k,,, and is so defined as t o have the dimension, time-’. The model assumed above is different than t h a t proposed b y Khan (9) in which adsorption does not contribute t o the retention volume, i.e., x2 = 2 4 = 0. His result may be obtained as a special case of that presented below. Assuming t h a t the contributions at the gas-liquid and liquid-solid interfaces are additive, the contribution of adsorption t o the plate height may be deduced from Equation 34 of (2).
-
T o this must be added the plate height terms for gas phase and liquid phase diffusion. If the liquid forms a uniform layer of depth d, its contribution is H,
=
2Rvd2 (23*/3
+
24*
+
24
* ‘/XS* ) / D I (9
It is important to note t h a t this is functionally different from the previous expressions for the liquid term. This is no longer true when x3* = x4* = 0 . The gas phase term (4) is not changed in form by adsorption, and consequently need not be considered here. LITERATURE CITED
(1) Giddings, J. C., J . Chem Phys. 31,
1462 (1959).
(2) Giddings, J. C., J . Chromatog. 3, 443
(1960). (3j zbid., 3,520 (1960). (4) Zbid., 5 , 45 (1961).
(5) Giddings, J. C., Aature 188, 847 (1960). (6) Golay, M. J. E., “Gas Chromatography,” p. 36, D. H. Desty, ed., Academic Press, Xew Ycrk, 1958. (7) Hishta, C., Messerly, J. P., Reschke, R. F.,ANAL.CHEM.32, 1730 (1960). (8) Jones, W. L., Gas Chromatography Symposium, U. S.Public Health Service, Cincinnati, Ohio, Feb. 21, 1957. (9) Khan, M. A., lVature 186, 800 (1960). (10) Kieselbach, R., ASAL. CHEM. 33, 23 (1961). (11) Littlewood, A. B., “Gas Chromatography,” p. 23, D. H. Desty, ed., Academic Press, New York, 1958. (12) Martin, R. L., ANAL.CHEM.33, 347 (1961). (13) Scheidegger, A. E., “The Physics of Flow Through Porous Media,” p. 7, Macmillan, Xew York, 1957. J. CALVISGIDDIKGS
Department of Chemistry University of Utah Salt Lake City 12, Utah RECEIVEDfor review March 20, 1961. Accepted April 10, 1961. Work supported by research grant, A-2402 (C3), from the National Institutes of Health, Public Health Service. Presented in part Division of Analytical Chemistry, 139th Meeting, ACS, St. Louis, Mo., September 1961.
Loss of Carbon-14 Radioactivity by Counting (Hexadecyl-1-C”1trimethylammonium Bromide in Glass Planchets SIR: I n counting radioactive samples one does not usually consider the material of which the planchet is constructed to be critical. Occasionally, however, errors can be caused b y the use of planchet material which is later found to be unsuitable [Blair, D. G. R., Potter, V. R., J . Am. Chem. SOC.82, 3223 (1960)l. Concave glass planchets are advantageous for drying and counting radioactive solutions, particularly of low-energy beta emitters such as carbon14. Much better counting efficiency may be obtained than with flat planchets, presumably because of better geometry and perhaps also because of lower self-absorption losses. The use of such planchets (of borosilicate glass) in counting (hexadecyl1-C14)trimethylammonium bromide led, however, to loss of radioactivity, which could be avoided b y using nickelplated planchets. Counting rates, measured with a thin-end window, gasflow Geiger counter are given for a solution of the bromide (Table I). The solution had been dried in glass and
nickel-plated planchets, respectively, under a 250-watt infrared heating lamp before the first count was made, and then heated successively for l/phour
Table 1.
Effect of Heating on Count
Planchet Type Flat, cupped nickelplated Concave elass I
C.P.M. after Successive 1/2-Hour Heating Periodsapb 1086, 1096,‘ 1085, 1094, 1095, 1078, 1083. 676dv; 1871. 1859. 1837. 1820. 1809, 1817,c lj47, ’ 1743, 93Odva
1 ml. of an aqueous solution of (hexadecyl - 1 - C14)trimethylammonium bromide containing 1.55 mg./ml. b 10-minute counting period. Counted after standing a t room temperature over the weekend in the chamber of a thin-end window, gas-flow counter (without a flow of gas). After addition of 1 ml. of 0.2% NazCOS solution and heating. 30-minute counting period. (1
0
intervals before each additional count. (Similar decreases in count upon heating were obtained with several other glass planchets.) One milliliter of 0.2% sodium carbonate solution was finally added to the contents of the nickel-plated planchet, after the prolonged drying without loss of radioactivity, and the contents were dried again under the heating lamp. The marked drop in count seemed t o confirm the explanation that the loss in radioactivity in the glass planchet is due t o reaction with the alkali of the glass, presumably by volatilization (under heat of the lamp) of active hexadecene formed b y a Hofmann degradation. Addition of sodium carbonate solution to a sample in a glass planchet caused a similar loss of activity. The loss of activity could not be accounted for by increased self-absorption due t o the alkali added. WILLIAMSEAMAN DAVIDSTEWART, JR. American Cyanamid Co. Organic Chemicals Division Bound Brook, N. J. VOL. 33, NO. 7, JUNE 1961
963
