731
ANALYTICAL CHEMISTRY
talum when heated alone ignited instantaneously (but only partially) to form an oxide which was discontinuous with respect to the one-turn secondary current. Residual unburned tantalum remained. Use of the flux remlted in a smooth slag of completely burned sample. The results obtained by the conductometric method unfortunately involved a large correction for carbon in the steel Aux. The slight discrepancy between the two methods is probably attributable to this cause, and also to an uncertainty in the blank in the conductometric method-that is, a new freshly fired crucible is used for each analysis. If standards and unknowns are of the same material, the temperature acquired during the combustion is probably reproducible, and any carbon dioxide evolved by the crucible does not introduce an error by virtue of the method of calibration. However, tantalum burns to a higher temperature than the steels used for calibration. Consequently, in so far as this liberates more carbon dioxide from the crucible, the results for tantalum may be slightly high. The latter source of error is not inherent in the low pressure
combustion method, in which a single crucible, never exposed to the atmosphere, is used for a series of analyses. The results presented indicate that high precision can be obtained by either method. The absolute accuracy of the low pressure combustion method is probably within 0.001% of carbon, and perhaps even better if the discussion of the comparison of methods is valid. ACKNOWLEDGMENT
Thanks are due David Whittemore for aid in design and construction of the sample holder, and R. H. Lux for much of the experimental work. LITERATURE CITED
(1) Bennet, E. L.,Harley, J. H., and Fowler, R. M., ANAL.CHEY., 22,445 (1950). (2) Murray, W. M., and Niedrach, L. W., ~ N D .ENG.CHEW,AXAL. ED.,16,634 (1944). RECEIVED for review September 17, 1953. Accepted Sovember
2 5 , 1953.
An Explicit Function for Specific Surface Area M. J. KATZ Signal Corps Engineering Laboratories, Fort Monmouth,
the purpose of this paper to show that an explicit function Ias TaforISconsequence the specific surface area of an adsorbent may be obtained of the Brunauer, Emmett, Teller theory (1).
It has been the writer’s experience that this has been largely overlooked by investigators in the field. For example, Harkins and Jura (5) observed that . . no single equation of state is capable of transforming these data [Le., experimental parameters such as pressures, volumes, and weights of adsorbed vapors] into a cprrect area for a solid in every case.” As a result, numerous investigations have been directed toward developing new equations, graphical methods of solution, and new principles of surface area measurement (2,4-6). It is not the intention, here, to analyze these principles and techniques. It is considered, however, that the present treatr ment offers, for many purposes, a simpler and more expeditious method. In the usual procedure, adsorption data are plotted according to the equation.
“.
N. J. tensive tabulation of data involving rather time-consuming computations. Because the slopes obtained are large numbers, even for materials with large surface areas, one must have a t least five or six adsorption points in the relative pressure range 0.05 to 0.38 to determine the intercept accurately. The raw data may be handled in many ways. In some laboratories, for example, the “point B” method is used-Le., graphical deduction of the point of monolayer formation. However, this and other similar methods involve enough computation to make an analytical solution preferable, in the opinion of the writer. The method for surface area measurement that is now described has been applied to a wide variety of adsorbents in the writer’a laboratory-. It depends essentially on the fact that the quantity 1 El - EP is appreciable. Therefore C is large and ATm is a small C number. In fact, it may be assumed that the straight line passes 1 through the origin or that N , = ~0. Furthermore, C is large with respect to unity. so that we may write C > > 1 and
where
N, N,
number of moles adsorbed per gram of adsorbent number of moles needed to form a monolayer p pressure a t which adsorption is measured Po saturation vapor pressure of the adsorbate a t the temperature of measurement RT log C C = a constant defined by the equation E1 - E2 = = = =
where E1 is the average heat of adsorption in the first layer and EPis the heat of liquefaction of the adsorbate. This plot gives a
c-
1
straight line, the slope of which is -and the intercept, -. NmC N mC Equating these quantities to the experimentally determined slope and intercept of the straight line gives two equations which may be solved for N,. From this value and the crosssectional area of the adsorbate molecule, the specific surface area of the absorbent may be calculated directly. In order to perform the indicated calculation it is necessary to make an ex-
Now the quantity of gas in the dead space may be estimated by assuming the relationship q = pzh
(3)
where q is the number of moles of gas in the dead space a t equilibrium pressure p2 and b is a constant which is a function of the size of the sample bulb. Let pl be the initial pressure and so chosen that upon exposing the sample to the adsorbate (without changing the volume of the measuring system) an equilibrium pressure pz is obtained within the relative pressure range 0.15 to 0.35. Then the number of moles of gas adsorbed per gram of adsorbent ( N ) . is given by (4)
V O L U M E 26, NO. 4, A P R I L 1 9 5 4
735
where
the method may be used in any system which follows the BET equation. Some typical results are given below:
g = weight of sample a = constant =
V --
RT
Sample Silica gel African MnOz Synthetic MnOr ExDerirnental carbon black Shawinigan carbon black MnCO,
u being the volume of the measuring system, T is the absolute
temperature, and R is the gas constant. If nitrogen is the adsorbate a t 78” K, po S 760. Assuming liquidlike packing leads to a value for a molecular area of 16.2 sq. A. or 9.85 X lo4 square meters per mole. From Equations 1 and 2,
Combining Equations 5 , 4, and 2 and inserting the constants for nitrogen gives, for the specific surface area,
Thus, if the constants a and b for a particular system have been determined, one equilibrium point suffices for a surface area measurement. By comparison of Equation 1 with Equation 5 it may be seen that
490 15.0 95.0 482 65.2 26.6
479 15.1 99.0 485 64.4 26.3
The object of this work %-asto underscore an aspect of the BET theory which has not received sufficient attention. It is not suggested, of course, that the technique here described should be used in lieu of the BET theory, which has been very valuable in understanding the mechanism of adsorption. The present concern was with the use of the theory essentially as a surfacemeasuring device. It is believed that the method described offers a very simple and expeditious means of meamring specific surface area and a t the same time gives very satisfactory agreement with the results obtained from a complete adsorption isotherm. ACKNOWLEDGMENT
The author wishes to acknowledge his indebtedness to Robert C. Clarke of this laboratory for making adsorption measurements and performing the calculations needed to test the method.
(7) Thus for p / p o = 0.2 and C = 100, one obtains an error of 4% assuming the BET value to be correct. It is apparent, however, from an examination of Equation 7 that one may not apply the method in cases with much smaller C values without introducing an appreciable error. It is evident also, that the value of p / p , should be high (at least 0.15) to minimize any discrepancy which might result from a low C value. In any case, i t is recommended that the method be applied only after some experience with a particular adsorbate-adsorbent system. With these reservations understood,
Specific Surface Area Square Meters/Gram, BET Equation 6
LITERATURE CITED
(1) Brunauer, S., Emmett, P. H., and Teller, E., J . Am. Ckem. Soc., 60, 309 (1938). (2) Dallavalle, J. M., Orr, C., Jr., and Blocker, H. G., “Research on Surface Properties on Fine Particles,” Quart. Rept. of dpril 1952, Contract KO.DA-36-039-sc-5411, Department of the Army, Project 3-99-15-022. (3) Harkins, W. D., and Jura, G., J . Am. Chem. Soc., 6 6 , 1 3 7 2 (1944). (4) Innes, W. B., ANAL.CHEM.,23, 759-63 (1951). (5) Jura, G., and Powell, R. E., J . Chem. Phys., 19, 251-2 (1951).
(6) Miles, F. T., and McMillian, W. G., “Graphical Surface Area
Calculations,” Technical Information Division, Oak Ridge, Tenn., MDDC-1086(1947).
RECEIVED for review August 20, 1953. Accepted December 23, 1953.
Determination of Small Amounts of Tin with Dithiol MARIE FARNSWORTH and JOSEPH PEKOLA Research Laboratory, M e t a l
0
& Thermit Corp., Rahway, N. 1.
F T H E organic reagents for the colorimetric determination of tin, dithiol ( 2 , 3, 6) appears to be the most promising. Even the dithiol method has been unsatisfactory, however, principally because it has been necessary t o compare visually the depth of color (with those of standards) by means of reflected light; therefore the highest precision was not obtainable. Until recently ( 4 , 5, 7 ) , the method was not studied photometrically. In a record of the Manhattan Project (5),it is reported that, in the absence of a dispersant, the red color of the tin-dithiol complex, in the range of 10 t o 60 y of tin in a volume of 10 ml., remains clear for 15 minutes; thus the transmittancy can be read a t 540 mr. An alternative procedure using agar-agar is also mentioned in (6). This solution, however, is unsuitable for absorptiometric measurement. Kenyon and Ovenston (4)used Belloid T.D. t o disperse the tin-dithiol complex and measured the color spectrometrically. They state that solutions with up to 10 y of tin per ml. are stable from 1 to 2 hours. Williams and Whitehead ( 7 ) report Teepol X to be a suitable dispersing agent for the tindithiol complex. Using this dispersant, they report that the transmittance of light through the solutions obey8 Beer’s law up
to 16 y of tin per ml. and that the color is stablc for a t least 3 hours. EXPERIMENTAL
The authors obtained some Belloid T.D. but did not have much success with the initial experiments. Teepol X was unobtainable; the authors therefore turned to dispersants easily available in America. A very suitable dispersing agent was found, Santomerse S (30’%,),made by the Monsanto Chemical Co. This reagent, when used as recommended below, renders the tin-dithiol complex entirely suitable for absorptiometric measurements. It is recommended that the transmittance be read a t 530 mp, since absorption curves (Figure 1) transmit the least a t that wave length. A calibration curve prepared from standard solutions as described below, shows that the relationship between the percentage transmittance and the tin concentration, up to 16 y of tin per ml., is linear; thus, Beer’s law ip obeyed. Solutions were checked also for stability and found to be stable for a t least 3 hours. While a concentration of 1.5 ml. of sulfuric acid in the
