1 ml. of HCl; the cupferron-chloroform extraction, reduction, and titration were then carried out as directed above. Results are shown in Table I. Various NBS standard samples of steel were analyzed by the proposed method. The Precipitated WOs was ellowed to digest 16 hours (or 36 hours
when snalyiing samples high in molybdenum) before filtration. Results are shown in Table 11. LITERATURE CITED
(1) Am., SOC. TesAin
Materials, Philad T M Methods of
delphs, Pa.,
Chemical An&’& of Met%” P. 1161 (2f$:&e, s. G,, 52, 466, 527 ( 1927). (3) Luke, C. L., ANAL. CHEM.33, 1365 ( 1961).
C. L. LUKXI Bell Tele hone Laboratories, Inc. Murray gill, N. J.
A New Plotting of the BET Method SIR: In the gas adsorption method for obtaining the surface areas of solid powders, usually the BET linear equation (1) is used as follows X 1 C-lx (1) V(1 - X ) = Kc + v,c where V is the adsorption value a t the relative pressure, X,which is the equilibrium pressure normalined by the saturation vapor pressure of the adsorbate a t the same temperature, V , is the adsorption value corresponding to the monolayer, and C = exp.(El-EL)/RT. Plotting the left-hand side of Equation 1 against X with adsorption measurement data, we have the value of V , from both the intercept and the slope of the straight line. The surface area of the adsorbent can easily be obtained from V , value with the cross-sectional area of the adsorbate molecule. This procedure, however, has the disadvantage of having to carry out the adsorption measurement a t several relative pressures to test the linearity of Equation 1. For remedying this situation, some simplified methods of BET plotting have been proposed. The “one-point” method (4) gives the reciprocal of a line connecting the original point with only one experimental point in the BET plot as an approximate value for 8,. A convenient method for rapid measurement has been proposed by Innes (W), who used the relation, surface area = 3.5V0.~,where V0.2is the adsorption value at X = 0.2. Hisrelation, which is calculated from Equation 1 with C = 80 and the nitrogen cross section = 15.4 sq. A,, gives values within 5% of BET values as long as C
Table 1.
No.
Solid Sample
1 2 3 4 5
FezO~-Al~Os clinker NiO clay
6
CTz+-AlzOs
Active AbOa
Si02-AlzOn
Active charcoal
2
0‘
Figure 1. 1. 2. 3.
6
4
8
1 0 1 2
I ’
4
I?.
New plotting of BET method
4. Active AlzOa
FezOa-AleOa clinker NiO clay CrzOa-AIaOa
5. 6.
SlOa-AlzOs Active charcoal
exceeds 50. One of the present authors (3) proposed a modification in which an adsorption value a t relative pressure nearly equal to 0.1 was taken approximately as V,. This modification is based on the facts that V = V , a t X = 1/(1 G )which , is concluded from Equation 1, and that most experimental values of C are about 100. I t seems to the present authors that BET plotting has the further disadvantage of erroneous estimation of the intercept, l/V,C, which is always very small because of the large value of C. Here, we would like to add a revised method for the plotting itself. Our revised method is based on the other form of the BET linear equation (f) as
+
1
1
V(1
1
- X) = v, + v,c
Comparative Values
Vm 1.99 34.3 44.3 76.4 79.1 270
C 251 194 226 54 84 371
Present Method V , (one point) at
V, 1.89 34.9 44.7 76.3 79.3 262
The error of t h i i one-point method is due mainly to the contribution of the second term, which is ignored, and may not exceed few percentage at X = 0.35. This one-point method is congruent with the one-point method quoted above, since the procedure in the latter method is based on the relation
X V
V =
I, X F
which is the same as Equation 3. Experimentaf data obtained in our laboratory for the adsorption of nitrogen on solid powders were used to check the present method, and are compared 1-x with ) the BET plotting in Table I. (7 (2) .
Plotting the left-hand side of Equation 2 against (1- X ) / X , we have the value of V,,, from only the intercept (Figure
BET Method
1). The value of C, if necessary, can be obtained from the slope of the line with the value of V , obtained in advance. The value of C, of course, cannot be obtained precisely as well as in the case of the original BET plotting. Moreover, a simplified version of the present plotting may be considered. In the region of relative pressure, 0.05 < X < 0.35, appropriate to the BET theory in many adsorption systems, the second term in Equation 2 is so small compared with the first that it may be ignored. Accordingly, the following approximate form of the BET equation may be used to evaluate the value of V , from one point of adsorption isotherm in the appropriate region. v, = V(1- X ) (3 1
c
x = 0.2
378 191 125 50 79 271
1.92 34.3 44.0 70.4 76.7 265
LITERATURE CITED
(1) Brunauer, S., Emmett, P. H., Teller, E., J . Am. Chem. SOC.60,309 (1938). . 759 (2) Innes, W. B., ANAL. C ~ Y 23, (1951). (3) Kfiii T., “Surface Chemistry,” Vol. 7, dxperimental Chemistry,” Japan Chemical Society, 1956. (4) Orr, C. Jr., Dallavalle, J. M., “Fine Particle heasurernent,” p. 183, Macmillan, New York, 1959.
TOMINAQA KEII TOKUJI TAKAGI SETSUKO KANETAKA Department of Chemical Engineering Tokyo Institute of Technology Meguro-ku, Tokyo, Japan VOL. 33, NO. 13, DECEMBER 1961
1965
