1410
COMMUNICATION TO THE EDITOR
synthesis. The activity of the former was approximately equal to the activity of the latter a t 61OoC. So far w the life of the catalyst in the reaction was concerned, the sample of figure 1 was about twice as strong as that of figure 2. There was some relationship between the activities and the crystalline states of the catalysts. SHIGETO YAMAGUCHI.
Scientific Research Institute 31 Kamifujimae Komagome Bunkyo-ku, Tokyo, Japan June 23, 1951
ON THE CALCULATION OF SURFACE AREA The much desired surface-area values have been measured by a method due to Brunauer, Emmett, and Teller (J. Am. Chem. SOC.60, 309 (1938)). An independent method developed later by Harkins and Jura (J. Am. Chem. SOC.66, 1366 (1944)) gave values in good agreement with the B.E.T. values. Both methods have since received wide recognition. The usefulness of the H.J. method has been greatly hampered by lack of knowledge of the general behavior of the constant k in the equations: log p / p c = B
- A/V2
with the surface area
z
= kA”2
(2)
The constant k is determined for each gas on a certain type of surface at a certain temperature. The comparison between the two methods is more difficult because of the fact that the B.E.T. method yields V , directly in milliliters and the H.J. method yields a value in a geometrical unit. The value of the crosssectional area to be assigned to the adsorbed molecule has frequently been under dispute. I t would therefore be a great convenience if the two methods could be made to give values of the same unit, e.g., V , in milliliters at S.T.P. I t would further be a great advantage if the constant 12 in the H.J. method could be converted into some universal constant. The present note is aimed at achieving both ends. Such an achievement, while very useful, should not be surpising, because if both methods give values bearing the same relationship to the true surface area, the variation due to different gases might be eliminated, since the values from the two methods should always agree. The present approach starts with a hypothetical case where the effects due to temperature and the characteristics of the adsorbate and adsorbent can be neglected, and then extends the deduction to actual cases.
1411
COMMUNICATION TO THE EDITOR
Equations 1 and 2 can be combined as:
- (K/Vrn)*/e2
log P / P O = B c
0.5
.IO00
01
c 5.5
I
I.5
I
I
'
'100
I
2
0
(3)
6
4 1/82
FIG. 1. Hypothetical B.E.T. adsorption isotherms TABLE 1 Sample. , . . . , . , . . . , No. 350 Gas used.. . . . . . . . . Krypton Working temperature, OK.. .. ,... . 78 Point B . . , . . . . , . . 38.0 B.E.T.V,. . . . . . . . . 3 8 . 0 Equation 7 (=A'/Z). . . . . 38.3
No. 414 Krypton
No. 3WA* Nitrogen
v,
KC1 No. IIt Nitrogen Argon
1
85 0.49 0.489 50.5
I
5.3
0.496
I I
89.9 0.49 0.717
1
0.45
Rutile$ Nitrogen
I ~
77.3 2.50 2.35 2.37
* The nitrogen-adsorption isotherm was measured Miss B. McPhee, t o whom the author expresses his thanks. t The results with potrissium chloride are those of Keenan and Holmes (J. Phys. & Colloid Chem. 63,1309 (1949)). The B.E.T. V , value for argon given by the original authors is apparently out of line. $ The rutile data are those of Morrison and Szasz (J. Chem. Phys. 18,280 (1948)). where 8 = V / V , and K is a value to be determined. The B.E.T. equation may be written as: Po-p
1
1 + c l-
e
c
c
. P Po
(4)
1412
COMMUNICATION TO THE EDITOR
Based upon equation 4, hypothetical isotherms for various values of c can be constructed and such isotherms are in turn plotted according to equation 3 for the evaluation of K . The results for c = 100 and lo00 are shown in figure 1 a~ examples. The straight-line portions have a slope of (- 1) in both cases. Thus:
- ( K / V J 2 = -1
(5)
and
K
= V,
Equation 3 may thus be reduced to
x-
log p = v:/v* (7) A comparison between equations 1 and 7 identifies A as V:. Or, in treating experimental data, the results can be plotted as log p us. l/V2, and V , can be obtained by taking the square root of the absolute value of the slope. This method haa been tested in numerous cases. Some are shown in table 1, where the point B values are given along with the values of V , obtained from both the B.E.T. equation and equation 7. Good agreement is shown in all cases. Division of Chemistry National Research Council Ottawa, Canada May 15, 1951
S, CHULUNG.
