NOTE OK THE ABSORPTION OF OXYGEN BY SHEETS O F RUBBER BY GEORGE A. LINHART
Very interesting and commercially very important experiments have recently been made in the Bell Telephone Laboratories by G. T. Kohman' on the absorption of oxygen by sheets of rubber. No attempt, however, was made to interpret the results mathematically. It is true, of course, that any empirical equation to express the course of the process would he merely a sort of garnish. It would be interesting, however, to show that these processes are not unique. Some years ago the writer2 published an equation which described the progress of many processes in the fields of chemistry, botany, biology, bacteriology, etc. The form of this equation is,
C, b tR c=--.--.-
~ f b t '
It is based upon the results of the tossing of a coin and represents in fact the law of uni-directional probability. The derivation of the equation is rather lengthy. In this note the equation will he applied to the process of the absorption of oxygen by sheets of rubber. In the original article cited above the numerical data are not given, but they are so well shown on the graphs that the results may be read off to within one per cent. The amounts of oxygen, therefore, given in the table of this note are expressed in millimeters read off on the original graph, while the time is expressed in hours. I n Table I, C denotes the amount of oxygen absorbed at any time, t, and a and b are constants. Usually, a is the same for a given series of experiments even when the temperature varies, provided the other conditions are the same. However, in this note, the temperatures are the same, but the conditions under which each experiment is conducted are different, inasmuch as the sheets of rubber are subjected to different amounts of anti-agers. We should not, therefore, expect a to be the same for all experiments. Still, it does not differ to any great extent, as a glance at the table will show. The equation in this note is of such nature that from the second differential with respect to (log t ) , we obtain the value for C,, since at this point (point of inflection with respect to log t ) , C = C,/2. In many processes 1
J. Phys. Chem., 33, 226 (1929).
* Riverside Junior College Journal (Occasional Papers)
May and June (1929); Eureka Junior College Journal (Occasional Papers) September (192I ) .
ABSORPTION OF OXYGEN BY SHEETS OF RUBBER
GEORGE A. LINHART
1910
05
-1 -W
1911
ABSORPTION O F OXYGEN BY SHEETS O F RUBBER
TABLEI Figure 8 (original article) Curve 2 Curve 3 Curve 4 a = 3.296 a = 3.257 a = 3.490 a = 3.465 log b = -9.15901 log h = -8.99790 log b = -9.94334 log h = -10.01614 C(obs.) C(ca1c.) C(ohs.) C(ca1c.) C(obs.) C(ca1c.) C(obs.) C(ca1c.) Curve I
t 200
2.0
1.30
2.0
1.6
1.0
0.6
300 400
4.6
4.55
4.6
5.5
2.3
2.3
4.0 7.5
11.1
500
600 700
800 900 1000
I100 I200
1300
..
10.36 17.65 24.50 31.15 35.90 39.55 41.5 42.15 44.0 44.00 45.0 45.35 46.5 46.35 11.0
12.0
12.0
19.0 26.5 33.0 36.5 39.5
21.5
19.9 27.5 33.8 38.6 42.0 44.5 46.3 47.6 48.5
50.00
29.0 35.5 39.0 42.0 44.5 46.0 47.0 49.0
52 . o
5.8
16.0 24.5 29.5 33.5 37.0 39.0
16.8 22.6 29.1 33.6 37.0 39.6 41.0 41.5 43.5 42.9 48 .o
0.3 1.6 1 . 2 3.0 3.0 4.0 6.1 6.5 9.6 1 1 . 5 13.5 1 5 . 5 18.9 20.0 20.6 22.5 23.3 2 5 . 0 25.4 1.0
27.0 2 7 . 0
28.5 28.3 33 . o
C, is known a t the start. For example, in a chemical reaction, C, is the initial concentration of the reacting substance. I n other cases, C, is only approximately known and is therefore given more accurately by the point of inflection. This is obvious from the symmetry of the curve where C is plotted against log t . The straight line plots are obtained by transforming the equation given above into the logarithmic form,
c .
L o g c c = a Log t
+ Log b
Considering the difficulty of controlling conditions in heterogeneous systems such as these, the agreement between the observed and calculated values is quite satisfactory. Mathematics Department, Riverside Junior College, Riverside, California.
