Note 3 — Chapter XIX · PHOSPHORUS AND THE OTHER ELEMENTS OF THE FIFTH GROUP
George Kamensky translation
The absorption of the oxygen of the atmosphere at a constant ordinary temperature by a large surface of phosphorus proceeds so uniformly, regularly, and rapidly, that it may serve, as Ikeda (Tokio, 1893) has shown, for demonstrating the law of the velocity (rate) of reaction, which is considered in theoretical chemistry, and shows that the rate of reaction is proportional to the active mass of a substance—i.e. dx/dt = k(A - x) where t is the time, A the initial mass of the reacting substance—in this case oxygen—x the amount of it which has entered into reaction, and k the coefficient of proportionality. Ikeda took a test-tube (diameter about 10 mm.), and covered its outer surface with a coating of phosphorus (by melting it in a test-tube of large diameter, inserting the smaller test-tube, and, when the phosphorus had solidified, breaking away the outer test-tube), and introduced it into a definite volume of air, contained in a Woulfe's bottle (immersed in a water bath to maintain a constant temperature), one of whose orifices was connected with a mercury manometer showing the fall of pressure, x. Knowing that the initial pressure of the oxygen (in air nearly 750 × ·0209) was about 155 mm. = A, the coefficient of the rate of reaction k is given, by the law of the variation of the rate of reaction with the mass of the reacting substance, by the equation: k= 1 / t log A / A-x , where t is the time, counting from the commencement, of the experiment in minutes. When the surface of the phosphorus was about 11 sq. cm., the following results were actually obtained.
t=10 20 30 40 50 60 minutes
x=10·5 21·5 31·1 40·7 49·1 57·3 mm
10,000 k=32 32 32 33 33 33
The constancy of k is well shown in this case. The determination takes a comparatively short time, so that it may serve as a lecture experiment, and demonstrates one of the most important laws of chemical mechanics.