Fig. 2.

values of the partial pressure of oxygen in each interval as abscissæ. The actual numbers, which are easily calculated

from those given in Table II., are not included in that Table, in order to avoid unnecessary complication. A glance at

log

At

curve I. (fig. 2) will show that the velocity of the reaction beginning with the value 0 at 700 millim. increases at first very rapidly as the pressure falls, then varies between narrow limits over a considerable range of pressure (viz., from 500100 millim.), and finally decreases again rapidly. Curve II. Ap (fig. 2) is obtained by dividing the values of from which curve I. is constructed by the corresponding values of P the rate of evaporation of the phosphorus. That is, it represents the rate at which the reaction would go forward if the rate of evaporation of the phosphorus were constant. The numbers so obtained (represented in the figure by circles) evidently lie on a straight line passing through the origin. That is, the corrected velocities are proportional to the partial pressures of the oxygen. This, however, is only true up to a pressure of about 520 millim. At higher pressures the curve changes its direction, and the velocity very quickly decreases to 0.

P-p''

A more accurate way of testing the truth of this relationship is to be found in the calculation of the values of the constant K in equation 2 b. On looking over the numbers given in Table II., it will be seen that the values of K (at 20°) are approximately constant at pressures smaller than 550 millim. The numbers sometimes increase, sometimes decrease; the variations may therefore be ascribed to experimental error.

The same is true for the experiments made at 30°, for pressures between 200 and 25 millim. (no measurements were made at pressures greater than 200 millim.). Below 25 millim., however, there is always a marked decrease in the values of K, and traces of a similar behaviour are to be found in the experiments at 20°, and also in the one experiment at 9°. This diminution in the velocity of the reaction at low pressures may possibly have been due to the steam and nitrogen with which the oxygen was mixed hindering the interdiffusion of the oxygen and phosphorus

vapour.

We may conclude, therefore, that wet oxygen at ordinary temperatures acts on phosphorus with a velocity which may be represented by the equation

Above a certain limiting pressure (which probably varies with the temperature) this ceases to be true, the reaction taking place very much more slowly.

PHOSPHORUS AND DRY Oxygen.

Turning now to the action of dried oxygen on phosphorus quite a different result is obtained.

The experiments were made by the method and with the apparatus already described. The water in the glass vessel at A (fig. 1) was merely replaced by phosphorus pentoxide. In the first experiment the oxygen was allowed to remain in contact with the phosphorus pentoxide for a week, in the second, for two days. The numbers obtained are given in the following Table.

TABLE III.-Phosphorus and Dry Oxygen.

Temperature 20°-87 to 21°.26.

Pressure of phosphorus-vapour = 0·12 millim.

TABLE III.Phosphorus and Dry Oxygen (continued).

Temperature =20°-4 to 20°.65.

Pressure of phosphorus-vapour=1.035 mm. bromnaphth.

naphthalene. naphthalene.

The reaction now first began at a much lower pressure than formerly. Under a pressure of oxygen of 377 millim. it did not begin; it just began when the pressure was reduced to 202 millim. Čurve I. (fig. 3) shows the connexion between

Fig. 3.-Phosphorus and Dry Oxygen.

0

Pressure.

the pressure of the oxygen and the velocity with which it
acts on the phosphorus. The curve is constructed from the
figures given in Table III. in the same way as before. Setting

200

out from the pressure of 200 millim., at which the velocity of the reaction is 0, it appears to increase continuously as the pressure falls, and not to reach a maximum value as is the case when the gas is moist. Curve II. (fig. 3) is obtained by dividing the values of the rate of reaction from which curve Ï. is drawn by the corresponding values of the rate of evaporation of the phosphorus, and plotting the numbers so obtained against the pressures. The numbers are so irregular that it is not easy to make out the true nature of the curve. The values of the ordinates of the part of the curve between 0 and 70 millim., however, appear to be proportional to the square roots of the corresponding values of the pressure.

We have, accordingly,

which is the same equation as has already been found to hold good for phosphorus and moist oxygen, except that the velocity of the reaction is put proportional to the square root of the partial pressure of the oxygen instead of to the pressure itself.

This equation may be integrated by expanding the logarithm in the same way as before: this gives, neglecting small terms,

2

2a

—K,t=33 (P—a)' + (2a −1)(P-a)*+const.

-K1t=

The value of the constant is obtained from the condition that P=Po, when t=0; Po being the total pressure at the beginning of the experiment. Introducing the value of the constant, we obtain

2

K1t= 3p'

32, [(Po—a)3 — (P—a)'] + (2a -−1 )[(Po− a)3 — (P—a)3]. (su 1) — It is by means of this expression that the values of K1 given in Table III. have been calculated. The numbers show that K1 is approximately constant from a pressure of 60-70 millim. downwards; at higher pressures it diminishes. The irregularity of the numbers is probably due, in part at any rate, to the deposition of a coating of oxide on the surface of the phosphorus. We may therefore say that the rate of evaporation of the phosphorus being supposed constant, it is acted on by dry oxygen with a velocity which is proportional to the square root of its pressure. This is only true (at 20°) up to a pressure of some 60-70 millim. ; above this pressure the velocity decreases. It is of interest that the greatest