Page:Scientific Papers of Josiah Willard Gibbs.djvu/437

from the memoir cited, except that the correction of the barometric pressures has been applied by the present writer in accordance with the data furnished in that memoir. The two next columns contain the values of ${\text{P}}_{2}$ and ${\text{P}}_{3}$. These would naturally be calculated from ${\text{M}}_{2}$ and ${\text{M}}_{3}$ by equations (15). But since the values of ${\text{M}}_{2}$ and ${\text{M}}_{3}$ have not been given explicitly, those of ${\text{P}}_{2}$ and ${\text{P}}_{3}$ have been calculated from the recorded values of $\pi$ and $\delta$. Since the weight of the possible perchloride is ${\frac {7.2}{2.22}}{\text{M}}_{2}$, we have

$\delta ={\frac {7.2{\text{M}}_{2}kt}{2.22v\pi }}={\frac {7.2}{\pi }}{\text{P}}_{3}\cdot$

Moreover,

$p-\pi ={\text{P}}_{3}-{\text{P}}_{2},$

since both members of the equation express the pressure due to the excess of the protochloride. The values of ${\text{P}}_{2}$ and ${\text{P}}_{3}$ were obtained by these equations.

The eighth column of the table gives the values of $p$ calculated from the preceding values of $t_{\text{C}},{\text{P}}_{2}$, and ${\text{P}}_{3}$, by equation (16); and the last column, the difference of the observed and calculated values of $p$. The average difference is 18^mm, or a little more than two per cent., the observed pressure being almost uniformly less than the calculated value. This deficiency of pressure is doubtless to be accounted for by a fact which MM. Troost and Hautefeuille have noticed in this connection. The protochloride of phosphorus deviates quite appreciably from the laws of Mariotte, Gay-Lussac, and Avogadro, the product of the volume and pressure of a given quantity of vapor at 180° and the pressure of one atmosphere being 1.548 per cent, less than at the same temperature and the pressure of one-half an atmosphere.^[1] Now we may assume as a general rule that when the product of volume and pressure of a gas is slightly less than the theoretical number (calculated by the laws of Mariotte, Gay-Lussac, and Avogadro) the difference for any same temperature is nearly proportional to the pressure.^[2] It is therefore probable that between 160° and 180°, at pressures of about one atmosphere, the product of volume and pressure for protochloride of phosphorus is somewhat more than three per cent, less than the theoretical number. The experiments of Wurtz, as exhibited in Table IX, show that the pressure, and therefore the product of volume and pressure (we may evidently give the volume any constant value as unity), in a mixture consisting principally of the protochloride is on the average a little more than two per cent, less than is demanded by theory, the differences being greater when the proportion of the protochloride is

1. Troost and Hautefeuille, Comptes Rendus, vol. lxxxiii (1876), p. 334.
2. Andrews, "On the Gaseous State of Matter," Phil. Trans., vol. clxvi (1876), p. 447.