Page:Scientific Papers of Josiah Willard Gibbs.djvu/436

would belong to each of these if existing by itself with the same volume and temperature. These quantities will be connected by the equations

${\text{P}}_{2}={\frac {kt{\text{M}}_{2}}{2.22v}},$⁠${\text{P}}_{3}={\frac {kt{\text{M}}_{3}}{4.98v}},$

(15)

where $k$ denotes the same constant as on page 381. From the evident relations

${\text{P}}_{2}=p_{2}+p_{5},$⁠${\text{P}}_{3}=p_{3}+p_{5},$⁠$p=p_{2}+p_{3}+p_{5},$

we obtain

$p_{5}={\text{P}}_{2}+{\text{P}}_{3}-p,$⁠$p_{2}=p-{\text{P}}_{3},$⁠$p_{3}=p-{\text{P}}_{2},$

and by substitution of these values in equation (14),

$\log {\frac {{\text{P}}_{2}+{\text{P}}_{3}-p}{(p-{\text{P}}_{2})(p-{\text{P}}_{3})}}={\frac {5441}{t_{\text{C}}+273}}-13.751.$

(16)

In view of the relations (15), this may be regarded as an equation between the pressure, the temperature, the volume, and the quantities of protochloride of phosphorus and chlorine into which the gas-mixture is resolvable.

Table IX.—Perchloride and Protochloride of Phosphorus.
Experiments on the Mixed Vapors by Wurtz.

No. of exp.		$t_{\text{C}}$		$p$ (obs.)		$\pi$		$\delta$		${\text{P}}_{2}$		${\text{P}}_{3}$		$p$ calculated by eq. (16).		Excess of obs. value of $p$.
XII		173.29		756.1		423		6.68		392.4		725.5		760.7		-4.6
X		165.4		748.4		413		6.80		390.1		725.5		747.9		+.5
VII		176.24		751.0		411		6.88		392.7		732.7		773.1		-22.1
VIII		169.35		724.1		394		7.16		391.8		721.9		750.5		-26.4
V		175.26		743.3		343		7.03		334.9		735.2		764.4		-21.1
II		164.9		758.5		338		7.38		346.4		766.9		782.9		-24.4
XI		175.75		760.0		318		7.00		309.2		751.2		776.8		-16.8
IV		175.26		756.3		271		7.06		265.7		751.0		770.9		-14.6
IX		160.47		753.5		214		7.44		221.1		760.6		766.8		-13.3
I		165.4		760.0		194		7.25		195.3		761.3		768.5		-8.5
VI		170.34		751.2		174		8.30		200.6		777.8		787.6		-36.4
III		174.28		742.7		168		7.74		180.6		755.3		766.5		-23.8

It is in this form that we shall apply the equation to the experiments of M. Wurtz, the results of which are exhibited in Table IX. The first column gives the number distinguishing each experiment in the original memoir; the second, the temperature; the third, the observed pressure ($p$) of the mixture of PCl₅, PCl₃, and Cl₂, which is the barometric pressure corrected for the small quantity of air remaining in the flask; the fourth, the pressure $\pi$ due to the possible perchloride, found by subtracting the pressure due to the excess of protochloride (this pressure is calculated from the theoretical density of the protochloride) from the total pressure; the fifth, the density $\delta$ of the possible perchloride calculated from its pressure $\pi$ with the temperature and volume. The numbers of these five columns are taken