Phosphorus trichloride `(PCl_(3))` contains `22.57 %` of phosphorus, phosphine `(PH_(3))` contains `91.18 %` of phosphorus. Hydrochloric acid `(HCl)` contains `97.23 %` of chlorine. Show that the data is according to the Law of Reciprocal Proportions.

Explanation

Let us fix `1g` of phosphorus (P) as the fixed weight
In phosphorus trichloride `(PCl_(3))`
Weight of phosphorus `= 22.57 g`
Weight of chlorine `= 100 - 22.57`
`=77.43 g`
`22.57 g` of phosphorus have combined with chlorine `= 77.43 g`
`1.0 g` of phosphorus has combined with chlorine `= (77.43)/(22.57)g=3.43g`
In phosphine `(PH_(3))`
Weight of phosphorus `= 91.18 g`
Weight of hydrogen `=100-91.18 = 8.82 g`
`91.18 g` of phosphorus have combined with hydrogen `=8.82 g`
`1.0 g` of phosphorus has combined with hydrogen `= (8.82)/(91.18)g=0.097g`
Thus, the ratios by weights of chlorine and hydrogen combining with a fixed weight of phosphorus in the two compounds is :
`3.43 : 0.097` (This ratio is not the same)...(i)
In hydrochloric acid gas `(HCl)`,
Weight of chlorine `=97.23 g`
Weight of hydrogen `=100-97.23 = 2.77 g`
Thus, chlorine and hydrogen have combined in the ratio
`97.23 : 2.77` ....(ii)
Let us compare the two ratios. These are related to each other as :
`(3.43)/(0.097):(97.23)/(2.77)or35.37:35.10or 1:1("approximately")`
Since these two ratios are nearly the same `(1:1)`, the data is according to the Law of Reciprocal Proportions.