Two different compounds, each containing only phosphorus and chlorine, were decomposed into their constituent elements. one produced 0.2912 g p for every gram of cl; the other produced 0.1747 g p for every gram of cl. show that these results are consistent with the law of multiple proportions.

Dalton's law is fulfilled, since the elements in each compound of the example are related to each other in different proportions forming two different compounds;  so for case a) and b) you have 15.54% and 9.323% P respectively for each compounds,  that are equivalent to 0.2912 g P for every g Cl and the other produced 0,1747 g P for every g Cl.

Explanation:

Dalton's Law ( law of multiple proportions):

When two or more elements combine to give more than one compound, a variable mass of one of them joins a fixed mass of the other, and the first is related to canonical and indistinct numbers.

a) for the compounds A:

⇒ 0.2912 g P / gCl * ( 35.45 g CL / mol CL) * ( mol Cl / mol PCl ) * ( mol PCl / 66.427 g PCl ) = 0.1554 g P / g PCl

⇒ % P = 0.1554 * 100 = 15.54 %

b) for the compunds B:

⇒ 0.1747 g P / g Cl * ( 35.45 g Cl / mol Cl ) * ( mol Cl / mol PCl ) * ( mol PCl /  66.427 g PCl ) = 0.09323 g P / g PCl

⇒ % P = 9.323 %