Phosphorus and chlorine form two compounds.The first compound contains 22.54% by mass of phosphorus and 77.46% by mass of chlorine. In the second compound the percentages are 14.88 for phosphorus and 85.12 for chlorine. Show that these data are consistent with the law of multiple proportions.

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Ques: Phosphorus and chlorine form two compounds The first compound contains 22.54% by mass of phosphorus and 77.46% by mass of chlorine. In the second compound the percentages are 14.88 for phosphorus and 85.12 for chlorine. Show that these data are consistent with the law of multiple proportions.

Ans: In the first compound,

       Percentage of phosphorus = 22.54 

       Percentage of chlorine = 77.46

Thus, 22.54 g of phosphorus combines with 77.46 g chlorine.

In the second compound,

       Percentage of phosphorus = 14.88

       Percentage of chlorine = 85.12

Thus, 14.88 g of phosphorus combine with 85.12 g of chlorine.

Let us fix the mass of phosphorus as 1 g and find the different masses of chlorine which combine with 1 g of phosphorus in two compounds.

In the first compound,

     Mass of chlorine which combines with 22.54 g of phosphorus = 77.46 g

    The mass of chlorine which combines with 1 g of phosphorus = 77.46 / 22.54 = 3.44 g

In the second compound,

     Mass of chlorine which combines with 14.88 g of phosphorus = 85.12 g

    Mass of chlorine which combines with 1 g of phosphorus = 85.12 / 14.88 = 5.72

The ratio of the masses of chlorine which combines with the fixed mass of phosphorus (1 g) in the two compounds is 

3.44 : 5.72

1: 1.66 or 3:5 (approximately)

This is a simple whole number ratio. Therefore, the data is in agreement with the law of multiple proportions.

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