Answer to Question #68699 in General Chemistry for aman

Question

sulphur and oxygen are known to form two compounds.the sulphur content in one of these is 51% while in other is 41%.show that this data is in agreement with law of multiple proportions.

Answer 1

Solution
The law of multiple proportions is formulated as the following: If two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers.

Assume that we have certain amounts of the two different compounds of oxygen and sulphur and each of them contains, for example, 100 grams of sulphur. From the mass contents of sulphur in these compounds we can calculate the corresponding masses of the compounds and the masses of oxygen in both of them (we can name them oxide 1 and oxide 2):
m(oxide 1)=m(S)/ω(S) =100/0.51≈196.08g;
m(O in oxide 1)=m(oxide 1)-m(S)=196.08-100=96.08g;
m(oxide 2)=m(S)/ω(S) =100/0.41≈243.90g;
m(O in oxide 2)=m(oxide 2)-m(S)=243.90-100=143.90g.
Now we can find the ratio between the masses of oxygen in oxide 1 and oxide 2:
m(O in oxide 2) ∶m(O in oxide 1)=143.90∶96.08=1.498∶1≈1.5∶1=3∶2.
So, we found out that oxide 1 has the formula SO2 and oxide 2 is SO3. If we will perform the same calculations with the mass of sulphur equal to its molar mass (32.065 g/mol), we will obtain the masses of oxygen close to 32 and 48 grams, respectively. The small deviations from the whole numbers are caused by the fact that elements often have their atomic masses being not whole numbers due to the existence of a few isotopes.