Question

By means of the given analytical results show that the law of multiple proportions is true.

Mercurous chloride	Mercuric chloride
Mercury = 84.92%	Mercury = 73.80%
Chlorine = 15.08%	Chlorine = 26.20%

Answer 1

Hint: The Law of multiple proportions, which is also known as Dalton’s law states that when one element combines with another element forming more than one compound, the mass ratio of the elements in the compounds is in the ratio of the simple whole number of each other.

Complete Step by step solution:
-The law of multiple proportions was first expressed by John Dalton in his observation in the year 1804. The French chemist named Joseph Proust a few years ago proposed the law of definite proportions which stated that the elements combined to form compounds in well-defined proportions rather than mixing in any random proportion. Antoine Lavoisier proved the law of conservation of mass, which supported Dalton’s law.
-Let us consider the given cases one by one and check whether they follow the law of multiple proportions or not.
-In case 1, that is Mercurous chloride, it is given that 84.92% of mercury combines with 15.08% of chlorine. Considering 100% as 100 gm, therefore, 84.92 g of mercury combines with = 15.08 g of chlorine
Therefore, 1 g of mercury will combine with $=\dfrac{15.08}{84.92}=0.178g$ chlorine -(1)
-In case 2, that is Mercuric chloride, it is given that 73.8% of mercury combines with = 26.2% of chlorine. Considering 100% as 100gm, therefore 73.8 g of mercury combines with = 26.2 g of chlorine.
Therefore, 1 g of mercury will combine with $=\dfrac{26.2}{73.8}=0.35g$ chlorine -(2)
-Taking the ratio of 1 g of mercury from equations (1) and (12) which will react with 1g of chlorine is $0.178:0.35=1:1.96\simeq 1:2$

Hence, the given compounds follow the law of multiple proportions.

Note: The law of multiple proportions had certain limitations. This law is best when considered simple compounds. For example, if we try to demonstrate this law using the hydrocarbons decane and undecane which have chemical formula as ${{C}_{10}}{{H}_{22}}$ and ${{C}_{11}}{{H}_{24}}$ respectively, we will find that 100 grams of carbon reacts with 18.46 grams of hydrogen to produce decane ow it can react with 18.31 grams of hydrogen to produce undecane. The ratio of hydrogen masses, in this case, is 121:120 which is not a ratio of ‘small’ whole numbers. Hence the law of multiple proportions failed with non-stoichiometric compounds and also didn’t work well with polymers and oligomers.