Question

Carbon and oxygen forms two compounds. Carbon content in one of them is $42.9\% $ while in the other is $27.3\% $. The given data is in support with:
A.Law of definite proportions
B.Law of reciprocal proportions
C.Law of multiple proportion
D.Law of conservation of mass

Answer 1

Hint: Carbon has a valency of 4. So it forms the compound by sharing the electrons as it requires a large amount of energy in completing its octet by gaining or losing electrons. We know that carbon and oxygen generally together form two compounds namely carbon monoxide and carbon dioxide.

Step by step answer: It is given that in the two compounds formed by carbon and oxygen, the carbon contents are $42.9\% $ and $27.3\% $ respectively. Let us consider both the cases one by one.
Case 1: -In this case carbon first reacts with oxygen to form carbon monoxide.
\[C + O \to CO\]
Let $100\,gm$ be the total mass of compound;
The mass of carbon = $42.9gm$
The mass of oxygen = \[\left( {{\rm{ }}100 - {\rm{ }}42.9} \right) = 57.1gm\]
Since in the reaction one carbon reacts with only one oxygen atom,
So, mass of one gram of carbon$\left( {100 - 27.3} \right) = 72.7$ $ = \dfrac{{42.9}}{{57.1}} = 0.751$gm of carbon atom
Case 2: -$C + {O_2} \to C{O_2}$
In 100 gm of compound;
The mass of carbon = $27.3gm$
The mass of oxygen =$\left( {100 - 27.3} \right) = 72.7$gm
Since in this case one carbon reacts with two oxygen molecules,
So, mass of one gram of carbon$ = \dfrac{{27.3}}{{72.7}} = 0.375$
Hence the ratio of carbon in both cases will be$ = \dfrac{{0.751}}{{0.375}} = 2:1$
Hence the law of multiple proportions is verified.

Hence, option (C) Law of multiple proportions, is the correct option.

Note: The different reactions which occur are classified based on the balanced chemical equation so be careful while balancing them.Thus, Law of multiple proportion states that the masses of one element combined with a fixed mass of the other element are in a ratio of whole numbers.