Question

1 mole of \[{C_x}{H_y}\] requires 12 moles of \[{O_2}\] for combustion. If the molecular mass of the hydrocarbon is 112g. Then molecular formula of \[{C_x}{H_y}\] is
(A) \[{C_6}{H_{10}}\]
(B) \[{C_8}{H_{16}}\]
(C) \[{C_8}{H_8}\]
(D) \[{C_9}{H_7}\]

Answer 1

Hint: Here in the question, they have asked us to find the molecular formula of the hydrocarbon of molecular mass 112g. Since the molecular mass has already been given, we can find the molecular formula by using a combustion analysis method.

Complete step by step solution:
In order to find the molecular formula of the compound \[{C_x}{H_y}\], we can use the combustion analysis method. First, let us see what combustion analysis method is. It is a method which is used to determine the element’s composition in the hydrocarbon. The elements which can take place in the combustion analysis are Hydrogen, Carbon, Oxygen, Nitrogen and Sulphur. If we are able to find the number of moles of each combustion product, then we can easily determine the molecular formula of the Hydrocarbon.
By using the formula of combustion analysis, i.e.
\[{C_x}{H_y} + (x + \dfrac{y}{4}){O_2} \to xC{O_2} + \dfrac{y}{2}{H_2}O\]…. (1)
It is given that 12 moles of \[{O_2}\]are required for combustion, therefore
\[x + \dfrac{y}{4} = 12\]…... (2)
Multiply equation (2) by 4, we get
\[4x + y = 48\]…… (3)
Also, molar mass of \[{C_x}{H_y}\]= 112g
Consider \[{C_x}{H_y}\],
It can be written as \[12 \times x + 1 \times y = 112g\]…… (4)
Comparing equation (3) and (4), we get
\[8x = 64\]
Therefore,
\[x = 8\]
Putting the value of x in equation (3), we get
\[32 + y = 48\]
\[y = 16\]
Finally substituting x and y in \[{C_x}{H_y}\], we get \[{C_8}{H_{16}}\].

Therefore, the correct answer is option (B) \[{C_8}{H_{16}}\].

Additional information:
Combustion reaction used for the following purposes.
- Mostly it is used in chemical reactions.
- In the internal combustion engine.
- In the propulsion of the rocket.
- heating devices also make use of this.
- In explosives.

Note: Combustion reaction works as follows: In order to find the molecular formula of a substance, we will be combusting that substance whose molecular mass is already known. Then we would obtain a product of carbon dioxide and water which are captured. Then the products are weighed. From this mass of the product, we can calculate the amount of carbon, oxygen and hydrogen.