Question

A gaseous alkane is exploded with oxygen. The volume of $ {O_2} $ for complete combustion of alkane to $ C{O_2} $ formed is in the ratio 7:4. The molecular formula of alkane is:
(A) $ {C_2}{H_6} $
(B) $ {C_3}{H_8} $
(C) $ C{H_4} $
(D) $ {C_4}{H_{10}} $

Answer 1

Hint: By dividing the mass of a single element in one mole of a compound by the mass of one mole of the total compound, percent composition may be determined from a molecular formula. This number is shown as a percentage. The molecular formula is used to compute the percent composition of a compound: divide the mass of each element contained in one mole of the compound by the total molar mass of the compound.

Complete answer:
The chemical reaction in which a hydrocarbon interacts with oxygen to produce carbon dioxide, water, and heat is known as hydrocarbon combustion. Hydrocarbons are molecules that have both hydrogen and carbon in them. They are well known as the main component of fossil fuels such as natural gas, petroleum, and coal. As a result, fossil fuels are commonly referred to as hydrocarbon resources. Fossil fuels are used to generate energy by combusting them. Despite the presence of contaminants in fossil fuels, hydrocarbon combustion is the fundamental process of fossil fuel combustion.
 $ {C_x}{H_y} + N({O_2}) \leftrightarrow x(C{O_2}) + \dfrac{y}{2}({H_2}O) $
x denotes the number of carbon atoms in the hydrocarbon, whereas y denotes the amount of hydrogen atoms.
The number of oxygen atoms required in the hydrocarbon combustion process is denoted by the letter N. Hence it can be modified as
 $ {{\mathbf{C}}_{\text{n}}}{{\mathbf{H}}_{2{\text{n}} + 2}} + \left[ {{\mathbf{n}} + \dfrac{{{\mathbf{n}} + {\mathbf{1}}}}{{\mathbf{2}}}} \right]{{\mathbf{O}}_2} \to {\mathbf{nC}}{{\mathbf{O}}_2} + ({\mathbf{n}} + {\mathbf{1}}){{\mathbf{H}}_2}{\text{O}} $
Given,
 $ \dfrac{{{\mathbf{n}} + \dfrac{{{\mathbf{n}} + 1}}{2}}}{{\text{n}}} = \dfrac{7}{4} $
 $ {\mathbf{n}} = {\mathbf{2}} $
Hence, the alkane is $ {{\text{C}}_2}{{\text{H}}_6} $
Hence, the correct option is A.

Note:
Because various hydrocarbons have varying hydrogen-to-carbon ratios, they create variable water-to-carbon dioxide ratios. In general, the higher the carbon-to-hydrogen ratio, the longer and more complicated the molecule. As a result, identical amounts of various hydrocarbons will produce varying amounts of carbon dioxide, depending on the carbon to hydrogen ratio in each molecule.