Question

If a LPG cylinder contains mixture of butane and isobutane, then the amount of oxygen that would be required for combustion of \[1\;\,kg\] of it will be:
(A) $2.50 \times {10^3}\,kg$
(B) $4.50 \times {10^3}\,kg$
(C) $1.8 \times {10^3}\,kg$
(D) $3.58 \times {10^3}kg$

Answer 1

Hint: Isobutane is a structural isomer of butane and both hydrocarbons have the same molecular formula. They belong to the Alkane family of the hydrocarbons and their molecular formula is ${C_4}{H_{10}}$. The mixture of these gases is widely used as domestic fuels.

Complete step by step answer:
Butane is mainly used as a gasoline mixture, either alone or in with propane, and also as feedstock for the production of ethane and butadiene. Butane and propane these two gases come from natural gas or petroleum refineries and are generally found together. Butane is stored as a liquid in the form of LPG. This mixture is widely used as domestic fuels in the household in cylinders.
The reaction of standard combustion enthalpy of butane represents the combustion when $1$ mole of butane or isobutene is burned in the presence of oxygen. The reaction is given by the equation:
\[{C_4}{H_{10}}(g) + \dfrac{{13}}{2}\,{O_2}\,(g) \to 4C{O_2}(g) + 5{H_2}O(l)\]
From the reaction, we can deduce that $1$ mole of butane requires $\dfrac{{13}}{2} \times 32 = 208g$ of oxygen.
Now we will calculate the amount of oxygen required to burn $1$ kg of Mixture.
Oxygen required to burn $58g$ of mixture $ = 208g$
 Oxygen required to burn $1g$ of mixture $ = \dfrac{{208}}{{58}}$
Oxygen required to burn $1000g$ of mixture $ = \dfrac{{208}}{{58}} \times 1000 = 3.58 \times {10^3}kg$
Hence, we can say that the amount of oxygen that would be required for the combustion of \[1\;\,kg\] LPG mixture is $3.58 \times {10^3}kg$.
Therefore, option (D) is correct.

Note:
Butane exists as a gas at room temperature. It is the fourth member of the homologous series of alkane. It is a saturated hydrocarbon with a $4$ carbon member ring with an unbranched structure. Structure isomerism is that isomerism in which the molecular formula of the remains is the same but its structural formula is different. Isobutane shows structural isomerism.