Question

What mass of octane should be taken in a total $100gm$ mixture of octane and oxygen gas so as to obtain maximum $C{O_2}\left( {gm} \right)$ on complete combustion?
A.$100gm$
B.$50gm$
C.$23.54gm$
D.$22.17gm$

Answer 1

Octane is an alkane that reacts with oxygen to form carbon dioxide and water. One mole of octane reacts with $12.5$ moles of oxygen gas to form the products. Calculating the number of moles of each reactant and equating them according to the chemical equation gives the mass of octane in grams.

Complete answer: Given that octane and oxygen gas were reacted. Octane is an alkane or saturated hydrocarbon; it reacts with oxygen to produce carbon dioxide and water vapor.
The balanced chemical equation is:
${C_8}{H_{18}} + \dfrac{{25}}{2}{O_2} \to 8C{O_2} + 9{H_2}O$
Given that the total mass of the mixture is $100gm$
Let the mass of octane is $xgm$ and the mass of oxygen gas be $\left( {100 - x} \right)gm$
The molar mass of octane is $114amu$ and the molar mass of oxygen gas is $32amu$
The number of moles of a substance will be equal to the ratio of the mass of a substance to the molar mass of a substance.
The number of moles of octane will be $\dfrac{x}{{114}}$ moles
The number of moles of oxygen gas will be $\dfrac{{100 - x}}{{32}}$ moles
According to the chemical equation, one mole of octane will be equal to $\dfrac{{25}}{2}$ moles of oxygen gas. The above two equations must be written as:
$\dfrac{{\dfrac{x}{{114}}}}{1} = \dfrac{{\dfrac{{100 - x}}{{32}}}}{{\dfrac{{25}}{2}}}$
By simplifying the above values, the value of x will be
$x = \dfrac{{22800}}{{1028}} = 22.17$
Thus, the mass of octane is $22.17gm$
Option D is the correct one.

Note:
The number of moles of each reactant must be calculated accurately. The balanced chemical equation must be considered while calculating the number of moles. The number of moles of oxygen gas required to react with the number of moles of octane must be written from a balanced chemical equation.