The minimum number of moles of

Question:

The minimum number of moles of $\mathrm{O}_{2}$ required for complete combustion of 1 mole of propane and 2 moles of butane is ______ .

Solution:

(18)

Complete combustion of hydrocarbons can be represented by the following reaction.

$\mathrm{C}_{x} \mathrm{H}_{y}+\left(x+\frac{y}{4}\right) \mathrm{O}_{2} \longrightarrow x \mathrm{CO}_{2}+\frac{y}{2} \mathrm{H}_{2} \mathrm{O}$

For propane combustion reaction is

$\mathrm{C}_{3} \mathrm{H}_{8}+\left(3+\frac{8}{4}\right) \mathrm{O}_{2} \longrightarrow 3 \mathrm{CO}_{2}+\frac{8}{2} \mathrm{H}_{2} \mathrm{O}$

$\therefore \mathrm{C}_{3} \mathrm{H}_{8}+5 \mathrm{O}_{2} \longrightarrow 3 \mathrm{CO}_{2}+4 \mathrm{H}_{2} \mathrm{O}$

Similarly, for butane is

$\mathrm{C}_{4} \mathrm{H}_{10}+\left(4+\frac{10}{4}\right) \mathrm{O}_{2} \longrightarrow 4 \mathrm{CO}_{2}+\frac{10}{2} \mathrm{H}_{2} \mathrm{O}$

$\therefore \mathrm{C}_{4} \mathrm{H}_{10}+\frac{13}{2}, \mathrm{O}_{2} \longrightarrow 4 \mathrm{CO}_{2}+5^{2} \mathrm{H}_{2} \mathrm{O}$

$\because$ For $1 \mathrm{~mol}$ of $\mathrm{C}_{4} \mathrm{H}_{10}$ required $\mathrm{O}_{2}=\frac{13}{2} \mathrm{~mol}$

$\therefore$ For $2 \mathrm{~mol}$ of $\mathrm{C}_{4} \mathrm{H}_{10}$ required $\mathrm{O}_{2}=\frac{13}{2} \times 2=13 \mathrm{~mol}$