Question

Assuming that petrol is octane $\left( {{C_8}{H_{18}}} \right)$and has density $0.8$g/ml, $1.425$litre of petrol on complete combustion will consume:
A.50 mole of ${O_2}$
B.100 mole of ${O_2}$
C.125 mole of ${O_2}$
D.200 mole of ${O_2}$

Answer 1

To solve this question, the knowledge of combustion and density are needed. Combustion means reaction of a substance with oxygen.

Formula used:
${\text{d = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}{\text{ = }}\dfrac{{\text{m}}}{{\text{v}}}$.
${\text{n = }}\dfrac{{{\text{mass}}}}{{{\text{mol}}{\text{.wt}}{\text{.}}}}$

Complete step by step answer:
Molecular weight of octane $\left( {{C_8}{H_{18}}} \right)$=$\left[ {12 \times 8} \right] + \left[ {18 \times 1} \right]$=$96 + 18 = 114$ ${\text{gmo}}{{\text{l}}^{ - 1}}$
As density ${\text{d = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}{\text{ = }}\dfrac{{\text{m}}}{{\text{v}}}$
Therefore, volume of octane= $1.425$ litre, density =$0.8$ ${\text{g/mL}}$,
It’s mass = $0.8 \times 1.425 \times 1000$=$1140$g.
Now, no. of moles,
${\text{n = }}\dfrac{{{\text{mass}}}}{{{\text{mol}}{\text{.wt}}{\text{.}}}}$ = $\dfrac{{1140}}{{114}}$ = $10$moles of $\left( {{C_8}{H_{18}}} \right)$
The reaction between $\left( {{C_8}{H_{18}}} \right)$and ${O_2}$for the combustion is:
$2{C_8}{H_{18}} + 25{O_2} \to 16C{O_2} + 18{H_2}O$
So for 2 moles of octane, 25 moles of oxygen is required.
Therefore $10$ mole of octane will consume, $\dfrac{{25}}{2} \times 10$ = 125 moles of ${O_2}$

So, the correct answer is option C.

Note:
1.This is the reaction that takes place in the internal combustion engine of any vehicle. The petrol is combusted in presence of oxygen and carbon dioxide and water vapour are released as products. This is an exothermic reaction and a high amount of heat energy is generated due to the combustion. This heat energy is converted into kinetic energy which runs the vehicle.
2.Burning of 1 L petrol releases about $2.3$kg of carbon dioxide.
3.In this combustion reaction, hydrogen from the petrol combines with oxygen from air to form water vapour, while the carbon from the petrol combines with oxygen from air to form carbon dioxide.
4.The heat energy released during the reaction is from the dissociation of the bonds that store energy in the form of potential energy.