Question

Assuming that petrol is octane ${{C}_{8}}{{H}_{18}}$ and has a density of $0.8gm{{L}^{-1}}$, 1.425 litre of petrol on combustion will consume:
A. 100 mole of oxygen
B. 125 mole of oxygen
C. 150 mole of oxygen
D. 175 mole of oxygen

Answer 1

Hint: When petrol on combustion produces carbon monoxide, and nitrogen oxides that are poisonous gases. We will find the number of moles by the formula:
\[Number\text{ }of\text{ }moles=\dfrac{Given\text{ }mass}{Molecular\text{ }mass}\]

Complete Solution :
- We are being provided with density= $0.8gm{{L}^{-1}}$,
- And volume of octane is=1.425 litre
- As we know that formula of density is
\[density=\dfrac{mass}{volume}\]
- So, by putting values of density and volume in above formula, we get:
\[0.8=\dfrac{mass}{1.425}\]

- So, mass of octane=
$\begin{align}
 & 0.8\times 1.425\times 1000 \\
 & =1140g \\
\end{align}$
 - Here, we have converted litre into grams.

 Now, we will find the molecular mass of octane:
\[\begin{align}
 & {{C}_{8}}{{H}_{18}} \\
 & = 8\times \left( 12 \right)+18\times \left( 1 \right) \\
 & = 96 + 18 \\
 & = 114g \\
\end{align}\]
- The molecular mass of octane is: 114g

- Now we will calculate the number of moles,
\[Number\text{ }of\text{ }moles=\dfrac{Given\text{ }mass}{Molecular\text{ }mass}\]
\[\begin{align}
  & =\dfrac{1140}{114} \\
 & = 10mole \\
\end{align}\]
- Now, we will see the reaction of combustion of octane:
\[2{{C}_{8}}{{H}_{18}}+25{{O}_{2}}\to 16C{{O}_{2}}+18{{H}_{2}}O\]

- Number of moles of oxygen required for the combustion of one mole octane= 12.5 moles
- Therefore, we can say that the number of moles of oxygen required for the combustion of 10 mole of octane=
$\begin{align}
 & 12.5\times 10 \\
 & =125mole \\
\end{align}$
- Hence, we can conclude that the correct option is (B), that is 1.425 litres of octane will consume about 125 moles of oxygen.
So, the correct answer is “Option B”.

Note: - We should not forget to write units after solving any question.
- Octane is hydrocarbon, which is very harmful, if one swallowed it. It is found to be flammable. It actually forms explosive mixtures when reacted with air.