Question

Assuming that petrol is octane $({C_8}{H_{18}})$ and has density $0.8gm{L^{ - 1}}, 1.425$ litre of the petrol on complete combustion will consume:
A. $50$ moles of ${O_2}$
B. $100$ moles of ${O_2}$
C. $125$ moles of ${O_2}$
D. $200$ moles of ${O_2}$

Answer 1

At first we will write what is given in the question. Then we will write the density formula and from there we will calculate the mass of the octane. From there we will calculate the moles of the octane. Then we will write the equation of octane combustion. Once we write the balanced equation we will find the moles of oxygen needed. Then we will choose the correct option.

Complete answer:
Step1. We have given the octane. The density of the octane is $0.8g/ml$.
The amount of the petrol is $1.425l$
We need to find the moles of oxygen needed.
Step2. The density formula is the mass divided by the volume.
$density = \dfrac{{mass}}{{volume}}$
Here the density and the volume is given.
$0.8 = \dfrac{{mass}}{{1.425}}$
Mass will be $1140g$ of octane.
Step3. Now we will calculate the moles of the octane
$moles = \dfrac{{mass}}{{mole.mass}} = \dfrac{{1140}}{{114}} = 10$. It is 10 moles
Step4. Now will write the equation of combustion of the octane. It would produce carbon dioxide and water. The reaction is given below.
$2{C_8}{H_{18}} + 25{O_2} \to 16C{O_2} + 18{H_2}O$
From here we can see that for the combustion of the one mole of the octane we need $12.5$models of the oxygen.
To the ten moles of octane will take the $125$ moles of the oxygen.
Step5. So we find that the $1.425l$ of octane will take $125$ moles of the oxygen for combustion. Hence the, ‘C. $125$ moles of ${O_2}$’ is the correct answer.

Note: Combustion reactions happen when the hydrogen carbon reacts to the oxygen. It produces a lot of heat and produces water and carbon dioxide. Petrol is highly inflammable. It is used in vehicles.