\(\mathrm{C}_{15} \mathrm{H}_{30}+\frac{45}{2} \mathrm{O}_2 \rightarrow 15 \mathrm{CO}_2+15 \mathrm{H}_2 \mathrm{O}\)
Given, volume of fuel \(=1 \mathrm{~L}=1000 \mathrm{ml}\)
And density of fuel \(=0.756 \mathrm{~g} / \mathrm{ml}\)
We know,
\(\mathrm{d}=\frac{\mathrm{w}}{\mathrm{v}} \)
\(\Rightarrow 0.756=\frac{\mathrm{W}}{1000} \)
\(\Rightarrow \mathrm{W}=756 \mathrm{gm} \)
\(\therefore \text { weight of fuel }=756 \mathrm{gm} \)
\(\text { Molar mass of } \mathrm{C}_{15} \mathrm{H}_{30}=15 \times 12+30=210 \)
\(\therefore \text { Moles of } \mathrm{C}_{15} \mathrm{H}_{30}=\frac{756}{210}\)
\(\therefore\) weight of fuel \(=756 \mathrm{gm}\)
Molar mass of \(\mathrm{C}_{15} \mathrm{H}_{30}=15 \times 12+30=210\)
\(\therefore\) Moles of \(\mathrm{C}_{15} \mathrm{H}_{30}=\frac{756}{210}\)
From equation you can see,
1 mole of \(\mathrm{C}_{15} \mathrm{H}_{30}\) react with \(\frac{45}{2}\) mole of \(\mathrm{O}_2\)
\(\therefore \frac{756}{210}\) moles of \(\mathrm{C}_{15} \mathrm{H}_{30}\) react with \(\frac{45}{2} \times \frac{756}{210}\) moles of \(\mathrm{O}_2\)
\(\therefore\) Moles of \(\mathrm{O}_2\) required \(=\frac{45}{2} \times \frac{756}{210}\)
\(\therefore\) Mass of \(\mathrm{O}_2\) required \(=\frac{45}{2} \times \frac{756}{210} \times 32=2592 \mathrm{~g}\)
Also,
From 1 mole of \(\mathrm{C}_{15} \mathrm{H}_{30} 15\) moles of \(\mathrm{CO}_2\) formed
\(\therefore\) From \(\frac{756}{210}\) moles of \(\mathrm{C}_{15} \mathrm{H}_{30} 15 \times \frac{756}{210}\) moles of \(\mathrm{CO}_2\) formed
\(\therefore\) Moles of \(\mathrm{CO}_2\) formed \(=15 \times \frac{756}{210}\)
\(\therefore\) Mass of \(\mathrm{CO}_2\) formed \(=15 \times \frac{756}{210} \times 44= 2376 \mathrm{~g}\)