If a rocket runs on a fuel (\(\mathrm{C}_{15} \mathrm{H}_{30}\)) and liquid oxygen, the weight of oxygen required and \(\mathrm{CO}_{2}\) released for every litre of fuel respectively are: (Given: density of the fuel is \(0.756 \mathrm{~g} / \mathrm{mL}\))

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Some Basic Concepts of Chemistry

If a rocket runs on a fuel (

C_{15} H_{30}

) and liquid oxygen, the weight of oxygen required and

CO_{2}

released for every litre of fuel respectively are: (Given: density of the fuel is

0.756 g / mL

)

Answer: (C)

The balanced combustion equation is

C_{15} H_{30} + \frac{45}{2} O_{2} \to 15 CO_{2} + 15 H_{2} O

. For 1 litre (1000 mL) of fuel, mass =

0.756 \times 1000 = 756

g. Moles of fuel =

\frac{756}{210} = 3.6

mol. From stoichiometry, moles of

O_{2}

required =

3.6 \times \frac{45}{2} = 81

mol, so mass of

O_{2} = 81 \times 32 = 2592

g. Moles of

CO_{2}

produced =

3.6 \times 15 = 54

mol, so mass of

CO_{2} = 54 \times 44 = 2376

g. Answer: (C) 2592 g and 2376 g.

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option