JEE MAIN - Chemistry (2022 - 24th June Morning Shift - No. 1)

If a rocket runs on a fuel (C15H30) and liquid oxygen, the weight of oxygen required and CO2 released for every litre of fuel respectively are :

(Given : density of the fuel is 0.756 g/mL)

1188 g and 1296 g
2376 g and 2592 g
2592 g and 2376 g
3429 g and 3142 g

Explanation

C15H30 + $${{45} \over 2}$$O2 $$\to$$ 15CO2 + 15H2O

Given, volume of fuel = 1L = 1000 ml

And density of fuel = 0.756 g/ml

We know,

$$d = {w \over v}$$

$$ \Rightarrow 0.756 = {w \over {1000}}$$

$$\Rightarrow$$ w = 756 gm

$$\therefore$$ weight of fuel = 756 gm

Molar mass of C15H30 = 15 $$\times$$ 12 + 30 = 210

$$\therefore$$ Moles of C15H30 = $${{756} \over {210}}$$

From equation you can see,

1 mole of C15H30 react with $${{45} \over 2}$$ mole of O2

$$\therefore$$ $${{756} \over {210}}$$ moles of C15H30 react with $${{45} \over 2} \times {{756} \over {210}}$$ moles of O2

$$\therefore$$ Moles of O2 required = $${{45} \over 2} \times {{756} \over {210}}$$

$$\therefore$$ Mass of O2 required = $${{45} \over 2} \times {{756} \over {210}}$$ $$\times$$ 32 = 2592 g

Also,

From 1 mole of C15H30 15 moles of CO2 formed

$$\therefore$$ From $${{756} \over {210}}$$ moles of C15H30 15 $$\times$$ $${{756} \over {210}}$$ moles of CO2 formed

$$\therefore$$ Moles of CO2 formed = 15 $$\times$$ $${{756} \over {210}}$$

$$\therefore$$ Mass of CO2 formed = 15 $$\times$$ $${{756} \over {210}}$$ $$\times$$ 44 = 2376 g

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