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)
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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