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Stoichiometric Calculations

In a closed v...

Question

In a closed vessel at STP, $50 L$ of $C H_{4}$ is ignited with $750 L$ of air (containing $20$ % $O_{2}$ ). The number of moles of $O_{2}$ remaining in the vessel on cooling to room temperature is closest to:

A

5.8

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B

2.2

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C

4.5

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D

6.7

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Solution

The correct option is B $2.2$
At STP, 22.4 L of any gas $= 1$ mole.

$50 L$ of $C H_{4} = \frac{50 L}{22.4 L / m o l} = 2.23$ moles.

$750 L$ of air $= \frac{750 L}{22.4 L / m o l} = 33.48$ moles.

The air contains $20$ % $O_{2}$ .
The number of moles of $O_{2} = 33.48 \times \frac{20}{100} = 6.697$ moles.

$C H_{4} + 2 O_{2} \to C O_{2} + 2 H_{2} O$

2.23 moles of $C H_{4}$ will react with $2 \times 2.23 = 4.46$ moles of $O_{2}$ .

$6.697 - 4.46 ≃ 2.2$ moles of $O_{2}$ will remain in the vessel on cooling to room temperature.

Hence, option $B$ is correct.

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