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Ideal Gas Equation

A 100 ml ve...

Question

A $100 m l$ vessel containing $O_{2} (g)$ at $1.0 a t m$ and $400 K$ is connected to a $300 m l$ vessel containing $N O (g), 1.5 a t m$ and $400 K$ by means of a narrow tube of negligible volume where gases react to form $N O_{2}$ . Final pressure of mixture will be:

1.375 a t m

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0.125 a t m

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1 a t m

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1.5 a t m

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Solution

The correct option is A $1.375 a t m$
Using $P V = n R T$

As T is constant,

$P_{i} V_{i} = P_{f} V_{f}$

$P_{1} V_{1} + P_{2} V_{2} = P_{f} (V_{1} + V_{2})$

$\Rightarrow P_{f} = \frac{P_{1} V_{1} + P_{2} V_{2}}{V_{1} + V_{2}}$

$∴ P_{f} = \frac{1 \times 100 + 1.5 \times 300}{100 + 300} = \frac{100 + 450}{400} = 1.375$

Hence, option A is correct.

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