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A vessel has 6 gram Oxygen gas at pressure P and temperature 400K. A hole is made in the vessel and Oxygen gas leaked find out how much amount of Oxygen gas leaked out if final pressure is P/2 and temperature is 300K.​

Answer»

Answer:

2g

Explanation:

Given

P_{1} = P \\ P_{2} = \frac{P}{2} \\ V_{1} = V \\ V_{2} = V \\ T_{1} = 400 \: K \\ T_{2} = 300 \: K

\bold{Now, \: we \: need \: n_{1} \: and \: n_{2}}

n_{1} = \frac{6}{32} \\ n_{2} = \frac{M}{32}

We KNOW that

\frac{P_{1}V_{1}}{n_{1}T_{1}} = \frac{P_{2}V_{2}}{n_{2}T_{2}}

On PUTTING all the VALUES

= > \frac{P \times V}{400 \times \frac{6}{32} } = \frac{ \frac{P}{2} \times V}{300 \times \frac{M}{32} }

= > \frac{ \cancel{P} \times \cancel{V} \times \cancel{32}}{ 400 \times 6} = \frac{ \cancel{P} \times \cancel{V} \times \cancel{32}}{ 2 \times {300} \times M} \\ = > 2400 = 600M \\ = > M = \frac{ \cancel{2400}}{ \cancel{600}} \\ = > \boxed{M = 4g}

\bold{Amount \: of \: leaked \: gas = 6g - 4g} \\ \bold{Amount \: of \: leaked \: gas = 2g}


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