The initial pressure of a gas is $1 atm$ . To compress it to $1 / 4^{t h}$ of its initial volume, what will be the pressure required at constant temperature?

1 atm

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2 atm

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1 torr

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4 atm

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Solution

The correct option is D $4 atm$
Consider the initial volume and pressure of the gas to be $V L$ and $P_{1} atm$ respectively and the final pressure and volume to be $P_{2}$ and $V_{2}$ respectively.
According to the question $V_{2} = \frac{V}{4}$ also $P_{1} = 1 atm$ .
According to Boyle's law,
$P_{1} V_{1} = P_{2} V_{2}$ at constant $T$ & $n$
$P_{2} = \frac{P_{1} V_{1}}{V_{2}} = \frac{1 atm \times V}{V / 4} = 4 atm$

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Boyle's Law

Standard XII Chemistry

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The initial pressure of a gas is 1 atm. To compress it to 1/4th of its initial volume, what will be the pressure required at constant temperature?

The initial pressure of a gas is $1 atm$ . To compress it to $1 / 4^{t h}$ of its initial volume, what will be the pressure required at constant temperature?