Question

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

• A. $1\text{atm}$
• B. $2\text{atm}$
• C. $1\text{torr}$
• D. $4\text{atm}$

Answer 1

The correct option is D $4\text{atm}$

Consider the initial volume and pressure of the gas to be $V\text{L}$ and $P_1\text{atm}$ 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 $P_1=1\text{atm}$.
According to Boyle's law,
$P_1{V}_1=P_2{V}_2$ at constant $T$ & $n$
$P_2=\frac{P_1{V}_1}{V_2}=\frac{1\text{atm}\times V}{V/4}=4\text{atm}$