# A gas occupies 50 L at a pressure of 2 atm. What is the volume when the pressure is increased to 10 atm?

May 31, 2017

$10$ $\text{L}$

#### Explanation:

We're asked to calculate the new volume of a gas when its pressure is increased.

To solve this, we can use the pressure-volume relationship of gases, illustrated by Boyle's law:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

where

• $P$ is the initial ($\text{1}$) and final ($\text{2}$) pressure of the gas, and

• $V$ is the initial ($\text{1}$) and final ($\text{2}$) volume of the gas.

Let's plug in our known variables, and rearrange this equation to solve for the final volume, ${V}_{2}$:

V_2 = (P_1V_1)/(P_2) = ((2cancel("atm"))(50"L"))/(10cancel("atm")) = color(red)(10"L"

Thus, when the pressure of the gas was increased by a factor of $5$ ($2 \text{atm}$ to $10 \text{atm}$), the volume decreased by a factor of $5$ ($50 \text{L}$ to $10 \text{L}$).