# If 16 L of a gas at room temperature exerts a pressure of 5 kPa on its container, what pressure will the gas exert if the container's volume changes to 2 L?

Jun 6, 2017

$40$ $\text{kPa}$

#### Explanation:

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

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

We're asked to find the final pressure, ${P}_{2}$. Let's plug in the known variables, and rearrange the equation to solve for ${P}_{2}$:

P_2 = (P_1V_1)/(V_2) = ((5"kPa")(16cancel("L")))/((2cancel("L"))) = color(red)(40 color(red)("kPa"

We know that from Boyle's law that a gas's pressure and volume it occupies are inversely proportional. Our result makes intuitive sense, because since the volume decreased (by a factor of $8$), our pressure must have increased (by a factor of $8$).