Question

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`?

Answer 1

`40` `"kPa"`

Explanation:

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

`P_1V_1 = P_2V_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`).