Question

What volume will a balloon occupy at 1.0 atm, if the balloon has a volume of 7.6 L at 3.8 atm?

Answer 1

`"29 L"`

Explanation:

The thing to remember here is that pressure and volume have an inverse relationship when temperature and number of moles of gas are kept constant -- this is known as Boyle's Law.

In other words, when temperature and number of moles of gas are kept constant, increasing the pressure will cause the volume to decrease; similarly, decreasing the pressure will cause the volume to increase.

Mathematically, this is written as

`color(blue)(bar(ul(|color(white)(a/a)color(black)(P_1 * V_1 = P_2 * V_2)color(white)(a/a)|)))`

Here

`P_1`, `V_1` are the pressure and volume of the gas at an initial state
`P_2`, `V_2` are the pressure and volume of the gas at a final state

Rearrange to solve for `V_2`

`P_1 * V_1 = P_2 * V_2 implies V_2 = P_1/P_2 * V_1`

Plug in your values to find

`V_2 = (3.8 color(red)(cancel(color(black)("atm"))))/(1.0color(red)(cancel(color(black)("atm")))) * "7.6 L" = color(green)(bar(ul(|color(white)(a/a)color(black)("29 L")color(white)(a/a)|)))`

The answer is rounded to two sig figs.

As you can see, decreasing the pressure of the gas caused its volume to increase.