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

Oct 29, 2016

$\text{29 L}$

#### 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

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{P}_{1} \cdot {V}_{1} = {P}_{2} \cdot {V}_{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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 ${V}_{2}$

${P}_{1} \cdot {V}_{1} = {P}_{2} \cdot {V}_{2} \implies {V}_{2} = {P}_{1} / {P}_{2} \cdot {V}_{1}$

Plug in your values to find

${V}_{2} = \left(3.8 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))))/(1.0color(red)(cancel(color(black)("atm")))) * "7.6 L" = color(green)(bar(ul(|color(white)(a/a)color(black)("29 L}} \textcolor{w h i t e}{\frac{a}{a}} |}}\right)$

The answer is rounded to two sig figs.

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