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

1 Answer
Oct 29, 2016

Answer:

#"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.