Question

I have 5.6 X 10(24) molecules of Helium gas to fill balloons at a ballgame. If each balloon holds 1.5 liters, how many balloons can I fill? Assume STP

Answer 1

You can fill 140 balloons.

This is a disguised ideal gas law problem.

http://socratic.org/questions/what-is-the-ideal-gas-law-1

We can use number of molecules of helium to calculate the number of moles. Then we can use the Ideal Gas Law to calculate the volume of helium and the number of balloons.

Method 1

In your problem,

`n` = 5.6 × 10²⁴ molecules × `(1"mol")/(6.022 × 10²³"molecules")` = 9.3 mol

`P` = 1 atm
`T` = 273.15 K

`PV = nRT`

`V = (nRT)/P = (9.3"mol" × 0.082 06"L·atm·K⁻¹mol⁻¹" × 273.15"K")/(1"atm")` = 208 L

Number of balloons = 208 L × `(1"balloon")/(1.5"L")` = 140 balloons

Method 2

We could also solve the problem by using the molar volume of an ideal gas at STP.

`V` = 9.3 mol ×`(22.414"L")/(1"mol")` = 208 L

This volume will again fill 140 balloons.

Note: The answers can have only two significant figures, because that is all you gave for the number of molecules and for the volume of each balloon. If you need more precision, you will have to recalculate.