how to find atoms given density

Question

How many atoms of He can a balloon that has a 21 cm diameter hold? The density of Helium is 1.18 g/L. (Assume the balloon is a sphere).

Answer 1

First, we have to find the volume of the sphere (balloon) because density is mass/volume. We know the density and so with the volume we can find the mass. Once we have the mass, we can find the moles, and from moles we can find atoms.

1). volume of a sphere = 4/3π r³ = 4/3 (3.1416)(10.5 cm)³ = 4849 cm³ = 4.849 L

2). mass of helium = 4.849 L x 1.18 g/L = 5.72 g

3). moles of helium = 5.72 g He x 1 mol He/4.00 g = 1.43 moles He

4). atoms of helium = 1.43 moles He x 6.02x10²³ atoms/mol = 8.61x10²³ atoms