An aluminum sphere contains 8.55 * 10²² aluminum atoms. What is the sphere’s radius in centimeters?

The density of aluminum is 2.70 g/cm³.

Transcribed Image Text:

SORT You are given the number of aluminum atoms in a sphere and the density of aluminum. You are asked to find the radius of the sphere. STRATEGIZE The heart of this problem is density, which relates mass to volume; though you aren't given the mass directly, you are given the number of atoms, which you can use to find mass. 1. Convert from number of atoms to number of moles using Avogadro's number as a conver- sion factor. 2. Convert from number of moles to mass using molar mass as a conversion factor. 3. Convert from mass to volume (in cm³) using density as a conversion factor. 4. Once you calculate the volume, find the radius from the volume using the formula for the volume of a sphere. GIVEN: 8.55 x 10²2 Al atoms d = 2.70 g/cm³ FIND: radius (r) of sphere CONCEPTUAL PLAN Number of Al atoms 1 mol Al 6.022 x 1023 Al atoms V (in cm³) V = mol Al πTr³ 26.98 g Al 1 mol Al g Al 1 cm³ 2.70 g Al V (in cm³)