We were given a 12 cm by 12 cm area of aluminum foil (it weighed 0.60 g) and were told to calculate the atomic mass of Aluminum atoms given that the radius of 1 aluminum atom is 143 picometers and the density is 2.7 grams per centimeter cubed, without using Avogrado's number. How do I go about doing this?

To calculate the atomic mass of aluminum atoms using the given information, you will need to apply the formula:

Atomic Mass = (Mass of sample / Number of aluminum atoms in the sample)

Step 1: Find the volume of the aluminum foil sample.
Since you have a 12 cm by 12 cm area of aluminum foil, and aluminum foil is thin, we can approximate its volume as the area multiplied by a small thickness. Let's assume the thickness is t cm.

Area = Length × Width
Area = 12 cm × 12 cm = 144 cm²

Volume = Area × Thickness
Volume = 144 cm² × t cm = 144t cm³

Step 2: Convert the volume to liters.
Since the density is in grams per cubic centimeter, we need to convert the volume to liters by dividing it by 1000:

Volume (in liters) = Volume (in cm³) / 1000

Step 3: Calculate the mass of the sample.
Given that the mass of the sample is 0.60 grams, there is no need for further calculation.

Step 4: Calculate the number of aluminum atoms in the sample.
To find the number of aluminum atoms, we need to determine the number of moles of aluminum atoms present in the sample. To do this, we will use the formula:

Number of moles = Mass / Atomic mass

Since we want to find the number of aluminum atoms, we'll rearrange the above formula:

Number of aluminum atoms = Mass / Atomic mass

Step 5: Calculate the atomic mass of aluminum atoms.
To obtain the atomic mass of aluminum, we'll rearrange the previous equation:

Atomic mass = Mass / Number of aluminum atoms

Plug in the known values and solve for the atomic mass.

It is important to note that Avogadro's number is not needed in this calculation as we are directly calculating the atomic mass using the mass and number of atoms in the given sample.