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Introduction:
What does Avogadro’s number mean? It is the theory that’s given by the Italian chemist Amedeo Avogadro which states that “equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties”. And the number of molecules or atoms in exactly 1 mole of a substance is 6.022 X1023. [1]
What is Density and how does it help us?
Density is defined as the ratio of mass to the volume of a substance: [2]
Density = mass/volume [2]
Density is an intensive property this means that it is independent of the amount of substance. For example the density of gold is the same for all gold substances regardless of their masses. This is a good way to distinguish
Procedure:
1. Take some tiny pellets of aluminum and put it on top of the measuring balance and record the mass (grams).
2. Add water to the measuring cylinder and record the initial volume.
3. Insert the tiny pellets of aluminum which you recorded the mass in step 1 of this procedure in the measuring cylinder containing water and record the final volume.
4. Calculate the volume of the tiny pellet by using this formula:
Volume of tine pellet = Final volume (step 3) – Initial volume (step 2)
5. Calculate the density (grams/ml) of tiny pellets of aluminum using formula:
Density = mass (step 1)/Volume (step 4)

Results and Discussion:
Below I will be discussing the results of each method and its accuracy and the errors and assumptions associated with each method.
Part 1: Cost of an atom of aluminum
Below is a table of the results for this experiment: Standard Household foil Piece of Aluminum
Length (m) 0.193
Width (m) 0.0920
Area (m2) 6.96 0.0178
Mass (grams) 279 0.713
Mass/area (g/m2) 40.1
Moles 10.3
Cost (\$) 3.56
Number of atoms 6.20 X 1024
Cost of atoms (\$) 5.74 X 10-25

• As you can see we have found the cost of one atom of aluminum to be \$5.74 X 10-25.
• To find the moles we used the atomic mass of aluminum and that’s 26.98
• So the equipment used here to calculate the thickness was the most precise as it calculates the thickness to 4 decimal places in centimeter, so I believe the equipment used here is the micrometer screw gauge which is more accurate than the Vernier calipers.
Method 4 (not tested):
• Tiny pellets of aluminum was used instead of the aluminum foil.
• The volume of tiny pellets were found by displacement of water but since there is no trapped air in between the tiny pellets, the volume will be more accurate than the aluminum foil used.
• This means the density will be more accurate.
• The percent error will also be less.

Conclusion:
To summarize everything up, this experiment tells us how important it is to find the cost of an atom so we can know how valuable each different atom is. Also it tells us the most precise and accurate way of calculating the density, which is important to find out what element we are dealing with.

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