How many layers of atoms were deposited on the pennies during the experiment?

[rachelle]

i don't know where to post this, but we did a little experiment on pennies, and I'm having trouble with analyzing the calculations...

basically the pennies turned into silver, the other gold.. after we heat it, etc

inc. in mass of the pennies .0006 g
density of the solid added to the coins = 7.65 g/cc
atomic mass of the solid added to the coins = 32.8 g/mol
diameter of ea coin = 2.12 cm
thickness of ea coin = 1.59 mm

assume coins are circular discs & atoms are tiny cubes which stack one on top of ea other. calculate the average number of laters of atoms deposited on your coins. also calculate the thickness of this layer

surface area of ea coin, top+bottom+ side = ? sq cm
millimoles of atoms added to surface of coins = ? mmol
total surface area covered y the plated metal (area covered if one atom thick) = ? sq cm
average layers of atoms added = ?
average thickness of plated metal coating = ?

Any Help/Hints? Much appreciated.. thank you

 

[sdekivit]

if we assume coins to be circular, the surface area of the coin can be calculated with $$\frac {1} {4}\cdot \pi\cdot d^{2}$$

If you know what the increase in mass of the coin is, you know how many grams of the atoms of the solution is added to the coin.

you can convert that to amount of atoms with the number of Avogadro and if you know the atom radius of the involved atoms, you can calculate the amount of layers on the coin.

 

[Blueshift5]

Based on the information provided, it is not possible to accurately determine the exact number of layers of atoms deposited on the pennies during the experiment. This is because the thickness of each layer of atoms will depend on the arrangement and packing of the atoms, which can vary. Additionally, the amount of atoms deposited may also vary depending on factors such as temperature and pressure during the experiment.

To determine an approximate number of layers, you can use the following calculations:

1. Calculate the surface area of each coin using the formula A = πr^2, where r is the radius of the coin (in this case, half of the diameter).

2. Convert the thickness of each coin from millimeters to centimeters (1.59 mm = 0.159 cm).

3. Calculate the volume of each coin using the formula V = πr^2h, where h is the thickness of the coin.

4. Convert the mass of the solid added to the coins from grams to milligrams (0.0006 g = 0.6 mg).

5. Use the density of the solid added to the coins to calculate the volume of the solid added (V = m/d).

6. Convert the atomic mass of the solid added from grams to milligrams (32.8 g/mol = 32,800 mg/mol).

7. Use the atomic mass and millimoles of atoms added to calculate the number of atoms deposited on each coin (n = mmol x 6.022 x 10^23 atoms/mol).

8. Divide the number of atoms by the surface area of each coin to get an approximate number of atoms per square centimeter.

9. Divide the volume of the solid added by the surface area of each coin to get the thickness of the layer of atoms deposited.

However, please keep in mind that these calculations will only provide an estimate and the actual number of layers may vary. It is also important to consider any potential errors in the measurements and calculations that may affect the accuracy of the results. It is always recommended to repeat the experiment multiple times and take an average to get a more accurate result.