the density of alumnium is 2.7 g/cm^3 and its molar mass is 27 g/mol. find the mass of an atom of aluminum and the numebr of alumuminum atoms per cubic meter.

Molar mass is the mass in grams of 1 mole of Al, that is, 1 mol Al has a mass of 27 g.

On the other hand, 1 mole of any element contains Avogadro's number of atoms, that is,
1 mol Al = 6.02x10^23 atoms of Al

Therefore; 6.02x10^23 atoms of Al = 27 g
1 single Al atom;
27 g / 6.02x10^23 atoms of Al = 4.48x10^-23 g

d = 2.7 g / cm^3 means that 1 cm^3 Al has a mass of 2.7 g.
1 m^3 = 10^6 cm^3 = 2.7x10^6 g
Mole of Al = 2.7x10^6 g / 27 g/mol = 1x10^5 mol Al

Since each mole contains 6.02x10^23 atoms of Al
1x10^5 mol Al will contain;
1x10^5 mol Al x 6.02x10^23 atoms of Al /mol =
6.02x10^28 atoms of Al will be per m^3 of Al

Find the volume of one mole (27/2.7 cm^3). Divide that by avag number, that will be the volume per atom.

To find the mass of an atom of aluminum, we need to first convert the molar mass from grams per mole to kilograms per mole:

Molar mass of aluminum = 27 g/mol = 0.027 kg/mol

Next, we can use Avogadro's number to find the mass of one aluminum atom:

Avogadro's number (NA) = 6.022 x 10^23 atoms/mol

Mass of an aluminum atom = Molar mass of aluminum / Avogadro's number

Mass of an aluminum atom = 0.027 kg/mol / (6.022 x 10^23 atoms/mol)

Now we can calculate the mass of an aluminum atom:

Mass of an aluminum atom ≈ 4.49 x 10^-26 kg

To find the number of aluminum atoms per cubic meter, we need to convert the density from g/cm^3 to kg/m^3:

Density of aluminum = 2.7 g/cm^3 = 2700 kg/m^3

Now we can use the density and the molar mass to calculate the number of aluminum atoms per cubic meter:

Number of aluminum atoms per cubic meter = (Density of aluminum / Molar mass of aluminum) x Avogadro's number

Number of aluminum atoms per cubic meter = (2700 kg/m^3 / 0.027 kg/mol) x (6.022 x 10^23 atoms/mol)

Now we can calculate the number of aluminum atoms per cubic meter:

Number of aluminum atoms per cubic meter ≈ 6.0 x 10^28 aluminum atoms/m^3.

To find the mass of an aluminum atom, we need to calculate the mass of one mole of aluminum atoms and then divide it by Avogadro's number.

1. Start by finding the mass of one mole of aluminum atoms:
- The molar mass of aluminum is 27 g/mol.
- This means that one mole of aluminum atoms has a mass of 27 grams.

2. Divide the mass of one mole of aluminum atoms by Avogadro's number (6.022 x 10^23) to find the mass of one aluminum atom:
- Mass of one aluminum atom = (Mass of one mole of aluminum atoms) / Avogadro's number
- Mass of one aluminum atom = 27 g / (6.022 x 10^23)
- Mass of one aluminum atom ≈ 4.48 x 10^-23 grams

So, the mass of one aluminum atom is approximately 4.48 x 10^-23 grams.

To find the number of aluminum atoms per cubic meter, we can use the density of aluminum.

3. Convert the given density from g/cm^3 to kg/m^3:
- Density in kg/m^3 = Density in g/cm^3 x 1000
- Density of aluminum in kg/m^3 = 2.7 g/cm^3 x 1000 = 2700 kg/m^3

4. Calculate the number of aluminum atoms per cubic meter using the formula:
- Number of aluminum atoms per cubic meter = (Density of aluminum in kg/m^3) / (Mass of one aluminum atom)

Number of aluminum atoms per cubic meter = 2700 kg/m^3 / (4.48 x 10^-23 grams)

As the units need to match, convert kg to grams:

Number of aluminum atoms per cubic meter = 2700000 g/m^3 / (4.48 x 10^-23 grams)

Number of aluminum atoms per cubic meter ≈ 6.03 x 10^28 atoms/m^3

Therefore, there are approximately 6.03 x 10^28 aluminum atoms per cubic meter.