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the density of aluminum is 2700 kg/m3. how many atoms are in a 2.0 cm 2.0 cm 2.0 cm cube of aluminum?

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To calculate the number of atoms in a given volume of aluminum, we need to use the concept of molar volume and Avogadro's number.

First, let's convert the dimensions of the cube from centimeters to meters:
Length = 2.0 cm = 0.02 m
Width = 2.0 cm = 0.02 m
Height = 2.0 cm = 0.02 m

Next, we need to calculate the volume of the cube:
Volume = Length * Width * Height
Volume = 0.02 m * 0.02 m * 0.02 m
Volume = 0.000008 m³

Now, we can calculate the number of moles using the density of aluminum:
Density = Mass / Volume
Mass = Density * Volume
Mass = 2700 kg/m³ * 0.000008 m³
Mass = 0.0216 kg

To find the number of moles (n), we use the formula:
n = Mass / molar mass

The molar mass of aluminum is approximately 27 g/mol, which is 0.027 kg/mol.

n = 0.0216 kg / 0.027 kg/mol
n ≈ 0.8 mol

Now, we can use Avogadro's number, which is approximately 6.022 × 10^23 atoms/mol, to calculate the number of atoms:

Number of atoms = n * Avogadro's number
Number of atoms ≈ 0.8 mol * (6.022 × 10^23 atoms/mol)
Number of atoms ≈ 4.818 × 10^23 atoms

Therefore, there are approximately 4.818 × 10^23 atoms in a 2.0 cm x 2.0 cm x 2.0 cm cube of aluminum.
User Jerryno
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