A soild cube of aluminum (density2.70g/cm^3) has a volume of 0.200cm^3 . It is known that 27.0g of aluminum contains 6.02x10^23 atoms .
How many aluminum atoms are contained in the cube ?
7 years ago
1 year ago
To determine the number of aluminum atoms in the cube, we can follow these steps:
Step 1: Calculate the mass of the aluminum cube.
The density of aluminum is given as 2.70 g/cm^3, and the volume of the cube is given as 0.200 cm^3. We can use the formula: Mass = Density x Volume.
Mass = 2.70 g/cm^3 × 0.200 cm^3
Mass = 0.54 g
Step 2: Calculate the number of moles of aluminum in the cube.
To calculate the number of moles, we need to divide the mass of aluminum by its molar mass. The molar mass of aluminum is 26.98 g/mol.
Number of moles = Mass / Molar mass
Number of moles = 0.54 g / 26.98 g/mol
Number of moles ≈ 0.020 mol
Step 3: Calculate the number of aluminum atoms.
One mole of any substance contains 6.02 × 10^23 particles (Avogadro's number). Therefore, the number of atoms in the cube is equal to the number of moles multiplied by Avogadro's number.
Number of atoms = Number of moles × Avogadro's number
Number of atoms = 0.020 mol × 6.02 × 10^23 atoms/mol
Number of atoms ≈ 1.205 × 10^22 atoms
Therefore, there are approximately 1.205 × 10^22 aluminum atoms in the cube.
1 year ago
To calculate the number of aluminum atoms in the cube, we need to use the given information about the density, volume, and the number of atoms in a known mass.
First, let's calculate the mass of the aluminum cube. We can use the density formula: density = mass/volume.
Given:
Density (d) = 2.70 g/cm³
Volume (V) = 0.200 cm³
Rearranging the formula, we have:
Mass (m) = density × volume
Substituting the given values:
Mass (m) = 2.70 g/cm³ × 0.200 cm³
Mass (m) = 0.54 g
Now, we need to find the number of moles (n) of aluminum in the cube. We can use the molar mass of aluminum to convert the mass into moles.
The molar mass of aluminum (Al) is 26.98 g/mol.
Number of moles (n) = mass (m) / molar mass (M)
Substituting the given values:
Number of moles (n) = 0.54 g / 26.98 g/mol
Number of moles (n) ≈ 0.020 mmol (approximate value)
Finally, we can use Avogadro's number (6.02 × 10^23) to calculate the number of aluminum atoms.
Number of atoms = number of moles × Avogadro's number
Number of atoms = 0.020 mmol × (6.02 × 10^23) atoms/mol
Number of atoms ≈ 1.20 × 10^22 atoms
Therefore, there are approximately 1.20 × 10^22 aluminum atoms contained in the cube.