1)The element nickel has ccp packing with a face-centered cubic unit cell. The density of nickel is 8900 kg/m3 and the cell volume is 4.376 x 10-23 cm3. Calculate the value of Avogadro's number to three significant figures based on these data. (Note: the value may differ from the tabular value).
2)
The cell volume is given, the density is given, mass of unit cell = volume x density.
mass of atom = atomic mass/N where N = Avogadro's number. There are 4 atoms to the unit cell; therefore,
Mass of unit cell = 4*atomic mass/N.
Solve for N
is it always 4 atoms in a unit cell
To calculate the value of Avogadro's number based on the given data, we can use the formula:
Avogadro's number = (density * cell volume) / (molar mass * number of atoms in the unit cell)
1) Given data:
Density of nickel = 8900 kg/m3
Cell volume = 4.376 x 10-23 cm3
To use these values, we need to convert the cell volume to the same unit as the density. Since we are given the density in kg/m3, we need to convert the cell volume from cm3 to m3.
1 m3 = 106 cm3
Therefore, the cell volume in m3 is:
Cell volume = 4.376 x 10-23 cm3 * (1 m3 / 106 cm3) = 4.376 x 10-29 m3
Now, we need to find the molar mass of nickel. The molar mass of nickel is typically given as 58.693 g/mol.
To convert the molar mass from g/mol to kg/mol, we need to multiply by the conversion factor:
1 g = 10-3 kg
Therefore, the molar mass of nickel in kg/mol is:
Molar mass = 58.693 g/mol * (10-3 kg / 1 g) = 0.058693 kg/mol
Next, we need to determine the number of atoms in the unit cell. For a face-centered cubic (fcc) unit cell (also known as ccp or cubic-closest packing), there are 4 atoms per unit cell.
Now, we can use the formula to calculate the value of Avogadro's number:
Avogadro's number = (density * cell volume) / (molar mass * number of atoms in the unit cell)
Avogadro's number = (8900 kg/m3 * 4.376 x 10-29 m3) / (0.058693 kg/mol * 4)
Calculating the above expression will give us the value of Avogadro's number.