The molar volume of a certain form of solid lead is 18cm3/mol. Assuming cubic closest packed structure, determine the number of Pb atoms per unit cell.
Cubic close packing is face centered cubic structure and that has four atoms per unit cell.
To determine the number of Pb (lead) atoms per unit cell in a cubic closest packed (CCP) structure, we need to know the volume of the unit cell.
In a cubic closest packed structure, each lattice point represents an atom. The atom at each lattice point is shared between multiple unit cells. Specifically, each atom is shared with 8 neighboring unit cells.
The volume of the unit cell in a cubic closest packed structure can be calculated using the formula:
Volume of unit cell = (4 * r^3 * sqrt(2)) / 3
where r is the radius of the atom.
To determine the number of atoms per unit cell, we need to use the relationship between the volume of the unit cell and the molar volume of the solid lead.
Molar volume is defined as the volume occupied by one mole of a substance.
Given that the molar volume of the solid lead is 18 cm^3/mol, we can use the following equation:
Molar volume = (Volume of unit cell) * (Number of atoms per unit cell) / Avogadro's number
Avogadro's number is approximately 6.022 x 10^23 mol⁻¹.
Let's calculate the number of Pb atoms per unit cell step-by-step:
Step 1: Convert the molar volume to m^3/mol.
18 cm^3/mol = (18 * 10^-6) m^3/mol.
Step 2: Calculate the volume of the unit cell.
Molar volume = (Volume of unit cell) * (Number of atoms per unit cell) / Avogadro's number
(18 * 10^-6) m^3/mol = (4 * r^3 * sqrt(2)) / 3 * Number of atoms per unit cell / (6.022 * 10^23 mol⁻¹).
Step 3: Rearrange the equation to solve for Number of atoms per unit cell:
Number of atoms per unit cell = (18 * 10^-6) m^3/mol * (6.022 * 10^23 mol⁻¹) * (3) / (4 * r^3 * sqrt(2)).
To determine the number of Pb atoms per unit cell, we need to know the radius of the lead atom. Please provide the radius of the lead atom.
To determine the number of Pb atoms per unit cell in a cubic closest packed (CCP) structure, we need to understand the arrangement of atoms in this type of structure.
In a CCP structure, each atom is surrounded by 12 nearest neighbors, forming a total of 12 contacts. Each atom also has 6 nearest neighbors in its own layer, forming a 2D hexagonal arrangement. Each layer is then arranged in an ABAB pattern vertically, resulting in a 3D cubic structure.
Now, let's calculate the number of atoms per unit cell:
1. Determine the number of atoms in each layer:
- In a hexagonal arrangement, there are 6 atoms in the first layer (A layer) and 6 atoms in the second layer (B layer).
2. Calculate the number of atoms in the unit cell:
- Each unit cell contains two complete layers (ABAB).
- Therefore, the number of atoms per unit cell is: 6 (A layer) + 6 (B layer) = 12 atoms.
So, there are 12 Pb atoms per unit cell in a cubic closest packed structure.