An element has hcp packing with a hexagonal unit cell. Its density is 4.5 g/cm3 and the unit cell volume is 3.53 x 10-23 mL. Calculate the molar mass (g/mol) of the element to three significant figures.
The mass = volume x density
You know the volume of the unit cell and the density; therefore, you can calculate the mass of the unit cell.
Divide the mass of the unit cell by the number of atoms per unit cell to obtain the mass a single atom; then multiply by Avogadro's number to arrive at the molar mass. Post your work if you get stuck. Your text or notes should contain information for the number of atoms per unit cell as well as the value to use for Avogadro's number.
90
To calculate the molar mass of the element, we need to determine the number of atoms present in the unit cell.
In a hexagonal close-packed (hcp) structure, each unit cell contains two atoms. So, the number of atoms per unit cell is 2.
Given the density (ρ) of the element is 4.5 g/cm³ and the unit cell volume (V) is 3.53 x 10^(-23) mL, we need to convert the volume to cm³.
1 mL = 1 cm³, so the unit cell volume in cm³ is:
3.53 x 10^(-23) mL = 3.53 x 10^(-23) cm³
Now, we can use the formula for density:
Density (ρ) = Mass (m) / Volume (V)
Rearranging the formula to solve for mass:
Mass (m) = Density (ρ) x Volume (V)
Substituting the given values:
Mass (m) = 4.5 g/cm³ x 3.53 x 10^(-23) cm³
Now, we have the mass of the unit cell. To find the molar mass, we need to find the mass of one mole of unit cells. Since there are two atoms in each unit cell, we can divide the mass of the unit cell by the number of atoms per unit cell:
Molar mass = Mass (m) / 2
Calculating the molar mass:
Molar mass = (4.5 g/cm³ x 3.53 x 10^(-23) cm³) / 2
Simplifying the calculation, we get:
Molar mass = 7.965 x 10^(-23) g
However, the molar mass is required to be expressed to three significant figures. Therefore, we need to round off the answer to three significant figures:
Molar mass = 8.00 x 10^(-23) g/mol
So, the molar mass of the element is 8.00 x 10^(-23) g/mol to three significant figures.