Question

Iridium has a face-centered cubic unit cell with an edge length of 383.3 pm. The density of iridium is 22.61 g/cm³. Use these data to calculate a value for Avogadro's number.

a) 6.02×10²³
b) 4.21×10²³
c) 8.92×10²³
d) 1.20×10²⁴

Answer 1

To calculate Avogadro's number for iridium, we need to calculate the effective volume of the face-centered cubic unit cell and the mass of the unit cell. Using the calculated mass and the molar mass of iridium, we can then find Avogadro's number.

Step-by-step explanation:

In a face-centered cubic (FCC) unit cell, each corner atom contributes 1/8th of itself to the unit cell while each of the 6 face-centered atoms contributes 1/2 of itself. By finding the effective volume of the unit cell, we can calculate the number of atoms in the unit cell. The volume of a FCC unit cell is determined using the formula: Volume = (4/3) × π × (radius of atom)³. The effective volume of the unit cell can be calculated by multiplying the volume of one atom by the number of atoms contributed per unit cell. Density can be calculated using the formula: Density = (mass of unit cell) / (volume of unit cell). We can rearrange this equation to find the mass of the unit cell: Mass = Density × (volume of unit cell). Using the given data, we can now calculate Avogadro's number as follows:

1. Calculate the volume of one iridium atom in the FCC unit cell: Volume of one Ir atom = (4/3) × 3.1415 × (radius of Ir atom)³
2. Calculate the effective volume of the FCC unit cell: Effective volume of unit cell = Volume of one Ir atom × (number of atoms per unit cell)
3. Calculate the mass of the unit cell: Mass = Density × (volume of unit cell)
4. Calculate Avogadro's number: Avogadro's number = Mass of unit cell / (molar mass of Ir)

By plugging in the given data for iridium, we can calculate the value for Avogadro's number.