The element Rb has bcc packing with a body-centered cubic unit cell. The density of Rb is 1.532 g/cm3 and the cell volume is 1.852 x 10-22 mL. Calculate the value of Avogadro's number to three significant figures based on these data.
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To calculate the value of Avogadro's number using the given data, you can follow these steps:
Step 1: Convert the given density from g/cm³ to g/mL.
Density of Rb = 1.532 g/cm³ = 1.532 g/mL
Step 2: Convert the given cell volume from mL to cm³.
Cell volume = 1.852 x 10^(-22) mL = 1.852 x 10^(-22) cm³
Step 3: Calculate the mass of one Rb atom in the unit cell.
Density = Mass / Volume
Mass = Density x Volume
Mass of Rb atom = (1.532 g/mL) x (1.852 x 10^(-22) cm³)
Step 4: Calculate the number of Rb atoms in one unit cell.
We know that a body-centered cubic (bcc) unit cell contains 2 atoms.
Number of Rb atoms = 2
Step 5: Calculate the mass of one Rb atom in grams.
Mass of one Rb atom = (Mass of Rb atom) / (Number of Rb atoms)
Step 6: Calculate Avogadro's number by dividing the mass of one Rb atom by the mass of one mole of Rb atoms.
Avogadro's number = (Mass of one Rb atom) / (Mass of one mole of Rb atoms)
Finally, perform the calculations to determine Avogadro's number:
Avogadro's number ≈ [(1.532 g/mL) x (1.852 x 10^(-22) cm³)] / [(Mass of one Rb atom) x (Number of Rb atoms)]
Please note that the provided data is incomplete as it does not specify the molar mass of Rb. The molar mass would be required to calculate the mass of one mole of Rb atoms and further determine Avogadro's number to three significant figures.