The element Xe has ccp packing with a face-centered cubic unit cell. The density of xenon is 3.783 g/mL and the cell volume is 2.306 x 10-22 mL. Calculate the value of Avogadro's number to three significant figures based on these data.
Same song; fourth verse.
To calculate the value of Avogadro's number based on the given information, we can use the following steps:
Step 1: Determine the number of atoms in one unit cell
In a face-centered cubic (FCC) unit cell, there are four atoms present. This can be determined since each corner atom is shared among eight adjacent cells, while each face-centered atom is shared by two adjacent cells. Therefore, (1/8) of each corner atom and all of each face-centered atom belong to the unit cell.
Step 2: Calculate the mass of one unit cell
The mass of one unit cell can be calculated using the density and the volume of the unit cell. The formula to calculate mass is:
mass = density x volume
Substituting the given values:
mass = 3.783 g/mL x 2.306 x 10^-22 mL
Step 3: Determine the molar mass of Xenon
The molar mass of xenon (Xe) is 131.3 g/mol.
Step 4: Calculate the number of moles of xenon in one unit cell
Using the calculated mass and the molar mass of xenon, the number of moles can be determined using the formula:
moles = mass / molar mass
Step 5: Calculate Avogadro's number
Since there are four atoms of xenon in one unit cell, and each mole contains Avogadro's number of particles (6.022 x 10^23), we can calculate Avogadro's number using the formula:
Avogadro's number = (moles x number of atoms in one unit cell) / number of moles in one mole
Therefore, the calculation is as follows:
moles = (3.783 g/mL x 2.306 x 10^-22 mL) / 131.3 g/mol
moles = 5.562 x 10^-23 mol
Avogadro's number = (5.562 x 10^-23 mol x 4) / (1 mol)
Avogadro's number = 2.225 x 10^-22
Therefore, the value of Avogadro's number, based on the given data, is approximately 2.225 x 10^22 to three significant figures.