The density of palladium (Pd) is 12.0 g/mL and the cell volume is 5.89 ✕ 10^−23 mL. Determine the number of atoms in the unit cell. (Because there cannot be a part of an atom in a unit cell, we must round the number of atoms to the nearest whole number.)
atomic mass ... 106.4
moles per ml ... 106 / 12
6.02E23 * (12.0 / 106) * 5.89E-23
atomic mass ... 106.4
moles per ml ... 12.0 / 106 ...OOPS...
6.02E23 * (12.0 / 106) * 5.89E-23
atomic mass=106*1.6726E-27 kg
mass per cell= 12g/ml*5.89E-23 g
=
the number of atoms per cell:
number= mass per cell/atommassperatom
= 7.06800e-25kg/106*1.6726E-27 =3.98656255
number per cell = 4
It's hard (for me) to follow the post by Scott but solve what he has written and the answer is right. Here it is in what I hope is a little easier to follow. Let y = # atoms/unit cell.
mass unit cell = y*atomic mass/6.02E23
volume = mass/density; therefore.
5.89E-23 = y*106.42/12*6.02E23
y = 5.89E-23*12*6.02E23/106.42=3.998 which rounds to 4.0
Pd is a face centered cubic structure which has 4 atoms to the unit cell.
To determine the number of atoms in the unit cell, we first need to find the mass of the unit cell.
Given:
Density of palladium (Pd) = 12.0 g/mL
Cell volume = 5.89 ✕ 10^−23 mL
We can use the formula for density:
Density = Mass / Volume
Rearranging the formula gives us:
Mass = Density ✕ Volume
Substituting the given values:
Mass = 12.0 g/mL ✕ (5.89 ✕ 10^−23 mL)
Now, we can calculate the mass:
Mass = 7.068 ✕ 10^−22 g
Next, we need to find the atomic mass of palladium (Pd) from the periodic table. The atomic mass of Pd is approximately 106.42 g/mol.
Now, we can use the following relationship:
1 mole of Pd = Atomic mass of Pd in grams
So, the number of moles of Pd in the unit cell can be calculated as:
Moles of Pd = Mass of unit cell / Atomic mass of Pd
Substituting the known values:
Moles of Pd = (7.068 ✕ 10^−22 g) / (106.42 g/mol)
Moles of Pd = 6.644 ✕ 10^−24 mol
Since 1 mole of any substance contains 6.022 ✕ 10^23 atoms (Avogadro's number), we can determine the number of atoms in the unit cell:
Number of atoms = Moles of Pd ✕ Avogadro's number
Number of atoms = (6.644 ✕ 10^−24 mol) ✕ (6.022 ✕ 10^23 atoms/mol)
Number of atoms = 0.3994 ≈ 0 atoms (rounded to the nearest whole number)
Therefore, the number of atoms in the unit cell of palladium is 0 (rounded to the nearest whole number).