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.)

Question

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.)

Answer 1

atomic mass ... 106.4

moles per ml ... 106 / 12

6.02E23 * (12.0 / 106) * 5.89E-23

Answer 2

atomic mass ... 106.4

moles per ml ... 12.0 / 106 ...OOPS...

6.02E23 * (12.0 / 106) * 5.89E-23

Answer 3

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

Answer 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.

Answer 5

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).