The metal palladium crystallizes in a face-centered cubic lattice with an edge length of 388.8 pm. What is the density of the palladium?
388.8 pm = 3.888E-8 cm
Volume = (3.888E-8)3 of the cube.
mass of cube with 4 atoms/unit cell.
4*atomic mass Pd/6.02E23 = ?
density = mass/volume
To determine the density of palladium, we can use the equation:
Density = mass / volume
Let's calculate each component step-by-step.
Step 1: Calculate the volume of the unit cell.
A face-centered cubic (FCC) unit cell consists of 4 atoms. The volume of an FCC unit cell can be calculated using the formula:
Volume = (edge length)^3 * (4 / 3)
Given that the edge length of the palladium unit cell is 388.8 pm (picometers), let's convert it to meters first:
1 pm = 1e-12 meters
Therefore, the edge length in meters would be:
388.8 pm * (1e-12 m / 1 pm) = 3.888e-10 m
Now, we can calculate the volume:
Volume = (3.888e-10 m)^3 * (4 / 3)
≈ 3.237e-29 m^3
Step 2: Determine the molar mass of palladium.
The molar mass of palladium is 106.42 g/mol.
Step 3: Calculate the mass of the unit cell.
The mass of the unit cell can be found by multiplying the molar mass by the number of atoms in the unit cell:
Mass = molar mass * number of atoms
Since there are 4 atoms in the FCC unit cell, the mass is:
Mass = 106.42 g/mol * 4
= 425.68 g
Step 4: Calculate the density.
Finally, we can calculate the density of palladium using the formula:
Density = mass / volume
Density = 425.68 g / 3.237e-29 m^3
≈ 1.315e7 g/m^3
Therefore, the density of palladium is approximately 1.315 x 10^7 grams per cubic meter (g/m^3).
To calculate the density of palladium, we first need to determine its volume. The volume of a unit cell in a face-centered cubic (FCC) lattice can be calculated using the following formula:
Volume of unit cell = (Edge length)^3 * (2^0.5) / 4
In this case, the edge length of the palladium unit cell is given as 388.8 pm (picometers), which is equivalent to 3.888 Å (angstroms).
Converting the edge length to angstroms:
1 pm = 0.01 Å
388.8 pm * 0.01 Å/pm = 3.888 Å
Now, we can calculate the volume:
Volume of unit cell = (3.888 Å)^3 * (2^0.5) / 4
Next, we need to determine the mass of the palladium unit cell. The molar mass of palladium (Pd) is 106.42 g/mol.
To find the mass, we need to calculate the number of atoms in the unit cell. In an FCC lattice, there are four atoms per unit cell.
Now, we can calculate the mass:
Mass of unit cell = (Number of atoms) * (Molar mass of palladium) / Avogadro's number
Finally, we can calculate the density:
Density = Mass of unit cell / Volume of unit cell
Plugging in the values and performing the calculations will give us the density of palladium.