The unit cell of palladiu m is a cube that is 389. 03 pm on a side. There are 4 Pd ato ms in the unit cell. Calculate the density of palladium in grams per
cubic centimeter.
To calculate the density of palladium in grams per cubic centimeter, we need to know the mass of the unit cell and the volume of the unit cell.
First, we need to determine the volume of the unit cell. Since the unit cell is a cube, we can calculate its volume using the formula:
Volume of a cube = side length^3
Given that the side length of the cube is 389.03 pm, we need to convert it to centimeters. There are 10^-10 centimeters in 1 picometer (pm). Thus, the side length in centimeters is:
389.03 pm x (1 cm / 10^10 pm) = 3.8903 x 10^-8 cm
Now, we can calculate the volume of the unit cell:
Volume = (side length)^3 = (3.8903 x 10^-8 cm)^3
Next, we need to determine the mass of the unit cell. We know that there are 4 Pd atoms in the unit cell, so we can calculate the mass of palladium in the unit cell by multiplying the number of atoms by the atomic mass of palladium. The atomic mass of palladium (Pd) is approximately 106.42 g/mol.
To find the molar mass of palladium in grams per unit cell, we can use the formula:
Molar mass = (number of atoms) x (atomic mass)
Molar mass = 4 Pd atoms x (106.42 g/mol)
Now, we can calculate the mass of the unit cell:
Mass of unit cell = (number of atoms) x (atomic mass) = 4 x (106.42 g/mol)
Finally, we can calculate the density:
Density = Mass / Volume
Density = (Mass of unit cell) / (Volume)
Plug in the values we calculated:
Density = (4 x (106.42 g/mol)) / ((3.8903 x 10^-8 cm)^3)
Simplify the expression and convert the resulting density to grams per cubic centimeter (g/cm^3) by multiplying by 10^24:
Density ≈ (4 x 106.42 g) / (3.8903 x 10^-8 cm)^3) x 10^24 g/cm^3
After performing the necessary calculations, you should obtain the density of palladium in grams per cubic centimeter.