The element lithium has bcc packing with a body-centered cubic unit cell. The volume of the unit cell is 4.32 x 10-26 L. Calculate the density (g/cm3) of the element.
There are two Li atoms per unit cell for a bcc structure.
mass = 2*massofmole Li/6.022 x 10^23 = mass of unit cell. You know the volume.
density = mass/volume.
Note that the problem asks for density in g/cc so you must change the volume in liters to cc in order to obtain the unit g/cc.
To calculate the density of an element, we need to know the mass and volume of the unit cell. Since the unit cell of lithium has a body-centered cubic (bcc) structure, it contains 2 lithium atoms.
Given:
Volume of the unit cell (V) = 4.32 x 10^(-26) L
Number of atoms per unit cell (n) = 2
To calculate the mass of the unit cell, we need to know the atomic mass of lithium (Li). The atomic mass of Li is approximately 6.94 g/mol.
Step 1: Calculate the mass of the unit cell
The mass of the unit cell can be calculated by multiplying the atomic mass of Li by the number of Li atoms in the unit cell:
Mass of unit cell (m) = Atomic mass of Li (6.94 g/mol) × Number of atoms per unit cell (2)
m = 6.94 g/mol × 2
m = 13.88 g
Step 2: Convert the volume to cm^3
1 L = 1000 cm^3
Therefore, 4.32 x 10^(-26) L = 4.32 x 10^(-26) × 1000 cm^3
V = 4.32 x 10^(-23) cm^3
Step 3: Calculate the density
Density (d) = Mass (m) / Volume (V)
d = 13.88 g / 4.32 x 10^(-23) cm^3
d ≈ 3.212 x 10^(-3) g/cm^3
Therefore, the density of lithium is approximately 3.212 x 10^(-3) g/cm^3.
To calculate the density of the element, we need to find the mass of the unit cell. We can then divide the mass by the volume of the unit cell to get the density.
The first step is to find the mass of the unit cell. To do this, we need to know the atomic mass of lithium (Li). The atomic mass of lithium is approximately 6.94 g/mol.
Next, we need to find the number of atoms in the unit cell. In a body-centered cubic (bcc) unit cell, there is one atom at the center of the cube and eight atoms on the corners. So, the total number of atoms in the unit cell is 1 + 8 = 9.
To find the mass of the unit cell, we multiply the atomic mass of lithium by the number of atoms:
Mass of unit cell = Atomic mass of lithium x Number of atoms in the unit cell
Mass of unit cell = 6.94 g/mol x 9 = 62.46 g
Now we have the mass of the unit cell, and we can calculate the density by dividing the mass by the volume of the unit cell:
Density = Mass of unit cell / Volume of unit cell
Since the volume of the unit cell is given in liters, we need to convert it to cubic centimeters (cm³):
1 L = 1000 cm³
So, the volume of the unit cell in cm³ is:
Volume of unit cell = 4.32 x 10^-26 L x 1000 cm³/L = 4.32 x 10^-23 cm³
Now we can calculate the density:
Density = 62.46 g / 4.32 x 10^-23 cm³
Since the density is usually expressed in g/cm³, we divide the mass by the volume and adjust the exponent:
Density ≈ 1.45 x 10³ g/cm³