The edge of a body-centered-cubic unit cell ( which contains two atoms per unit cell) of an element Y was found to be 2.16x10^-8cm. The density of the metal is 19.35g*cm^-3. What is the approximate molar mass of Y?
To find the approximate molar mass of element Y, we need to use the given information about its unit cell and density.
The body-centered-cubic (bcc) unit cell of element Y contains two atoms. The edge length of the bcc unit cell is given as 2.16x10^-8 cm.
First, we need to calculate the volume of the bcc unit cell. The volume of a bcc unit cell can be calculated using the formula:
Volume = (edge length)^3 * (4/3)
Substituting the given value, we have:
Volume = (2.16x10^-8 cm)^3 * (4/3)
Next, we need to convert the density of the metal from g/cm^3 to g/m^3. Since there are 100 cm in 1 m, we multiply the density by 100^3:
Density in g/m^3 = 19.35 g/cm^3 * (100 cm/m)^3
Now, let's calculate the molar mass.
The molar mass (M) can be calculated using the formula:
Molar mass = (mass per unit cell) / (Avogadro's number)
The mass per unit cell can be calculated using the formula:
Mass per unit cell = (density * volume) / (number of atoms per unit cell)
Substituting the values, we have:
Mass per unit cell = (19.35 g/m^3) * (volume) / (2 atoms)
Finally, substituting the mass per unit cell into the molar mass formula, we have:
Molar mass = (Mass per unit cell) / (Avogadro's number)
The value of Avogadro's number is approximately 6.022 x 10^23 mol^-1.
By following these steps and substituting the given values, you can calculate the approximate molar mass of element Y.