Question

Numerical based on relationship between density,molar mass,and,and edge length of unit cell on chemistry

Answer 1

To solve a numerical problem based on the relationship between density, molar mass, and edge length of a unit cell, we use the following formula:

$\rho = \frac{Z \times M}{a^3 \times N_a}$

Where:

• $\rho$ is the density of the crystalline substance.
• $Z$ is the number of atoms (or molecules) per unit cell. This depends on the type of unit cell (e.g., Z=1 for simple cubic, Z=2 for body-centered cubic (BCC), Z=4 for face-centered cubic (FCC)).
• $M$ is the molar mass of the substance.
• $a$ is the edge length of the unit cell (assuming a cubic unit cell).
• $N_a$ is Avogadro's number ($6.022 \times 10^{23} \text{ mol}^{-1}$).

This formula can be rearranged to solve for any of the variables if the others are known. For example, to find the edge length $a$:

$a^3 = \frac{Z \times M}{\rho \times N_a}$ $a = \left(\frac{Z \times M}{\rho \times N_a}\right)^{1/3}$

Answer 2

To solve a numerical problem based on the relationship between density, molar mass, and edge length of a unit cell, we use the following formula:

$\rho = \frac{Z \times M}{a^3 \times N_a}$

Where:

• $\rho$ is the density of the crystalline substance.
• $Z$ is the number of atoms (or molecules) per unit cell. This depends on the type of unit cell (e.g., Z=1 for simple cubic, Z=2 for body-centered cubic (BCC), Z=4 for face-centered cubic (FCC)).
• $M$ is the molar mass of the substance.
• $a$ is the edge length of the unit cell (assuming a cubic unit cell).
• $N_a$ is Avogadro's number ($6.022 \times 10^{23} \text{ mol}^{-1}$).

This formula can be rearranged to solve for any of the variables if the others are known. For example, to find the edge length $a$:

$a^3 = \frac{Z \times M}{\rho \times N_a}$ $a = \left(\frac{Z \times M}{\rho \times N_a}\right)^{1/3}