NH4Cl at temperature 20 degree lattice length 3.88 angstrum and density 1.5 gm/cm3 if the molecular weight 53.5 gm find the unit cell
To find the unit cell of NH4Cl, we need to use the given lattice length, temperature, and density information along with the molecular weight. Here's how we can proceed:
1. Start by calculating the number of formula units present in one unit cell. To do this, divide the density of NH4Cl by its molecular weight:
Number of formula units per unit cell = density / molecular weight
Number of formula units per unit cell = 1.5 gm/cm3 / 53.5 gm
Number of formula units per unit cell ≈ 0.0280 formula units
2. Next, calculate the volume of the unit cell. Since density is given in gm/cm3, we can assume that 1 cm3 is equal to 1 mL. We can then use the given lattice length to calculate the volume:
Volume of the unit cell = (lattice length)3
Volume of the unit cell = (3.88 angstrom)3
However, before proceeding, we need to convert the lattice length from angstroms to centimeters. 1 angstrom is equal to 1 x 10^-8 cm. Thus,
Volume of the unit cell = (3.88 x 10^-8 cm)3
3. Now, determine the length of one side of the unit cell by taking the cube root of the volume:
Length of one side of the unit cell = cube root (Volume of the unit cell)
Length of one side of the unit cell = cube root [(3.88 x 10^-8 cm)3]
4. Finally, to find the unit cell type, we compare the ratio of lattice lengths along the three axes with known crystal systems. This method helps identify the unit cell type. Here are the ratios for different crystal systems:
a = b, b = c, α = β = γ = 90° --> Cubic
a ≠ b ≠ c, α = β = γ = 90° --> Orthorhombic
a = b ≠ c, α = β = γ = 90° --> Tetragonal
a = b = c ≠ 90°, α = β = γ --> Hexagonal
a ≠ b ≠ c, α ≠ β ≠ γ --> Monoclinic
a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90° --> Triclinic
Compare the calculated lengths of the unit cell sides from step 3 to determine the unit cell type based on the above ratios.
By following these steps, you should be able to find the unit cell of NH4Cl using the given information.