The density of CaF2 (fluorite structure) is 3.18 g/cm3. The length of the side of the unit cell is:a)253 pmb)344 pmc)546 pmd)273 pmCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

d = zM/N_A × V
For flourite structure, z = 4 and M = 78
3.18 = (4 × 78)/6.023 × 10²³ × a³
a³ = 312/(6.023×10²³ × 3.18)
a³ = 16.28 × 10^-23
a = 546 pm

Answer

Answer

Molecular mass of CaF2 =78 Now we can find the volume Volume=(side)^3

Answer

C

Answer

The density of a substance can be determined using its mass and volume. In this case, we have been provided with the density of CaF2, which is 3.18 g/cm3. To find the length of the side of the unit cell, we need to use the concept of crystal structures.

Crystal structures define the arrangement of atoms within a crystalline solid. In the case of CaF2, it adopts the fluorite structure, which is a face-centered cubic (FCC) lattice. In an FCC lattice, the atoms are arranged in a cubic pattern with atoms at each corner of the cube and an additional atom at the center of each face.

The formula unit of CaF2 consists of one calcium ion (Ca2+) and two fluoride ions (F-). The calcium ion occupies the center of the unit cell, while the fluoride ions occupy the corners.

Now, let's calculate the length of the side of the unit cell.

Step 1: Determine the formula mass of CaF2
The atomic mass of calcium (Ca) is 40.08 g/mol, and the atomic mass of fluorine (F) is 18.99 g/mol. Since there are two fluoride ions in CaF2, we multiply the atomic mass of fluorine by 2.
Formula mass of CaF2 = (1 * atomic mass of Ca) + (2 * atomic mass of F)
= (1 * 40.08 g/mol) + (2 * 18.99 g/mol)
= 40.08 g/mol + 37.98 g/mol
= 78.06 g/mol

Step 2: Convert the density from g/cm3 to g/m3
Density of CaF2 = 3.18 g/cm3
To convert to g/m3, multiply by the conversion factor (100 cm/m)3.
Density of CaF2 = 3.18 g/cm3 * (100 cm/m)3
= 3.18 g/cm3 * 106 cm3/m3
= 3.18 * 106 g/m3

Step 3: Calculate the volume of the unit cell
The volume of a cube is given by the formula V = a3, where a represents the length of the side of the unit cell.
Density = mass / volume
Volume = mass / density
Volume = formula mass of CaF2 / density
= 78.06 g/mol / (3.18 * 106 g/m3)
= (78.06 * 10-3 kg/mol) / (3.18 * 103 kg/m3)
= 24.52 * 10-3 m3/mol

Step 4: Calculate the length of the side of the unit cell
V = a3
24.52 * 10-3 m3/mol = a3
a = (24.52 * 10-3 m3/mol)1/3
a ≈ 0.346 * 10-1 m/mol
a ≈ 0.346 nm/mol
a ≈ 346 pm/mol

Since the length of the side of the unit cell is given in picometers (pm), we divide by Avogadro's number (6.022 * 1023 mol-1) to obtain the length of the side of the unit cell in picometers per atom.
Length of the side of the unit cell

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