The well-known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are 4Ca^(2+) ions and 8F^(-) ions and that Ca^(2+) ions are arranged in a fce lattice. The F^(-) ions fill all the tetrahedral holes in the face-centred cubic lattice of Ca^(2+) ions. The edge of the unit cell is 5.46 xx 10^(-8) cm in length. The density of the solid is 3.18 g cm^(-3). Use this information to calculate Avogadro's number. [Molar mass of CaF_(2) = 78.08 g mol^(-1)]

The well-known mineral fluorite is chemically calcium fluoride. It is

1.	The well-known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are 4Ca^(2+) ions and 8F^(-) ions and that Ca^(2+) ions are arranged in a fce lattice. The F^(-) ions fill all the tetrahedral holes in the face-centred cubic lattice of Ca^(2+) ions. The edge of the unit cell is 5.46 xx 10^(-8) cm in length. The density of the solid is 3.18 g cm^(-3). Use this information to calculate Avogadro's number. [Molar mass of CaF_(2) = 78.08 g mol^(-1)]
Answer» Solution :The data provided suggests that the number of molecules per UNIT CELL is 4. `N_(A)=(zxxM)/(a^(3)xxd)` Here `z=4, M=78.08 " g mol"^(-1), a=5.46xx10^(-8)cm, d=3.18gcm^(-3)` SUBSTITUTING the values in the above RELATION, we have `N_(A)=(4xx78.08)/((5.46xx10^(-8))^(3)xx3.18)=(4xx78.08)/((5.46xx10^(-8))^(3)xx3.18)=(4xx78.08)/((5.46)^(3)xx10^(-24)xx3.18)=6.03xx10^(23)`