Question

AB crystallizes as rock salt type crystal. If the distance between $A6+$ and $B^-$ is 280 pm then the density of AB crystal is (At. Mass of A — 40 and B = 16)
A.0.211 g/ml
B.2.11 g/ml
C.4.22 g/ml
D.0.422 g/ml

Answer 1

Hint: Cubic Close Packing is a term that refers to the packing of cubes The term "closest packed" refers to the atoms being packed as tightly as possible. The FCC unit cell is made up of four cubic layers that are tightly packed together. The atoms in the first layer cram themselves together as tightly as possible.

Complete answer:
Rock salt (NaCl) is an ionic compound that forms white crystals in nature. It is obtained by evaporating seawater or extracting the mineral from halite. The face centred cubic unit cell is repeated to form the structure of NaCl. With a molar mass of 58.4 g/mol, it has a 1:1 stoichiometry ratio of Na:Cl.
Rock salt on NaCl crystallises into cubic close packing (ccp)
Hence, AB has cubic close packing
In cubic close packing number of formula units present “n” = 4
Shortest distance between $A+$ and $4B^-$ is 280 pm
Edge length “a” = 2 x 280 pm
a = 560 pm
a = 560 x $10^{-10}$ cm [1 pm =$ 10^{-10}$ cm]
Mass “m” of AB = 40 + 16 amu
m = 56 amu
Now, Density = \[\rho = \dfrac{{n \times m}}{{{a^3} \times {N_a}}}\]
\[\rho = \dfrac{{4 \times 56}}{{{{(560 \times {{10}^{ - 10}})}^3} \times 6.023 \times {{10}^{23}}}}\]
Density = $2.11 g/cm^3$
Density = 2.11 g/ml [$1 cm^3$ = 1ml]
Hence option B is correct.

Note:
The density of a unit cell is defined as the ratio of its mass to its volume. The product of the number of atoms in a unit cell and the mass of each atom in a unit cell equals the mass of a unit cell. Rock salt (NaCl) is an ionic compound that forms white crystals in nature. It is obtained by evaporating seawater or extracting the mineral from halite.