Question

Total number of voids in $0.5$ mole of a compound forming hexagonal closed packed structure are:
(A) $6.022 \times {10^{23}}$
(B) $3.011 \times {10^{23}}$
(C) $9.033 \times {10^{23}}$
(D) $4.516 \times {10^{23}}$

Answer 1

Hint:The nearest pressing of circles in two measurements has hexagonal evenness where each circle has six closest neighbors. Hexagonal close-pressing relates to an ABAB stacking of such planes. Every iota has twelve closest neighbors in hcp. In the ideal structure, the distance between the planes where an is the distance between the molecules.

Complete step-by-step answer:As we know, No of molecules present in $0.5$ moles of compound are equal to:
No of molecules = $0.5$ × Avogadro's number
Substituting the Avogadro number value in the above equation; we get:
$ \Rightarrow 0.5 \times 6.022 \times {10^{23}}$
Simplifying the above equation;
$3.011 \times {10^{23}}$ ions
Octahedral voids are the same as molecules in HCP.
As we know;Octahedral voids is equal to the no of molecules
$ \Rightarrow $ Octahedral voids = no of molecules
As,we know;Octahedral voids = $3.011 \times {10^{23}}$ voids
Tetrahedral voids are double the no as of molecules in HCP. Tetrahedral voids are the twice the number of molecules
$ \Rightarrow $ Tetrahedral voids = 2 × no of molecules
Tetrahedral voids = $2 \times 3.011 \times {10^{23}}$ voids
Simplifying it more;
Tetrahedral voids = $6.022 \times {10^{23}}$ voids
Now let us calculate the Complete no of voids:We know that Complete voids is the sum of both tetrahedral voids and octahedral voids.
$ \Rightarrow $ Complete voids = tetrahedral voids + octahedral voids
Substituting the values we got after computing in the above equation:
Complete voids = $6.022 \times {10^{23}}$ + $3.011 \times {10^{23}}$
$ \Rightarrow $ Complete voids = $9.033 \times {10^{23}}$ voids
In this way, $9.033 \times {10^{23}}$ voids will be available

Additional information:What is Avogadro’s number?The Avogadro number is the proportionality factor that relates the quantity of constituent particles (normally particles, iotas or particles) in an example with the measure of substance in that example. Its SI unit is the proportional mole. It is named after the Italian researcher Amedeo Avogadro. Although this is called Avogadro's steady (or number), he isn't the scientific expert who decided it's worth. Stanislao Cannizzaro clarified this number four years after Avogadro's passing while at the Karlsruhe Congress in 1860. The numeric estimation of the Avogadro constant communicated in complementary mole, a dimensionless number, is known as the Avogadro number, here and there signified $N$ or ${N_0}$, which is in this way the quantity of particles that are contained in one mole.
The estimation of the Avogadro steady was picked with the goal that the mass of one mole of a substance compound, in grams, is mathematically equivalent (overall) to the normal mass of one particle of the compound, in Daltons (widespread nuclear mass units); one Dalton being $\frac{1}{12}$of the mass of one carbon-12 molecule, which is around the mass of one nucleon (proton or neutron). Twelve grams of carbon contains one mole of carbon particles.

Note: The Avogadro steady additionally relates the molar volume of a substance to the normal volume ostensibly involved by one of its particles, when both are communicated in similar units of volume. For a glasslike substance, it likewise relates its molar volume, the volume of the rehashing unit cell of the precious stones , and the quantity of atoms in that cell.