Question

The number of unit cells in 58.5g of NaCl is nearly
(A) $6\times {{10}^{22}}$
(B) $3\times {{10}^{22}}$
(c) $1.5\times {{10}^{23}}$
(D )$0.5\times {{10}^{24}}$

Answer 1

Hint: Avogadro’s constant is a physical value. Mole concept is used to tell the amount of substance.Molar mass of a substance is the sum of individual atomic masses of the atoms.

Complete answer:
Mole concept is a convenient way of expressing the amount of substance.According to mole concept, One mole of any compound has $6.022\times {{10}^{23}}$atoms/molecules/ions. This quantity is known as Avogadro’s constant, and denoted with ${{N}_{A}}$.
So, for the given compound, we have 58.5g of NaCl, and the molar mass of NaCl is 58.5g/mol. So, mole will be,
     \[mole=\dfrac{weight}{mol.weight}\]
     \[mole=\dfrac{58.5}{58.5}\]
therefore, mole of NaCl = 1.
So, for the given question there is one mole of NaCl, now we have to tell the number of unit cells in 58.5g of NaCl. So, according to Avogadro’s constant, in one mole of substance, there will be $6.022\times {{10}^{23}}$ unit cells.
NaCl has a rock salt type of structure. It is having FCC lattice. The atoms are present at the corners and at the face centres of the lattice with the ions of the opposite type occupying the alternate positions in between them. Therefore, in FCC lattice arrangement, there are 4 atoms in a cell. So, one mole have $6.022\times {{10}^{23}}$ unit cells of NaCl lattice.
So, the correct answer is “Option A”.

Note: The number of moles of a substance can be calculated by various means,these are, number of moles of molecules,number of moles of atoms,number of moles of gases (standard molar volume at STP=22.4Litre), number of moles of particles(molecules,atoms,ions),mole fraction.