Question

How many unit cells are present in a cube shaped ideal crystal of NaCl of mass 1.00 g?

Answer 1

$\boxed{ \boxed{ \sf \red{Key \: Ideas}}}$

• NaCl contains FCC unit cell therefore the unit cell of the crystal will be FCC of unit cell.

Find the mass by the formula $\sf \pink{mass \: = \: volume \: \times density}$

• Calculate the number of unit cell presents in one gram of crystal.

$\boxed{ \boxed{ \sf \red{Let \: us \: come \: to \: Question}}}$

$\sf{Mass \: of \: one \: unit \: cell \: (m) = volume \times density} \\ \\ \sf{ = {a}^{3} \times d = {a}^{3} \times \frac{Mz}{N_0 a^3} = \frac{Mz}{N_0 }}$

$\sf{Molecular \: mass \: (M) = 23 + 35.5 = 58.5 }$

$\sf{FCC \: of \: unit \: cell \: contains \: 4 \: molecules \: of \: NaCl}$

$\sf{m = \frac{58.5 \times 4}{6.02 \times {10}^{23} } \: g }$

$\sf{ \therefore \:Number \: of \: unit \: cells \: in \: 1g \: = \frac{1}{m} }$

$\implies \sf{ \frac{6.02 \times {10}^{23} }{58.5 \times 4 \: \: \: \: \: } = 2.57 \times {10}^{21} }$

Answer 2

How many unit cells are present in a cube shaped ideal crystal of NaCl of mass 1.00 g?