Question

How many unit cells are present in a cubic -shaped ideal crystal of NaCl of mass 1.00 g [Atomic masses: Na= 23, Cl = 35.5]

• A. $2.57\times {10}^{21}$ unit cells
• B. $5.14\times {10}^{21}$ unit cells
• C. $1.28\times {10}^{21}$ unit cells
• D. $1.71\times {10}^{21}$ unit cells

Answer 1

The correct option is A

$2.57\times {10}^{21}$ unit cells

$NaCl\Rightarrow C{l}^{-}$ occupies corners and face centres $\Rightarrow$ Effectively $4C{l}^{-}$ ions
$N{a}^{+}$ occupies octahedral voids.
$\Rightarrow$ Effectively $4N{a}^{+}ions$.
$\Rightarrow$ 1 unit cell has effectively 4 molecules of NaCl.
mass of unit cell $=\frac{4\times mass\left(NaCl\right)}{6.023\times {10}^{23}}=\frac{4\times 58.5}{6.023\times {10}^{23}}$
$\Rightarrow$ No. of unit cell in $1g=\frac{1g}{\frac{4\times 58.5}{6.023\times {10}^{23}}}=2.57\times {10}^{21}$ unit cells