Question

How many units cells are there in $1.00g$ cube shaped ideal crystal of $AB(Mw=60)$ which has a $NaCl$ type lattice?

• A. $6.02\times {10}^{23}$
• B. $1.00\times {20}^{22}$
• C. $2.50\times {10}^{21}$
• D. $6.02\times {10}^{24}$

Answer 1

The correct option is C $2.50\times {10}^{21}$

$NaCl$ has Rock salt type lattice, so Numbers of atoms per unit cell = 4
That means 4 $NaCl$ farms = 1 unit cell
So in $AB$ (mw = 60) $=4AB$ forms one unit cell.
Now 1.0 gram of $AB$ has Numbers of moles = $\frac{Givenmass}{molarmass}$
= $\frac{1}{60}$ mole
1 mole of $AB=$ $6.022\times {10}^{23}$
$\frac{1}{60}$ mole of $AB=\frac{1}{60}\times 6.022\times {10}^{23}$
= $1.004\times {10}^{22}AB$
$4AB$ forms = 1 unit all
$1AB$ forms = $\frac{1}{4}$ unit all
$1.004\times {10}^{22}$AB form = $\frac{1}{4}\times 1.004\times {10}^{22}$
$9.50\times {10}^{21}$
$0.250\times {10}^{22}$

$2.50\times {10}^{21}$

So, the answer is $2.50\times {10}^{21}$