Question

If the density of $NaCl$ is $2.165$ g/cc and the distance between $N{a}^{+}$ and $C{l}^{-}$ ion is $281$ pm, then the value of Avogadro's number is equal to :

• A. $6.012\times {10}^{23}mo{l}^{-1}$
• B. $6.023\times {10}^{23}mo{l}^{-1}$
• C. $6.089\times {10}^{23}mo{l}^{-1}$
• D. $6.099\times {10}^{23}mo{l}^{-1}$

Answer 1

Answer: (C)

$6.089\times {10}^{23}mo{l}^{-1}$

Given that the distance between $N{a}^{+}$ and $C{l}^{-}$ ion is $281$ pm.

So, $a\left(edgelength\right)=2\times 281=562$ pm= $562\times {10}^{-10}$ cm.

The formula for density is given below:

$d=\frac{zM}{N_A{a}^3}$, where $z$ is the number of atoms in a lattice type.

Substituting the values, we get

$\frac{4\times 58.5}{N_A\times {(562\times {10}^{-10})}^3}=2.165$ g/cc $⟹N_A={6.089\times 10}^{23}mo{l}^{-1}$