Question

KF has a rock-salt structure. Calculate the value of Avogadro's number $\left(N_o\right)$ from the following data:

Density of $KF$ is $2.48$ g cm${}^{-3}$.

Distance between $K^{+}$ and $F^{-}$ in $KF$ is $268$ pm.

• A. $6.2\times {10}^{23}$
• B. $7.22\times {10}^{23}$
• C. $6.07\times {10}^{23}$
• D. $6.02\times {10}^{23}$

Answer 1

The correct option is C $6.07\times {10}^{23}$

Edge length of unit cell in rock-salt structure $=2(r_c+r_a)$

Edge length in KF $=2(r_K+r_F)$ $=2\times \left(268\right)=536$ pm

Volume of unit cell $=(536\times {10}^{-10}{)}^3=154\times {10}^{-24}$ cm${}^3$

In rock-salt structure, one unit cell has $4$ formula units of the salt.
$\text{Density}=\frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}=\frac{z\times \text{Atomic mass}}{N_0\times V}$

For a rock salt type structure, $z=4$
$2.48=\frac{4\times 58}{N_0\times 154\times {10}^{-24}}$
$N_0=\frac{4\times 58}{154\times {10}^{-24}\times 2.48}=6.07\times {10}^{23}$

Hence, the correct option is $\text{C}$