Question

The unit cell length of $NaCl$ is observed to be $0.5627$ nm by X-ray difference studies; the measured density of $NaCl$ is $2.164$g $c{m}^{-3}$/ Calculate the difference of observed and calculated density. lso calculate $\%$ is missing $N{a}^{+}$ and $C{l}^{-}$ ions:

• A. $0.031,0.775\%$
• B. $3.96,0.031\%$
• C. $0.0031,7.75\%$
• D. $1.7,1.75\%$

Answer 1

Answer: (B)

$3.96,0.031\%$

$\rho =\frac{M_A\times Z}{N_A\times a^3}$

${\rho }_{observed}=2.164$ $gc{m}^{-3}$

$a=0.5627$ $nm$

$N_A=6.023\times {10}^{23}$

$Z_{observed}=?$

$2.164=\frac{58.5\times Z_{observed}}{6.023\times (5.627{)}^3\times {10}^{-24}\times {10}^{23}}$

$Z_{observed}=3.96$

$Z_{theoretical}=4$

${\rho }_{theoretical}=2.180$ $g/c{m}^3$

So, $\rho =\frac{4\times M_A}{N_A\times a^3}$

${\rho }_{theoretical}-{\rho }_{observed}=0.016$ $gm/c{m}^3$

Percentage of missing ions $=\frac{4-396}{4}\times 100=1\%$