Question

Ionic solid $B^{+}{A}^{-}$ crystallizes in rock salt type structure. $1.296\text{g}$ ionic solid salt $B^{+}{A}^{-}$ is dissolved in water to make one liter solution. The $pH$ of the solution is measured to be $6$ due to hydrolysis. If the value of face diagonal in the unit cell of $B^{+}{A}^{-}$ be $600\sqrt{2}\text{pm}$. Then which of the following statements is/are correct:
$(\text{Given}:T=298\text{K},K_b\text{for}BOH={10}^{-4},N_A=6.0\times {10}^{23})$

• A. Molar mass of the salt $B^{+}{A}^{-}$ is $129.6{\text{g mol}}^{-1}$
• B. Edge length of unit cell is $600\times {10}^{-10}\text{cm}$
• C. Density of the ionic solid is $4\text{g/cc}$
• D. Concentration of the salt is $0.02\text{M}$

Answer 1

Answer: (A), (B), (C)

Density of the ionic solid is $4\text{g/cc}$

We know,
$pH=\frac{1}{2}(p{K}_w-p{K}_b-logC)$
Where, $C=\text{concentration of the acid = concentration of the salt}$
Here, $pH=6,K_b={10}^{-4}$
Therefore,
$6=\frac{1}{2}(14-4-logC)$
$\Rightarrow 12=10-logC$
$\Rightarrow 2=-logC$
$\Rightarrow C=0.01\text{M}$
Given, mass of $B^{+}{A}^{-}=1.296\text{g}$
Therefore, concentration $C=\frac{1}{100}=\frac{1.296}{\text{Molar mass}}$
$\text{Molar mass}=129.6\text{g}$
Again, the value of face diogonal in the unit cell of $B^{+}{A}^{-}$ be $600\sqrt{2}\text{pm}$
Thus if we take edge length to be $a$, then $a\sqrt{2}=600\sqrt{2}\text{pm}$
Thus edge length, $a=600\text{pm}=600\times {10}^{-10}\text{cm}$
Now, density of the solid can be calculated by using the formula, $\frac{Z}{N_A}\left(\frac{M}{a^3}\right)$
Here, effective number of atom $Z=4$
Therefore, density $=\frac{4}{6\times {10}^{23}}\left[\frac{129.6}{(600{)}^3\times {10}^{-30}}\right]\text{g/cc}$
$=4\text{g/cc}$