Solid StateHard

Question

A quantity of 80.0 g of a salt (XY) of strong acid and weak base is dissolved in water to form 2.0 L aqueous solution. At 298 K, the pH of the solution is found to be 5.0. If XY forms CsCl type crystal and the radius of X+ and Y– ions are 160 pm and 186.4 pm, respectively, then the correct information is

(Given: Kb of XOH = 4 × 10−5, NA = 6 × 1023, $\sqrt{3}$= 732)

Options

A.molar mass of the salt is 100 g/mol.
B.the degree of hydrolysis of salt is 2.5 × 10−5.
C.unit cell edge length of XY crystal is 400 pm.
D.density of solid XY is 2.6 g/cm3.

Solution

(a)$P^{H} = 7 + \frac{1}{2}\left( P^{K_{a}} + \log c \right) \Rightarrow 5.0 = 7 - \frac{1}{2}\left( 4.4 + \log c \right)$

$\therefore\mspace{6mu}\mspace{6mu} c = 0.4 = \frac{80/M}{2} \Rightarrow M = 100$

(b) $h = \sqrt{\frac{K_{h}}{K_{b} \times c}} = \sqrt{\frac{10^{- 14}}{4 \times 10^{- 5} \times 0.4}} = 2.5 \times 10^{- 5}$

(c) $\sqrt{3}a = 2\left( r_{x^{+}} + r_{y^{-}} \right) \Rightarrow a = \frac{2 \times (160 + 186.4)}{\sqrt{3}} = 400\text{pm}$

(d) $d = \frac{Z.M}{N_{A}.V} = \frac{1 \times 100}{6 \times 10^{23} \times \left( 400 \times 10^{- 10} \right)} = 2.6\text{gm/c}\text{m}^{3}$

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