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Characteristics of Equilibrium Constant

ZnOH2 is an a...

Question

$Z n {(O H)}_{2}$ is an amphoteric hydroxide which is involved in the following two equilibria existing simultaneously in aqueous solution.

$Z n {(O H)}_{2} (s) ⇌ {Z n}^{2 +} (a q) + 2 {O H}^{-} (a q)$ ; $K_{s p} = 1.2 \times 10^{- 17}$

$Z n {(O H)}_{2} (s) + 2 {O H}^{-} (a q) ⇌ {[Z n ({O H)}_{4}]}^{2 -} (a q)$ ; $K_{c} = 0.12$

At what $p H$ the solubility of $Z n (O H)_{2}$ will be minimum?

A

p H = 4.11

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B

p H = 6.32

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C

p H = 7.68

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D

p H = 9.99

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Solution

The correct option is D $p H = 9.99$
$Z n {(O H)}_{2 (s)} ⇌ {Z n}_{a q}^{+ 2} + 2 {O H}_{(a q)}^{-}; K_{s p}$

$Z n {(O H)}_{2 (s)} + 2 {O H}^{-} ⇌ {[Z n {(O H)}_{4}]}_{(a q)}^{- 2}; K_{C}$

Dissolved $Z n {(O H)}_{2}$ is present in form of ${Z n}^{+ 2}$ and $[Z n {(O H)}_{4}^{- 2}]$ .

So, solubility $s = [{Z n}^{+ 2}] + {[Z n {(O H)}_{4}]}^{- 2}$

$s = \frac{K_{s p}}{{[{O H}^{-}]}^{2}} + K_{C} {[{O H}^{-}]}^{2}$

For minimum solubility, $\frac{d s}{d [{O H}^{-}]} = 0$
$\Rightarrow$ $\frac{- 2 K_{s p}}{{[{O H}^{-}]}^{3}} + 2 K_{C} [{O H}^{-}] = 0$

$[{O H}^{-}] = 9.8 \times 10^{- 5}$

$p O H = 4.00869$

$p H = 14 - p O H = 9.9913$
$p H = 9.99$

So, $s = 10^{- 9} M$

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Similar questions

Q. Which two sets of reactants best represent the amphoteric character of

Z n {(O H)}_{2}

Z n {(O H)}_{2} (s)

{O H}^{-} (a q)

Z n {(O H)}_{2} (s)

H_{2} O (l)

Z n {(O H)}_{2} (s)

H^{+} (a q)

Z n {(O H)}_{2} (s)

{N H}_{3} (a q)

Q. Calculate the solubility of solid zinc hydroxide at a

p H

5

Z n {(O H)}_{2} (s) ⇌ Z n {(O H)}_{2} (a q)

k_{1} = 10^{- 6} M . . . . . . . . . (1)

Z n {(O H)}_{2} (a q) ⇌ Z n {(O H)}^{+} + {O H}^{-}

k_{2} = 10^{- 7} M . . . . . . . . . (2)

Z n {(O H)}^{+} ⇌ {Z n}^{2 +} + {O H}^{-}

k_{3} = 10^{- 4} . . . . . . (3)

Z n {(O H)}_{2} (a q) + {O H}^{-} ⇌ Z n {(O H)}_{3}^{-}

k_{4} = 10^{3} M^{- 1} . . . . . . . (4)

Z n {(O H)}_{3}^{-} (a q) + {O H}^{-} ⇌ Z n {(O H)}_{4}^{2 -}

k_{5} = 10 M^{- 1} . . . . . . . . . . (5)

A l (O H)_{3}

is involved in the following two equilibria.

A l (O H)_{3} (s) ⇌ A l^{3 +} (a q) + 3 O H^{-} (a q); K_{s p}

A l (O H)_{3} (s) + O H (a q) ⇌ A l (O H)_{4}^{-} (a q); K_{c}

Which of the following relationship is correct when the solubility is minimum?

Q. In the quantitative analysis

B i^{3 +}

is detected by precipitation of [BiO (OH) (s)] [bismuthyl hydroxide). Calculate the pH when the following equilibria exists.

B i O (O H) (s) ⇌ B i o^{\oplus} (a q) + ⊝ O H (a q) (K = 4 \times 10^{- 10})

Q. In the dissociation of

N H_{4} O H

N H_{4} O H (a q) ⇌ N H_{4}^{+} (a q) + O H^{-} (a q)

N H_{4} C l

is added to it, how will the

p H

N H_{4} O H

solution change?

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