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Ionic Equilibrium question

2019 · 12 Apr · Shift 2 · Q4
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  5. /2019 · 12 Apr · Shift 2 · Q4

Ionic Equilibrium question

2019 · 12 Apr · Shift 2 · Q4

JEE MainChemistryIonic EquilibriumMCQ+4 / −1
The molar solubility of Cd(OH)2Cd(OH)_2Cd(OH)2​ is 1.84 × 10–5 M in water. The expected solubility of Cd(OH)2Cd(OH)_2Cd(OH)2​ in a buffer solution of pH = 12 is :
  1. A
    2.49 × 10–10 M
  2. B
    1.84 × 10–9 M
  3. C
    6.23 × 10–11 M
  4. D
    2.491.84×10−9M{{2.49} \over {1.84}} \times {10^{ - 9}}M1.842.49​×10−9M
View written solutionFree

Correct answer: A

  1. Write the dissolution equilibrium

For cadmium hydroxide:

Cd(OH)2(s)⇌Cd2++2OH−Cd(OH)_2(s) \rightleftharpoons Cd^{2+} + 2OH^-Cd(OH)2​(s)⇌Cd2++2OH−

If its molar solubility in pure water is s=1.84×10−5 Ms = 1.84 \times 10^{-5}\,Ms=1.84×10−5M, then at equilibrium:

[Cd2+]=s,[OH−]=2s[Cd^{2+}] = s, \qquad [OH^-] = 2s[Cd2+]=s,[OH−]=2s

So,

Ksp=[Cd2+][OH−]2=s(2s)2=4s3K_{sp} = [Cd^{2+}][OH^-]^2 = s(2s)^2 = 4s^3Ksp​=[Cd2+][OH−]2=s(2s)2=4s3

  1. Calculate KspK_{sp}Ksp​

Ksp=4(1.84×10−5)3K_{sp} = 4(1.84 \times 10^{-5})^3Ksp​=4(1.84×10−5)3

First,

1.843≈6.231.84^3 \approx 6.231.843≈6.23

and

(10−5)3=10−15(10^{-5})^3 = 10^{-15}(10−5)3=10−15

Thus,

Ksp=4×6.23×10−15=24.92×10−15=2.49×10−14K_{sp} = 4 \times 6.23 \times 10^{-15} = 24.92 \times 10^{-15} = 2.49 \times 10^{-14}Ksp​=4×6.23×10−15=24.92×10−15=2.49×10−14

  1. Use the buffer pH to find [OH−][OH^-][OH−]

Given:

pH=12pH = 12pH=12

Therefore,

pOH=14−12=2pOH = 14 - 12 = 2pOH=14−12=2

so,

[OH−]=10−2 M[OH^-] = 10^{-2}\,M[OH−]=10−2M

  1. Find solubility in the buffer

Let the solubility in buffer be s′s's′. Then:

Ksp=[Cd2+][OH−]2=s′(10−2)2K_{sp} = [Cd^{2+}][OH^-]^2 = s'(10^{-2})^2Ksp​=[Cd2+][OH−]2=s′(10−2)2

2.49×10−14=s′×10−42.49 \times 10^{-14} = s' \times 10^{-4}2.49×10−14=s′×10−4

Hence,

s′=2.49×10−1410−4=2.49×10−10 Ms' = \frac{2.49 \times 10^{-14}}{10^{-4}} = 2.49 \times 10^{-10}\,Ms′=10−42.49×10−14​=2.49×10−10M

  1. Match with options

2.49×10−10 M\boxed{2.49 \times 10^{-10}\,M}2.49×10−10M​

This corresponds to Option A.

  1. Comparison with stored correct answer

Stored correct answer: A

Derived answer: A

They agree.

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