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Ionic Equilibrium question

2002 · Shift 0 · Q6
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Ionic Equilibrium question

2002 · Shift 0 · Q6

JEE MainChemistryIonic EquilibriumMCQ+4 / −1
Let the solubility of an aqueous solution of Mg(OH)2Mg(OH)_2Mg(OH)2​ be x then its Ksp is :
  1. A
    4x3
  2. B
    108x5
  3. C
    27x4
  4. D
    9x
View written solutionFree

Correct answer: A

  1. Write the dissolution equilibrium

Mg(OH)2(s)⇌Mg2+(aq)+2OH−(aq)Mg(OH)_2(s) \rightleftharpoons Mg^{2+}(aq) + 2OH^-(aq)Mg(OH)2​(s)⇌Mg2+(aq)+2OH−(aq)

  1. Let the solubility be xxx

If the solubility of Mg(OH)2Mg(OH)_2Mg(OH)2​ is x mol L−1x\,\text{mol L}^{-1}xmol L−1, then at equilibrium:

  • [Mg2+]=x[Mg^{2+}] = x[Mg2+]=x
  • [OH−]=2x[OH^-] = 2x[OH−]=2x
  1. Write the expression for KspK_{sp}Ksp​

For the salt Mg(OH)2Mg(OH)_2Mg(OH)2​,

Ksp=[Mg2+][OH−]2K_{sp} = [Mg^{2+}][OH^-]^2Ksp​=[Mg2+][OH−]2

Substitute the concentrations:

Ksp=(x)(2x)2K_{sp} = (x)(2x)^2Ksp​=(x)(2x)2

Ksp=x⋅4x2=4x3K_{sp} = x \cdot 4x^2 = 4x^3Ksp​=x⋅4x2=4x3

  1. Match with the options
  • A: 4x34x^34x3
  • B: 108x5108x^5108x5
  • C: 27x427x^427x4
  • D: 9x9x9x

So the correct option is A.

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