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Ionic Equilibrium question

2025 · 22 Jan · Shift 2 · Q11
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  5. /2025 · 22 Jan · Shift 2 · Q11

Ionic Equilibrium question

2025 · 22 Jan · Shift 2 · Q11

JEE MainChemistryIonic EquilibriumMCQ+4 / −1
The molar solubility(s) of zirconium phosphate with molecular formula (Zr4+)3(PO43−)4\left(\mathrm{Zr}^{4+}\right)_3\left(\mathrm{PO}_4^{3-}\right)_4(Zr4+)3​(PO43−​)4​ is given by relation :
  1. A
    (Ksp5348)16\left(\frac{\mathrm{K}_{\mathrm{sp}}}{5348}\right)^{\frac{1}{6}}(5348Ksp​​)61​
  2. B
    (Ksp8435)17\left(\frac{\mathrm{K}_{\mathrm{sp}}}{8435}\right)^{\frac{1}{7}}(8435Ksp​​)71​
  3. C
    (Ksp6912)17\left(\frac{K_{s p}}{6912}\right)^{\frac{1}{7}}(6912Ksp​​)71​
  4. D
    (Ksp9612)13\left(\frac{\mathrm{K}_{\mathrm{sp}}}{9612}\right)^{\frac{1}{3}}(9612Ksp​​)31​
View written solutionFree

Correct answer: C

  1. Write the dissolution equilibrium

For zirconium phosphate,

Zr3(PO4)4(s)⇌3 Zr4++4 PO43−\mathrm{Zr_3(PO_4)_4(s)} \rightleftharpoons 3\,\mathrm{Zr^{4+}} + 4\,\mathrm{PO_4^{3-}}Zr3​(PO4​)4​(s)⇌3Zr4++4PO43−​

If the molar solubility is sss, then at equilibrium:

[Zr4+]=3s,[PO43−]=4s[\mathrm{Zr^{4+}}] = 3s, \qquad [\mathrm{PO_4^{3-}}] = 4s[Zr4+]=3s,[PO43−​]=4s
  1. Write the solubility product expression

Using the stoichiometric coefficients as powers:

Ksp=[Zr4+]3[PO43−]4K_{sp} = [\mathrm{Zr^{4+}}]^3[\mathrm{PO_4^{3-}}]^4Ksp​=[Zr4+]3[PO43−​]4

Substitute the equilibrium concentrations:

Ksp=(3s)3(4s)4K_{sp} = (3s)^3(4s)^4Ksp​=(3s)3(4s)4
  1. Simplify
(3s)3=27s3(3s)^3 = 27s^3(3s)3=27s3 (4s)4=256s4(4s)^4 = 256s^4(4s)4=256s4

Therefore,

Ksp=27×256×s7K_{sp} = 27 \times 256 \times s^7Ksp​=27×256×s7 Ksp=6912 s7K_{sp} = 6912\,s^7Ksp​=6912s7
  1. Solve for sss
s7=Ksp6912s^7 = \frac{K_{sp}}{6912}s7=6912Ksp​​ s=(Ksp6912)1/7s = \left(\frac{K_{sp}}{6912}\right)^{1/7}s=(6912Ksp​​)1/7
  1. Match with the options

This corresponds to:

(Ksp6912)1/7\boxed{\left(\frac{K_{sp}}{6912}\right)^{1/7}}(6912Ksp​​)1/7​

So, Option C is correct.

  1. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They agree.

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