Zirconium phosphate (Zr3(PO4)4) dissociates into three zirconium cations of charge +4 and four phosphate anions of charge -3. If molar solubility of zirconium phosphate is denoted by S and its solubility product by Ksp, then which of the following relationships between S and Ksp is correct?

The dissociation of zirconium phosphate is given by:
Zr3(PO4)4(s) <=> 3Zr⁴⁺(aq) + 4PO₄³⁻(aq)
Let S be the molar solubility of Zr3(PO4)4. Then, at equilibrium:
[Zr⁴⁺] = 3S
[PO₄³⁻] = 4S
The solubility product Ksp is given by:
Ksp = [Zr⁴⁺]³[PO₄³⁻]⁴
Substituting the equilibrium concentrations:
Ksp = (3S)³(4S)⁴
Ksp = 27S³ * 256S⁴
Ksp = 6912S⁷
Solving for S:
S⁷ = Ksp/6912
S = (Ksp/6912)^(1/7)
However, this form isn't among the options. Let's re-examine the options. It seems there might be a typo in the options. The correct relationship should be S⁷ = Ksp/6912. None of the provided options accurately reflect this relationship.