Zirconium phosphate

Question:

Zirconium phosphate $\left[\mathrm{Zr}_{3}\left(\mathrm{PO}_{4}\right)_{4}\right]$ 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 $\mathrm{K}_{\mathrm{sp}}$ then which of the following relationship between $\mathrm{S}$ and $\mathrm{K}_{\mathrm{sp}}$ is correct ?

  1. $\mathrm{S}=\left\{\mathrm{K}_{\mathrm{sp}} / 144\right\}^{1 / 7}$

  2. $\mathrm{S}=\left\{\mathrm{K}_{\mathrm{sp}} /(6912)^{1 / 7}\right\}$

  3. $\mathrm{S}=\left(\mathrm{K}_{\mathrm{sp}} / 6912\right)^{1 / 7}$

  4. $S=\left\{K_{\mathrm{sp}} / 6912\right\}^{7}$

Correct Option: , 3

Solution:

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