Q35 / 160 · WBJEE 2011 · Chemistry

The solubility of \(\mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2\) in water is y moles / litre. Its solubility product is

  • A
    \(6 y^4\)
  • B
    \(36 y^4\)
  • C
    \(64 y^5\)
  • Correct answer
    D
    \(108 \mathrm{y}^5\)

Solution

\(\begin{aligned} & \text {Hints: } \mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2(\mathrm{~s}) \rightleftharpoons 3 \underset{3 \mathrm{~s}}{\mathrm{Ca}^{2+}}(\mathrm{aq})+\underset{2 \mathrm{~s}}{2 \mathrm{PO}_4}{ }^{3-}(\mathrm{aq}) \\ & \mathrm{~K}_{\mathrm{Sp}}=\left[\mathrm{Ca}^{2+}\right]^3 \cdot\left[\mathrm{PO}_4^{3-}\right]^2 \\ & =(3 \mathrm{~s})^3 \cdot(2 \mathrm{~s})^2 \\ & =27 \mathrm{~s}^3 \times 4 \mathrm{~s}^2 \\ & =108 \mathrm{~s}^5 \\ & \end{aligned}\)

Hence, the correct answer is option: 'D'.

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