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Solubility of Al(OH)(3) = S, K(sp) will ...

Solubility of `Al(OH)_(3) = S, K_(sp)` will be

A

`108 S^(3)`

B

`27 S^(3)`

C

`4 S^(2)`

D

`27 S^(4)`

Text Solution

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The correct Answer is:
To find the solubility product constant (\(K_{sp}\)) of aluminum hydroxide (\(Al(OH)_3\)) in terms of its solubility (\(S\)), we can follow these steps: ### Step 1: Write the Dissociation Reaction The dissociation of aluminum hydroxide in water can be represented as: \[ Al(OH)_3 (s) \rightleftharpoons Al^{3+} (aq) + 3 OH^{-} (aq) \] ### Step 2: Define the Solubility (\(S\)) Let the solubility of \(Al(OH)_3\) be \(S\) mol/L. This means that when \(Al(OH)_3\) dissolves, it produces: - \(S\) moles of \(Al^{3+}\) - \(3S\) moles of \(OH^{-}\) ### Step 3: Write the Expression for \(K_{sp}\) The solubility product constant (\(K_{sp}\)) is given by the expression: \[ K_{sp} = [Al^{3+}][OH^{-}]^3 \] Substituting the concentrations in terms of \(S\): \[ K_{sp} = [S][3S]^3 \] ### Step 4: Simplify the Expression Now, simplify the expression: \[ K_{sp} = S \cdot (3S)^3 = S \cdot 27S^3 = 27S^4 \] ### Step 5: Final Expression for \(K_{sp}\) Thus, the solubility product constant for aluminum hydroxide in terms of its solubility is: \[ K_{sp} = 27S^4 \] ### Conclusion The final expression for the solubility product constant \(K_{sp}\) of \(Al(OH)_3\) is: \[ K_{sp} = 27S^4 \]

To find the solubility product constant (\(K_{sp}\)) of aluminum hydroxide (\(Al(OH)_3\)) in terms of its solubility (\(S\)), we can follow these steps: ### Step 1: Write the Dissociation Reaction The dissociation of aluminum hydroxide in water can be represented as: \[ Al(OH)_3 (s) \rightleftharpoons Al^{3+} (aq) + 3 OH^{-} (aq) \] ...
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Knowledge Check

  • What is the solubility of Al(OH)_(3) , ( K_(sp)=10^(-33) ) in a buffer solution of pH=4?

    A
    `10^(-3)`M
    B
    `10^(-6)`M
    C
    `10^(-4)`M
    D
    `10^(-10)`M
  • If the solubility of Al(OH)_3 is S moles/litre, the solubility product is

    A
    `S^3`
    B
    `27S^4`
    C
    `S^2`
    D
    `4S^3`
  • Solubility of Ca(OH)_(2) is s mol L^(-1). The solubility product (K_(sp)) under the same condition is

    A
    `4s^(3)`
    B
    `3s^(4)`
    C
    `4s^(2)`
    D
    `s^(3)`
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