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Question: The pH of \(Mg{{(OH)}_{2}}\) solution is 10.45 at \(25{}^\circ C\). The solubility product of magnes...

The pH of Mg(OH)2Mg{{(OH)}_{2}} solution is 10.45 at 25∘C25{}^\circ C. The solubility product of magnesium hydroxide will be
A. 2.24×10−11M32.24\times {{10}^{-11}}{{M}^{3}}
B. 1.12×10−11M31.12\times {{10}^{-11}}{{M}^{3}}
C. 3.36×10−11M33.36\times {{10}^{-11}}{{M}^{3}}
D. 5.60×10−12M35.60\times {{10}^{-12}}{{M}^{3}}

Explanation

Solution

The solubility product is one of a type of equilibrium constant whose value depends on temperature. It is denoted byKsp{{K}_{sp}}. Solubility products usually increase with an increase in temperature due to increased solubility.

Complete answer:
Solubility is defined as that property of a substance in which solute is dissolved in a solvent in order to form a solution. Solute is that substance which gets dissolved (present in small amount) and solvent in which solute is dissolved (present in higher amount). The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. Solubility depends on a number of parameters out of which lattice enthalpy of salt and solvation energy of ions in the solution are most important.
pH of magnesium hydroxide solution is given i.e. 10.45.
We know that, pOH=14−10.45=3.55pOH=14-10.45=3.55
[OH−]=antilog⁡(−3.55)=0.000282M[O{{H}^{-}}]=anti\log (-3.55)=0.000282M
[Mg2+]=0.0002822=0.000141M[M{{g}^{2+}}]=\dfrac{0.000282}{2}=0.000141M
Solubility product of Mg(OH)2Mg{{(OH)}_{2}}can be calculated by:
(Ksp)Mg(OH)2=[Mg]2+[OH−]2{{({{K}_{sp}})}_{Mg{{(OH)}_{2}}}}={{[Mg]}^{2+}}{{[O{{H}^{-}}]}^{2}}
=0.000141×(0.000282)2=0.000141\times {{(0.000282)}^{2}}
= 1.12×10−11M31.12\times {{10}^{-11}}{{M}^{3}}

Option B is the correct answer.

Note:
pH and pOH are generally a quantity which is used to measure how acidic or how basic a solution is and for most solutions it is measured on a scale of 0 to 14. The lower the number on the pH scale the more acidic the solution is and higher the number on pH scale, more basic is the solution. Neutral solutions which are not acidic or basic have a pH of 7.