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Chapter 16: Problem 75

The solubility product of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is \(1.2 \times 10^{-11}\) What minimum \(\mathrm{OH}^{-}\) concentration must be attained (for example, by adding \(\mathrm{NaOH}\) ) to decrease the \(\mathrm{Mg}^{2+}\) concentration in a solution of \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) to less than \(1.0 \times 10^{-10} M ?\)

Short Answer

Expert verified
The minimum hydroxide ion concentration that must be attained in order to decrease the magnesium ion concentration in a solution of \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) to less than \(1.0 \times 10^{-10} M\) is \(0.3464 M\).

Step by step solution

01

Solubility Product Relationship

For the solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}\), the equation is \(\mathrm{Mg}(\mathrm{OH})_{2} \leftrightarrow \mathrm{Mg}^{2+} + 2\mathrm{OH}^{-}\). Hence, the solubility product \(K_{sp}\) expression is: \(K_{sp} = [\mathrm{Mg}^{2+}][\mathrm{OH}^{-}]^{2}\). The given solubility product \(K_{sp}\) of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is \(1.2 \times 10^{-11}\).
02

Insert The \(\mathrm{Mg}^{2+}\) Concentration

Now, rearrange the \(K_{sp}\) expression to solve for the hydroxide ion concentration, \([\mathrm{OH}^{-}]\). The problem aims to find \([\mathrm{OH}^{-}]\) when [\(\mathrm{Mg}^{2+}\)] is \(1.0 \times 10^{-10} M\). Thus, \([\mathrm{OH}^{-}]= \sqrt{K_{sp}/[\mathrm{Mg}^{2+}]}\).
03

Calculate The \(\mathrm{OH}^{-}\) Concentration

Substitute the known values into the equation from Step 2: \([\mathrm{OH}^{-}] =\sqrt{1.2 \times 10^{-11}/(1.0 \times 10^{-10})}\) which gives \([\mathrm{OH}^{-}] =\sqrt{0.12}\).
04

Evaluate The Calculation

Upon evaluating the square root of 0.12, we get \([\mathrm{OH}^{-}] = 0.3464 M\). This is the minimum \(\mathrm{OH}^{-}\) concentration needed to maintain a magnesium ion, \(\mathrm{Mg}^{2+}\), concentration in a solution of \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) to less than \(1.0 \times 10^{-10} M\).

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Most popular questions from this chapter

A student carried out an acid-base titration by adding \(\mathrm{NaOH}\) solution from a buret to an Erlenmeyer flask containing HCl solution and using phenolphthalein as indicator. At the equivalence point, she observed a faint reddish-pink color. However, after a few minutes, the solution gradually turned colorless. What do you suppose happened?

For which of the following reactions is the equilibrium constant called a solubility product? $$ \begin{array}{l} \text { (a) } \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{OH}^{-}(a q) \rightleftharpoons \\ \text { (b) } 3 \mathrm{Ca}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons \mathrm{Ca}_{3}(\mathrm{OH})_{4}^{2-}(a q) \end{array} $$ (c) \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons\) $$ \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) $$ (d) \(\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)\)

The \(p K_{a}\) of butyric acid (HBut) is \(4.7 .\) Calculate \(K_{b}\) for the butyrate ion (But- ).

A 0.2688 -g sample of a monoprotic acid neutralizes \(16.4 \mathrm{~mL}\) of \(0.08133 \mathrm{M}\) KOH solution. Calculate the molar mass of the acid.

A volume of \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) is titrated against a \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}\) solution added to it from a buret. Calculate the \(\mathrm{pH}\) values of the solution (a) after \(10.0 \mathrm{~mL}\) of \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) solution have been added, (b) after \(25.0 \mathrm{~mL}\) of \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) solution have been added, (c) after \(35.0 \mathrm{~mL}\) of \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) solution have been added.
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