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Chapter 15: Q57E (page 875)

Question: How many grams of Milk of Magnesia, \(Mg{(OH)_2}(s)(58.3g/mol)\)would be soluble in 200 mL of water. \({K_{sp}}\)=\(7.1 \times 1{0^{ - 12}}\) Include the ionic reaction and the expression for \({K_{sp}}\)in your answer\(\left( {{K_w} = 1 \times 1{0^{ - 14}} = } \right.\)\(\left. {\left( {{H_3}{O^ + }} \right)\left( {O{H^ - }} \right)} \right)\)

Short Answer

Expert verified

There is \(1.14 \times {10^{ - 3}}{\rm{g}}\)of milk of magnesia.

Step by step solution

01

Calculate grams of Milk of Magnesia:

\(Mg{(OH)_2}(s) \leftrightarrow M{g^{2 + }} + 2O{H^ - }\)

Find \({K_{{\rm{sp}}}}\),

\(\begin{array}{l}{K_{sp}} = \left( {M{g^{2 + }}} \right){\left( {O{H^ - }} \right)^2}\\ = 7.1 \times {10^{ - 12}}\end{array}\)

\(\begin{array}{l}\left( {M{g^{2 + }}} \right) = \sqrt(3){{\frac{{{K_{sp}}}}{4}}}\\ = \sqrt(3){{\frac{{7.1 \times {{10}^{ - 12}}}}{4}}}\\ = 1.21 \times {10^{ - 4}}M\end{array}\)

\(\begin{array}{l}m\left( {Mg{{(OH)}_2}} \right) = c\left( {M{g^{2 + }}} \right) \times V\left( {{H_2}O} \right) \times {M_r}\left( {Mg{{(OH)}_2}} \right)\\ = 1.21 \times {10^{ - 4}}M \times 0.2L \times 58.3g/mol\\ = 1.14 \times {10^{ - 3}}g\end{array}\)

The solution is \(1.14 \times {10^{ - 3}}{\rm{g}}\)of milk of magnesia.

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Most popular questions from this chapter

A volume of \(50mL\) of \(1.8MN{H_3}\)is mixed with an equal volume of a solution containing\(0.95g\;of\;MgC{l_2}\). What mass of \(N{H_4}Cl\)must be added to the resulting solution to prevent the precipitation of \(Mg{(OH)_2}?\)

Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that changes in the initial concentrations of the common ions can be neglected.

\(\begin{array}{l}(a)AgCl(\;s\;)in 0.025MNaCl \\(b)Ca{F_2}(\;\;s\;)in 0.00133MKF \\(c)A{g_2}S{O_4}(\;\;s\;)in 0.500\;L of a solution containing 19.50\;g of {K_2}S{O_4}\\(d)Zn{(OH)_2}(\;s\;)in a solution buffere data pHof 11.45\end{array}\)

Complete the changes in concentrations for each of the following reactions:

\(\begin{array}{l}(a)BaS{O_4}(S) \to nB{a^{2 + }}(aq) + SO_4^{2 - }(aq)\\ X - \\(b)A{g_2}S{O_4}(S) \to n2A{g^ + }(aq) + S{O_4}^{2 - }(a)\\ - X\\(c)Al{(OH)_3}(S) \to nA{l^{3 + }}(aq) + 3O{H^ - }(aq)\\ X \_ \\(d)Pb(OH)Cl(S) \to nP{b^{2 + }}(aq) + O{H^ - }(aq) + C{l^ - }(aq)\\ \_ X \_\\(e)C{a_3}{\left( {As{O_4}} \right)_2}(S) \to n3C{a^{2 + }}(aq) + 2AsO_4^{3 - }(aq)\\ 3x \_\end{array}\)

The following question is taken from a Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service. Solve the following problem:

MgF2 (S) ⇌ Mg2+(aq) + 2F- (aq)

In a saturated solution of MgF2 at 18 °C, the concentration ofMg2+is 1.21×10-3 M.

The equilibrium is represented by the preceding equation.

(a) Write the expression for the solubility-product constant, Ksp, and calculate its value at 18 °C.

(b) Calculate the equilibrium concentration of Mg2+ in 1.000 L of saturated MgF2solution at 18 °C to which 0.100 mol of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible.

(c) Predict whether a precipitate of MgF­2 will form whensolution of 100.0mL of a 3.00 ×10-3 -M Mg(NO3)2 is mixed with 200.0 mL of a 2.00 × 10–3 -M solution of NaF at 18 °C. Show the calculations to support your prediction.

(d) At 27 °C the concentration of Mg2+ in a saturated solution of MgF2 is 1.17×10-3 M. Is the dissolving of MgF2 in water an endothermic or an exothermic process? Give an explanation to support your conclusion.

What is the molar solubility of \({\bf{Pb}}{\left( {{\bf{OH}}} \right)_{\bf{2}}}\) in a \({\bf{0}}.{\bf{138}}{\rm{ }}{\bf{M}}\) solution of\({\bf{C}}{{\bf{H}}_{\bf{3}}}{\bf{N}}{{\bf{H}}_{\bf{2}}}\)?
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