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The Handbook of Chemistry and Physics (http://openstaxcollege.org/l/16Handbook) gives solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.

\(\begin{array}{l}(a)BaSe{O_4},0.0118\;g/100\;mL\\(b)Ba{\left( {Br{O_3}} \right)_2} \times {H_2}O,0.30\;g/100\;mL\\(c)N{H_4}MgAs{O_4} \times 6{H_2}O,0.038\;g/100\;mL\\(d)L{a_2}{\left( {Mo{O_4}} \right)_3},0.00179\;g/100\;mL\end{array}\)

Short Answer

Expert verified

The solubility product constant represented as Ksp can be defined as state in which a solid and its respective ions in given solution are in equilibrium. Its value indicates the extent to which a compound can undergo dissociation in water.

Step by step solution

01

Step 1: To calculate the solubility product for each of the following.

(a) \(BaSe{O_4},0.0118\;g/100\;mL\)

First, convert the given value to\(mol/L ,or M.\)

\(\frac{{0.118\;g/L}}{{280.28\;g/mol}} = 4.21 \times 1{0^{ - 4}}M\)

\(Then calculate the solubility product :\)

\(\begin{array}{l}{K_{sp}} = \left[ {B{a^{2 + }}} \right]\left[ {SeO_4^{2 - }} \right]\\{K_{sp}} = \left( {4.21 \times 1{0^{ - 4}}} \right)\left( {4.21 \times 1{0^{ - 4}}} \right)\\{K_{sp}} = 1.77 \times 1{0^{ - 7}}\end{array}\)

02

Step 2: To calculate the solubility product for each of the following.

(b) \(Ba{\left( {Br{O_3}} \right)_2} \times {H_2}O,0.30\;g/100\;mL\)

First, convert the given value to\(mol/L ,or M.\)

\(\frac{{3\;g/L}}{{411.147\;g/mol}} = 7.3 \times 1{0^{ - 3}}M\)

Then calculate the solubility product:

\(\begin{array}{l}{K_{sp}} = \left[ {B{a^{2 + }}} \right]{\left[ {BrO_3^ - } \right]^2}\\{K_{sp}} = \left( {7.3 \times 1{0^{ - 3}}} \right){\left( {2 \times 7.3 \times 1{0^{ - 3}}} \right)^2}\\{K_{sp}}\; = 1.6 \times 1{0^{ - 6}}\end{array}\)

03

 Step 3: To calculate the solubility product for each of the following .

(c) \(N{H_4}MgAs{O_4} \times 6{H_2}O,0.038\;g/100\;mL\)

First, convert the given value to\(mol/L ,or M.\)

\(\frac{{0.38g/L}}{{289.3544g/mol}} = 1.3 \times 1{0^{ - 3}}M\)

Then calculate the solubility product:

\(\begin{array}{l}{K_{sp}} = \left[ {NH_4^ + } \right]\left[ {M{g^{2 + }}} \right]\left[ {AsO_4^{3 - }} \right]\\{K_{sp}}\; = \;\left[ {\rm{x}} \right]\left[ {\rm{x}} \right]\left[ {\rm{x}} \right]\\{\rm{x}}\; = \;1.3 \times 1{0^{ - 3}}\\{K_{sp}} = {\left( {1.3 \times 1{0^{ - 3}}} \right)^3}\\{K_{sp}} = 2.2 \times 1{0^{ - 9}}\end{array}\)

04

Step 4: To calculate the solubility product for each of the following .

(d) \(L{a_2}{\left( {Mo{O_4}} \right)_3},0.00179\;g/100\;mL\)

First, convert the given value to\(mol/L ,or M.\)

\(\frac{{0.0179\;g/L}}{{757.62\;g/mol}} = 2.36 \times 1{0^{ - 5}}M\)

Then calculate the solubility product:

\(\begin{array}{l}{K_{sp}} = {\left[ {2 \times L{a^{3 + }}} \right]^2}{\left[ {3 \times MoO_4^{2 - }} \right]^3}\\{K_{sp}} = {\left( {2 \times 2.36 \times 1{0^{ - 5}}} \right)^2}{\left( {3 \times 2.36 \times 1{0^{ - 5}}} \right)^3}\\{K_{sp}} = 7.91 \times 1{0^{ - 22}}\end{array}\)

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Most popular questions from this chapter

What is the effect on the amount of\(CaHP{O_4}\) that dissolves and the concentrations of \(C{a^{2 + }}\;and\;HPO_4^ - \)when each of the following are added to a mixture of solid \(CaHP{O_4}\)and water at equilibrium?

\(\;(a)\;CaC{l_2}\)

\(\;(b)\;HCl\)

\(\;(c)\;KCl{O_4}\)

\(\;(d)\;NaOH\)

\(\;(e)\;CaHP{O_4}\)

Question: A roll of \(35 - mm\) black and white photographic film contains about \(0.27g\) of unexposed \(AgBr\) before developing. What mass of \(N{a_2}{S_2}{O_3} \cdot 5{H_2}O\) (sodium thiosulfate penta hydrate or hypo) in \(1.0L\)of developer is required to dissolve the \(AgBr\)as \(Ag\left( {{S_2}{O_3}} \right)_2^{3 - }\left( {{K_f} = 4.7 \times 1{0^{13}}} \right)?\)

The Handbook of Chemistry and Physics (http://openstaxcollege.org/l/16Handbook) gives solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.

\(\begin{array}{l}(a)BaSi{F_6},0.026\;g/100\;mL(contains Si{F_6}^2 - ions)\\(b)Ce{\left( {I{O_3}} \right)_4},1.5 \times 1{0^{ - 2}}\;g/100\;mL\\(c)G{d_2}{\left( {S{O_4}} \right)_3},3.98\;g/100\;mL\\(d){\left( {N{H_4}} \right)_2}PtB{r_6},0.59\;g/100\;mL(contains PtB{r_6}^{2 - } ions)\end{array}\)

Question: Calculate the cadmium ion concentration, \(\left( {C{d^{2 + }}} \right)\)in a solution prepared by mixing 0.100 L of 0.0100 M \(Cd{\left( {N{O_3}} \right)_2}\)with 1.150 L of 0.100 \(N{H_3}(aq)\).

Question: Using the dissociation constant, \({K_d} = 3.4 \times 1{0^{ - 15}}\), calculate the equilibrium concentrations of \(Z{n^{2 + }}\;and\;O{H^ - }in{\rm{\;}}\)\({\rm{\;}}a\;0.0465 - M\)solution of \(Zn(OH)_4^{2 - }\).

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