Chapter 15: Equilibria of Other Reaction ClassesContent check — Chemistry: Atoms First, Chapter 15: Equilibria of Other Reaction Classes

(a) BaSO₄

(b) Ag₂SO₄

(c) Al(OH)₃

(d) Pb(OH)Cl

(a) Ni(NO₃)₂

(b) KClO₄

(c) NiCO₃

(d) K₂CO₃

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

(a)
$$\begin{array}{ccc}\text{AgI}(s)⟶& {\text{Ag}}^{\text{+}}(aq)& +{\text{I}}^{\text{−}}(aq)\\ \\ & x& \_\_\_\_\_\end{array}$$

(b)
$$\begin{array}{ccc}{\text{CaCO}}_3(s)⟶& {\text{Ca}}^{\text{2+}}(aq)+& {\text{CO}}_3{}^{\text{2−}}(aq)\\ \\ & \_\_\_\_& x\end{array}$$

(c)
$$\begin{array}{ccc}\text{Mg}{(\text{OH})}_2(s)⟶& {\text{Mg}}^{\text{2+}}(aq)+& 2{\text{OH}}^{\text{−}}(aq)\\ \\ & x& \_\_\_\_\_\end{array}$$

(d)
$$\begin{array}{ccc}{\text{Mg}}_3({\text{PO}}_4{)}_2(s)⟶& 3{\text{Mg}}^{\text{2+}}(aq)+& 2{\text{PO}}_4{}^{\text{3−}}(aq)\\ \\ & x& \_\_\_\_\_\end{array}$$

(e)
$$\begin{array}{cccc}{\text{Ca}}_5({\text{PO}}_4{)}_3\text{OH}(s)⟶& 5{\text{Ca}}^{\text{2+}}(aq)+& 3{\text{PO}}_4{}^{\text{3−}}(aq)+& {\text{OH}}^{\text{−}}(aq)\\ \\ & \_\_\_\_\_& \_\_\_\_\_& x\end{array}$$

Write the ionic equation for the dissolution and the K_sp expression for each of the following slightly soluble ionic compounds:

(a) LaF₃

(b) CaCO₃

(c) Ag₂SO₄

(d) Pb(OH)₂

The Handbook of Chemistry and Physics 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.

(a) BaSeO₄, 0.0118 g/100 mL

(b) Ba(BrO₃)₂·H₂O, 0.30 g/100 mL

(c) NH₄MgAsO₄·6H₂O, 0.038 g/100 mL

(d) La₂(MoO₄)₃, 0.00179 g/100 mL

Assuming that no equilibria other than dissolution are involved, calculate the molar solubility of each of the following from its solubility product:

(a) KHC₄H₄O₆

(b) PbI₂

(c) Ag₄[Fe(CN)₆], a salt containing the ${\text{Fe(CN)}}_6{}^{\text{4–}}$ ion

(d) Hg₂I₂

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.

(a) AgCl(s) in 0.025 M NaCl

(b) CaF₂(s) in 0.00133 M KF

(c) Ag₂SO₄(s) in 0.500 L of a solution containing 19.50 g of K₂SO₄

(d) Zn(OH)₂(s) in a solution buffered at a pH of 11.45

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. State whether or not it is appropriate to neglect the changes in the initial concentrations of the common ions.

(a) TlCl(s) in 0.025 M TlNO₃

(b) BaF₂(s) in 0.313 M KF

(c) MgC₂O₄ in 2.250 L of a solution containing 8.156 g of Mg(NO₃)₂

(d) Ca(OH)₂(s) in an unbuffered solution initially with a pH of 12.700

Assuming that no equilibria other than dissolution are involved, calculate the concentrations of ions in a saturated solution of each of the following (see Appendix J for solubility products):

(a) AgI

(b) Ag₂SO₄

(c) Mn(OH)₂

(d) Sr(OH)₂·8H₂O

(e) the mineral brucite, Mg(OH)₂

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K_sp for each of the slightly soluble solids indicated:

(a) TlCl: [Tl⁺] = 1.21 $\times$ 10^–2 M, [Cl^–] = 1.2 $\times$ 10^–2 M

(b) Ce(IO₃)₄: [Ce⁴⁺] = 1.8 $\times$ 10^–4 M, $[{\text{IO}}_3{}^{\text{−}}]$ = 2.6 $\times$ 10^–13 M

(c) Gd₂(SO₄)₃: [Gd³⁺] = 0.132 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 0.198 M

(d) Ag₂SO₄: [Ag⁺] = 2.40 $\times$ 10^–2 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 2.05 $\times$ 10^–2 M

(e) BaSO₄: [Ba²⁺] = 0.500 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 2.16 $\times$ 10⁻¹⁰ M

Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Appendix J for K_sp values.)

(a) CaCO₃: [Ca²⁺] = 0.003 M, $[{\text{CO}}_{\text{3}}{}^{\text{2−}}]$ = 0.003 M

(b) Co(OH)₂: [Co²⁺] = 0.01 M, [OH^–] = 1 $\times$ 10^–7 M

(c) CaHPO₄: [Ca²⁺] = 0.01 M, $[{\text{HPO}}_{\text{4}}{}^{\text{2−}}]$ = 2 $\times$ 10^–6 M

(d) Pb₃(PO₄)₂: [Pb²⁺] = 0.01 M, $[{\text{PO}}_{\text{4}}{}^{\text{3−}}]$= 1 $\times$ 10^–13 M

Perform these calculations for nickel(II) carbonate. (a) With what volume of water must a precipitate containing NiCO₃ be washed to dissolve 0.100 g of this compound? Assume that the wash water becomes saturated with NiCO₃ (K_sp = 1.36 $\times$ 10^–7).

(b) If the NiCO₃ were a contaminant in a sample of CoCO₃ (K_sp = 1.0 $\times$ 10^–12), what mass of CoCO₃ would have been lost? Keep in mind that both NiCO₃ and CoCO₃ dissolve in the same solution.

What reagent might be used to separate the ions in each of the following mixtures, which are 0.1 M with respect to each ion? In some cases it may be necessary to control the pH. (Hint: Consider the K_sp values given in Appendix J.)

(a) ${\text{Hg}}_2{}^{\text{2+}}$ and Cu²⁺

(b) ${\text{SO}}_4{}^{\text{2−}}$ and Cl^–

(c) Hg²⁺ and Co²⁺

(d) Zn²⁺ and Sr²⁺

(e) Ba²⁺ and Mg²⁺

(f) ${\text{CO}}_3{}^{\text{2−}}$ and OH^–

Magnesium metal (a component of alloys used in aircraft and a reducing agent used in the production of uranium, titanium, and other active metals) is isolated from sea water by the following sequence of reactions:

${\text{Mg}}^{\text{2+}}(aq)+$ ${\text{Ca(OH)}}_2(aq)⟶$ ${\text{Mg(OH)}}_2(s)+$ ${\text{Ca}}^{\text{2+}}(aq)$

${\text{Mg(OH)}}_2(s)+$ $\text{2HCl(}aq)⟶$ ${\text{MgCl}}_2(s)+$ ${\text{2H}}_2\text{O}(l)$

${\text{MgCl}}_2(l)\stackrel{\text{electrolysis}}{\to }\text{Mg}(s)+$ ${\text{Cl}}_2(g)$

Sea water has a density of 1.026 g/cm³ and contains 1272 parts per million of magnesium as Mg²⁺(aq) by mass. What mass, in kilograms, of Ca(OH)₂ is required to precipitate 99.9% of the magnesium in 1.00 $\times$ 10³ L of sea water?

Perform the following calculations involving concentrations of iodate ions:

(a) The iodate ion concentration of a saturated solution of La(IO₃)₃ was found to be 3.1 $\times$ 10^–3 mol/L. Find the K_sp.

(b) Find the concentration of iodate ions in a saturated solution of Cu(IO₃)₂ (K_sp = 7.4 $\times$ 10^–8).

The carbonate ion concentration is gradually increased in a solution containing equal concentrations of the divalent cations of magnesium, calcium, strontium, barium, and manganese. Which of the following carbonates will precipitate first? Which will precipitate last? Explain.

(a) ${\text{MgCO}}_3•3{\text{H}}_2\text{O}$ $K_{\text{sp}}=$ $1\times 10^{-5}$

(b) ${\text{CaCO}}_3$ $K_{\text{sp}}=$ $8.7\times 10^{-9}$

(c) ${\text{SrCO}}_3$ $K_{\text{sp}}=$ $7\times 10^{-10}$

(d) ${\text{BaCO}}_3$ $K_{\text{sp}}=$ $1.6\times 10^{-9}$

(e) ${\text{MnCO}}_3$ $K_{\text{sp}}=$ $8.8\times 10^{-11}$

Sometimes equilibria for complex ions are described in terms of dissociation constants, K_d. For the complex ion ${\text{AlF}}_6{}^{\text{3−}}$ the dissociation reaction is:

${\text{AlF}}_6{}^{\text{3−}}\rightleftharpoons$ ${\text{Al}}^{\text{3+}}+$ $6{\text{F}}^{\text{−}}$ and $K_{\text{d}}=$ $\frac{[{\text{Al}}^{\text{3+}}]{[{\text{F}}^{\text{−}}]}^6}{[{\text{AlF}}_6{}^{\text{3−}}]}=$ $2\times {10}^{-24}$

Calculate the value of the formation constant, K_f, for ${\text{AlF}}_{\text{6}}{}^{\text{3−}}.$

Write the Lewis structures of the reactants and product of each of the following equations, and identify the Lewis acid and the Lewis base in each:

(a) ${\text{CO}}_2+$ ${\text{OH}}^{\text{−}}⟶$ ${\text{HCO}}_3{}^{\text{−}}$

(b) $\text{B}{(\text{OH})}_3+$ ${\text{OH}}^{\text{−}}⟶$ $\text{B}{(\text{OH})}_4{}^{\text{−}}$

(c) ${\text{I}}^{\text{−}}+{\text{I}}_2⟶{\text{I}}_3{}^{\text{−}}$

(d) ${\text{AlCl}}_3+$ ${\text{Cl}}^{\text{−}}⟶$ ${\text{AlCl}}_4{}^{\text{−}}$ (use Al-Cl single bonds)

(e) ${\text{O}}^{\text{2−}}+$ ${\text{SO}}_3⟶$ ${\text{SO}}_4{}^{\text{2−}}$

Using Lewis structures, write balanced equations for the following reactions:

(a) $\text{HCl}(g)+$ ${\text{PH}}_3(g)⟶$ $$

(b) ${\text{H}}_3{\text{O}}^{\mathrm{+}}+{\text{CH}}_3{}^{\text{−}}⟶$

(c) $\text{CaO}+{\text{SO}}_3⟶$

(d) ${\text{NH}}_4{}^{\mathrm{+}}+$ ${\text{C}}_2{\text{H}}_5{\text{O}}^{\text{−}}⟶$ $$

Boric acid, H₃BO₃, is not a Brønsted-Lowry acid but a Lewis acid. (Hint: See the equation in Exercise 15.76)

(a) Write an equation for its reaction with water.

(b) Predict the shape of the anion thus formed.

(c) What is the hybridization on the boron, and is it consistent with the shape you have predicted?

A 0.125-M solution of Mn(NO₃)₂ is saturated with H₂S ([H₂S] = 0.10 M). At what pH does MnS begin to precipitate?

$\text{MnS}(s)\rightleftharpoons$ ${\text{Mn}}^{\text{2+}}(aq)+$ ${\text{S}}^{\text{2−}}(aq)$ $K_{\text{sp}}=$ $2.3\times {10}^{\text{−13}}$

${\text{H}}_2\text{S}(aq)+$ $2{\text{H}}_2\text{O}(l)\rightleftharpoons$ $2{\text{H}}_3{\text{O}}^{\text{+}}(aq)+$ ${\text{S}}^{\text{2−}}(aq)$ $K=$ $1.0\times {10}^{\text{−26}}$

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:

${\text{MgF}}_2(s)\rightleftharpoons$ ${\text{Mg}}^{\text{2+}}(aq)+$ $2{\text{F}}^{\text{−}}(aq)$

In a saturated solution of MgF₂ at 18 °C, the concentration of Mg²⁺ is 1.21 $\times$ 10^–3 M. The equilibrium is represented by the preceding equation.

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

(b) Calculate the equilibrium concentration of Mg²⁺ in 1.000 L of saturated MgF₂ solution 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 when 100.0 mL of a 3.00 $\times$ 10^–3-M solution of Mg(NO₃)₂ is mixed with 200.0 mL of a 2.00 $\times$ 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 $\times$ 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 effect on the amount of CaHPO₄ that dissolves and the concentrations of Ca²⁺ and ${\text{HPO}}_4{}^{\text{2−}}$ when each of the following are added to a mixture of solid CaHPO₄ and water at equilibrium?

(a) CaCl₂

(b) HCl

(c) KClO₄

(d) NaOH

(e) CaHPO₄