Chapter 21

Use information from the chapter to write chemical equations to represent each of the following: (a) reaction of cesium metal with chlorine gas (b) formation of sodium peroxide \(\left(\mathrm{Na}_{2} \mathrm{O}_{2}\right)\) (c) thermal decomposition of lithium carbonate (d) reduction of sodium sulfate to sodium sulfide (e) combustion of potassium to form potassium superoxide

Use information from the chapter to write chemical equations to represent each of the following: (a) reaction of rubidium metal with water (b) thermal decomposition of aqueous \(\mathrm{KHCO}_{3}\) (c) combustion of lithium metal in oxygen gas (d) action of concentrated aqueous \(\mathrm{H}_{2} \mathrm{SO}_{4}\) on \(\mathrm{KCl}(\mathrm{s})\) (e) reaction of lithium hydride with water

Describe a simple test for determining whether a pure white solid is LiCl or KCl.

Describe two methods for determining the identity of an unknown compound that is either \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) or \(\mathrm{K}_{2} \mathrm{CO}_{3}.\)

Arrange the following compounds in the expected order of increasing solubility in water, and give the basis for your arrangement: \(\mathrm{Li}_{2} \mathrm{CO}_{3}, \mathrm{Na}_{2} \mathrm{CO}_{3}\) \(\mathrm{MgCO}_{3}.\)

The first electrolytic process to produce sodium metal used molten NaOH as the electrolyte. Write probable half-equations and an overall equation for this electrolysis.

An analysis of a Solvay-process plant shows that for every \(1.00 \mathrm{kg}\) of \(\mathrm{NaCl}\) consumed, \(1.03 \mathrm{kg}\) of \(\mathrm{NaHCO}_{3}\) are obtained. The quantity of \(\mathrm{NH}_{3}\) consumed in the overall process is \(1.5 \mathrm{kg}.\) (a) What is the percent efficiency of this process for converting NaCl to \(\mathrm{NaHCO}_{3} ?\) (b) Why is so little \(\mathrm{NH}_{3}\) required?

The Gibbs energies of formation, \(\Delta G_{\mathrm{f}}^{\circ},\) for \(\mathrm{Na}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) are \(-379.09 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(-449.63 \mathrm{kJ} \mathrm{mol}^{-1}\) respectively, at 298 K. Calculate the equilibrium constant for the reaction below at \(298 \mathrm{K} .\) Is \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) thermodynamically stable with respect to \(\mathrm{Na}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g})\) at \(298 \mathrm{K} ?\) $$ \mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s}) \longrightarrow \mathrm{Na}_{2} \mathrm{O}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) $$

The Gibbs energies of formation, \(\Delta G_{f}^{Q}\), for \(\mathrm{KO}_{2}(\mathrm{s})\) and \(\mathrm{K}_{2} \mathrm{O}(\mathrm{s})\) are \(-240.59 \mathrm{kJmol}^{-1}\) and \(-322.09 \mathrm{kJmol}^{-1}\) respectively, at \(298 \mathrm{K}\). Calculate the equilibrium constant for the reaction below at \(298 \mathrm{K}\). Is \(\mathrm{KO}_{2}(\mathrm{s})\) thermodynamically stable with respect to \(\mathrm{K}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g})\) at \(298 \mathrm{K} ?\) $$ 2 \mathrm{KO}_{2}(\mathrm{s}) \longrightarrow \mathrm{K}_{2} \mathrm{O}(\mathrm{s})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) $$

In the Dow process (Fig. \(21-13\) ), the starting material is \(\mathrm{Mg}^{2+}\) in seawater and the final product is Mg metal. This process seems to violate the principle of conservation of charge. Does it? Explain.

Which has the (a) higher melting point, MgO or BaO; (b) greater solubility in water, \(\mathrm{MgF}_{2}\) or \(\mathrm{MgCl}_{2}\) ? Explain.

Write chemical equations to represent the following: (a) reduction of \(\mathrm{BeF}_{2}\) to Be metal with Mg as a reducing agent (b) reaction of barium metal with \(\mathrm{Br}_{2}(1)\) (c) reduction of uranium(IV) oxide to uranium metal with calcium as the reducing agent (d) calcination of dolomite, a mixed calcium magnesium carbonate \(\left(\mathrm{MgCO}_{3} \cdot \mathrm{CaCO}_{3}\right)\) (e) complete neutralization of phosphoric acid with quicklime

Write chemical equations for the reactions you would expect to occur when (a) \(\operatorname{Mg}\left(\mathrm{HCO}_{3}\right)_{2}(\mathrm{s})\) is heated to a high temperature (b) \(\mathrm{BaCl}_{2}(1)\) is electrolyzed (c) \(\operatorname{Sr}(\text { s) is added to cold dilute } \operatorname{HBr}( \text { aq) }\) (d) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\) is added to \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) (e) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) is heated

Without per forming detailed calculations, indicate why you would expect each of the following reactions to occur to a significant extent as written. Use data from Appendix D as necessary. (a) \(\mathrm{BaCO}_{3}(\mathrm{s})+2 \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}) \longrightarrow \mathrm{Ba}^{2+}(\mathrm{aq})+\) \(2 \mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I})+\mathrm{CO}_{2}(\mathrm{g})\) (b) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{NH}_{4}+(\mathrm{aq}) \longrightarrow\) \(\mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{NH}_{3}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1)\) (c) \(\operatorname{BaF}_{2}(\mathrm{s})+2 \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Ba}^{2+}(\mathrm{aq})+2 \mathrm{HF}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

The molecule tetraborane has the formula \(\mathrm{B}_{4} \mathrm{H}_{10}\) (a) Show that this is an electron-deficient molecule. (b) How many bridge bonds must occur in the molecule? (c) Show that butane, \(\mathrm{C}_{4} \mathrm{H}_{10},\) is not electron deficient.

Write Lewis structures for the following species, both of which involve coordinate covalent bonding: (a) tetrafluoroborate ion, \(\mathrm{BF}_{4}^{-}\), used in metal cleaning and in electroplating baths (b) boron trifluoride ethylamine, used in curing epoxy resins (ethylamine is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) )

Write Lewis structures for the following species, both of which involve coordinate covalent bonding: (a) tetrafluoroborate ion, \(\mathrm{BF}_{4}^{-}\), used in metal cleaning and in electroplating baths. (b) boron trifluoride ethylamine, used in curing epoxy resins (ethylamine is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) ).

Write chemical equations to represent the (a) reaction of \(\mathrm{Al}(\mathrm{s})\) with \(\mathrm{HCl}(\mathrm{aq})\) (b) reaction of \(\mathrm{Al}(\mathrm{s})\) with \(\mathrm{NaOH}(\mathrm{aq})\) (c) oxidation of \(\mathrm{Al}(\mathrm{s})\) to \(\mathrm{Al}^{3+}(\) aq) by an aqueous solution of sulfuric acid; the reduction product is \(\mathrm{SO}_{2}(\mathrm{g}).\)

Write plausible equations for the (a) reaction of \(\mathrm{Al}(\mathrm{s})\) with \(\mathrm{Br}_{2}(1)\) (b) production of \(\mathrm{Cr}\) from \(\mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{s})\) by the thermite reaction, with Al as the reducing agent; (c) separation of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) impurity from bauxite ore.

In some foam-type fire extinguishers, the reactants are \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})\) and \(\mathrm{NaHCO}_{3}(\mathrm{aq}) .\) When the extinguisher is activated, these reactants mix, producing \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) and \(\mathrm{CO}_{2}(\mathrm{g}) .\) The \(\mathrm{Al}(\mathrm{OH})_{3}-\mathrm{CO}_{2}\) foam extinguishes the fire. Write a net ionic equation to represent this reaction.

Some baking powders contain the solids \(\mathrm{NaHCO}_{3}\) and \(\mathrm{NaAl}\left(\mathrm{SO}_{4}\right)_{2} .\) When water is added to this mixture of compounds, \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) are two of the products. Write plausible net ionic equations for the formation of these two products.

Describe a series of simple chemical reactions that you could use to determine whether a particular metal sample is "aluminum 2S" (99.2\% Al) or "magnalium" (70\% Al, 30\% Mg). You are permitted to destroy the metal sample in the testing.

In the purification of bauxite ore, a preliminary step in the production of aluminum, \(\left[\mathrm{Al}(\mathrm{OH})_{4}\right]^{-}(\mathrm{aq})\) can be converted to \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) by passing \(\mathrm{CO}_{2}(\mathrm{g})\) through the solution. Write an equation for the reaction that occurs. Could HCl(aq) be used instead of \(\mathrm{CO}_{2}(\mathrm{g}) ?\) Explain.

In \(1825,\) Hans Oersted produced aluminum chloride by passing chlorine over a heated mixture of carbon and aluminum oxide. In 1827 , Friedrich Wöhler obtained aluminum by heating aluminum chloride with potassium. Write plausible equations for these reactions.

A description for preparing potassium aluminum alum calls for dissolving aluminum foil in KOH(aq). The solution obtained is treated with \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) and the alum is crystallized from the resulting solution. Write plausible equations for these reactions.

Handbooks and lists of chemicals do not contain entries under the formulas \(\mathrm{Al}\left(\mathrm{HCO}_{3}\right)_{3}\) and \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{2} .\) Explain why these compounds do not exist.

Comment on the accuracy of a jeweler's advertising that "diamonds last forever." In what sense is the statement true, and in what ways is it false?

A temporary fix for a "sticky" lock is to scrape a pencil point across the notches on the key and to work the key in and out of the lock a few times. What is the basis of this fix?

Write a chemical equation to represent (a) the reduction of silica to elemental silicon by aluminum; (b) the preparation of potassium metasilicate by the high-temperature fusion of silica and potassium carbonate; (c) the reaction of \(\mathrm{Al}_{4} \mathrm{C}_{3}\) with water to produce methane.

Write a chemical equation to represent (a) the reaction of potassium cyanide solution with silver nitrate solution; (b) the combustion of \(\mathrm{Si}_{3} \mathrm{H}_{8}\) in an excess of oxygen; (c) the reaction of dinitrogen with calcium carbide to give calcium cyanamide (CaNCN).

Describe what is meant by the terms silane and silanol. What is their role in the preparation of silicones?

Describe and explain the similarities and differences between the reaction of a silicate with an acid and that of a carbonate with an acid.

Methane and sulfur vapor react to form carbon disulfide and hydrogen sulfide. Carbon disulfide reacts with \(\mathrm{Cl}_{2}(\mathrm{g})\) to form carbon tetrachloride and \(\mathrm{S}_{2} \mathrm{Cl}_{2}\) Further reaction of carbon disulfide and \(\overline{S_{2} C l_{2}}\) produces additional carbon tetrachloride and sulfur. Write a series of equations for the reactions described here.

Write plausible chemical equations for the (a) dissolving of lead(II) oxide in nitric acid; (b) heating of \(\operatorname{snCO}_{3}(\mathrm{s}) ;\) (c) reduction of lead(II) oxide by carbon; (d) reduction of \(\mathrm{Fe}^{3+}(\mathrm{aq})\) to \(\mathrm{Fe}^{2+}(\mathrm{aq})\) by \(\mathrm{Sn}^{2+}(\mathrm{aq});\) (e) formation of lead(II) sulfate during high-temperature roasting of lead(II) sulfide.

Write plausible chemical equations for preparing each compound from the indicated starting material: (a) \(\operatorname{SnCl}_{2}\) from \(\operatorname{SnO} ;\) (b) \(\operatorname{SnCl}_{4}\) from \(\operatorname{Sn} ;\) (c) \(\operatorname{PbCrO}_{4}\) from \(\mathrm{PbO}_{2}\). What reagents (acids, bases, salts) and equipment commonly available in the laboratory are needed for each reaction?

Would you expect the reaction of \(\mathrm{Pb}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) to yield \(\mathrm{PbCl}_{2}\) or \(\mathrm{PbCl}_{4} ?\)

Would you expect the reaction of \(\mathrm{Ge}(\mathrm{s})\) and \(\mathrm{F}_{2}(\mathrm{g})\) to yield GeF \(_{2},\) with germanium in the +2 oxidation state, or GeF \(_{4},\) with germanium in the +4 oxidation state?

A chemical that should exist as a crystalline solid is seen to be a mixture of a solid and liquid in a container on a storeroom shelf. Give a plausible reason for that observation. Should the chemical be discarded or is it still useful for some purposes?

The following series of observations is made: (1) a small piece of dry ice \(\left[\mathrm{CO}_{2}(\mathrm{s})\right]\) is added to \(0.005 \mathrm{M}\) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) .(2)\) Initially, a white precipitate forms.(3) After a short time the precipitate dissolves. (a) Write chemical equations to explain these observations. (b) If the \(0.005 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\) is replaced by 0.005. \(\mathrm{M} \mathrm{CaCl}_{2}(\mathrm{aq}),\) would a precipitate form? Explain. (c) If the \(0.005 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\) is replaced by 0.010 \(\mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}),\) a precipitate forms but does not re-dissolve. Explain why.

The melting point of \(\mathrm{NaCl}(\mathrm{s})\) is \(801^{\circ} \mathrm{C},\) much higher than that of \(\mathrm{NaOH}\left(322^{\circ} \mathrm{C}\right) .\) More energy is consumed to melt and maintain molten NaCl than NaOH. Yet the preferred commercial process for the production of sodium is electrolysis of \(\mathrm{NaCl}(\mathrm{l})\) rather than \(\mathrm{NaOH}(1)\) Give a reason or reasons for this discrepancy.

Although the triiodide ion, \(\mathrm{I}_{3}^{-}\), is known to exist in aqueous solutions, the ion is stable in only certain ionic solids. For example, \(\mathrm{CsI}_{3}\) is stable with respect to decomposition to CsI and \(\mathrm{I}_{2},\) but \(\mathrm{LiI}_{3}\) is not stable with respect to LiI and I \(_{2}\). Draw a Lewis structure for the \(I_{3}^{-}\) ion and suggest a reason why \(\mathrm{CsI}_{3}\) is stable with respect to decomposition to the iodide but \(\mathrm{LiI}_{3}\) is not.

The chemical equation for the hydration of an alkali metal ion is \(M^{+}(g) \rightarrow M^{+}(a q) .\) The Gibbs energy change and the enthalpy change for the process are denoted by \(\Delta G_{\text {hydr. }}^{\circ}\) and \(\Delta H_{\text {hydr. }}^{\circ}\) respectively. \(\Delta G_{\text {hydr. }}^{\circ}\) and \(\Delta H_{\text {hydr. values are given below for the alkali }}\) metal ions. $$\mathrm{M}^{+} \quad \mathrm{Li}^{+} \quad \mathrm{Na}^{+} \quad \mathrm{K}^{+} \quad \mathrm{Rb}^{+} \quad \mathrm{Cs}^{+}$$ $$\begin{array}{llllll} \Delta H_{\text {hydr. }}^{\circ} & -522 & -407 & -324 & -299 & -274 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$ $$\begin{array}{llllll} \Delta G_{\text {hydr. }}^{\circ} & -481 & -375 & -304 & -281 & -258 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$ Use the data above to calculate \(\Delta S_{\text {hydr. }}^{\circ}\) values for the hydration process. Explain the trend in the \(\Delta S_{\text {hydr. }}^{\circ}\) values.

Lithium superoxide, \(\mathrm{LiO}_{2}(\mathrm{s}),\) has never been isolated. Use ideas from Chapter \(12,\) together with data from this chapter and Appendix \(D\), to estimate \(\Delta H_{f}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) and assess whether \(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with respect to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}).\) (a) Use the Kapustinskii equation, along with appropriate data below, to estimate the lattice energy, \(U,\) for \(\left.\mathrm{LiO}_{2}(\mathrm{s}) . \text { (See exercise } 126 \text { in Chapter } 12 .\right)\) The ionic radii for \(L\) i \(^{+}\) and \(O_{2}^{-}\) are \(73 \mathrm{pm}\) and \(144 \mathrm{pm},\) respectively. (b) Use your result from part (a) in the BornFajans-Haber cycle to estimate \(\Delta H_{\mathrm{f}}^{2}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) [Hint: For the process \(\mathrm{O}_{2}(\mathrm{g})+\mathrm{e}^{-} \rightarrow \mathrm{O}_{2}^{-}(\mathrm{g}), \Delta H^{\circ}=.\) \(-43 \mathrm{kJ} \mathrm{mol}^{-1} .\) See Table 21.2 and Appendix \(\mathrm{D}\) for the other data that are required.] (c) Use your result from part (b) to calculate the enthalpy change for the decomposition of \(\mathrm{LiO}_{2}(\mathrm{s})\) to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) For \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s}), \Delta H_{\mathrm{f}}^{\circ}=-598.73\) \(\mathrm{kJmol}^{-1}.\) (d) Use your result from part (c) to decide whether \(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with respect to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) Assume that entropy effects can be neglected.

When a \(0.200 \mathrm{g}\) sample of \(\mathrm{Mg}\) is heated in air, \(0.315 \mathrm{g}\) of product is obtained. Assume that all the Mg appears in the product. (a) If the product were pure \(\mathrm{MgO}\), what mass should have been obtained? (b) Show that the 0.315 g product could be a mixture of \(\mathrm{Mg} \mathrm{O}\) and \(\mathrm{Mg}_{3} \mathrm{N}_{2}.\) (c) What is the mass percent of \(\mathrm{MgO}\) in the \(\mathrm{MgO}-\mathrm{Mg}_{3} \mathrm{N}_{2}\) mixed product?

The electrolysis of \(0.250 \mathrm{L}\) of \(0.220 \mathrm{M} \mathrm{MgCl}_{2}\) is conducted until \(104 \mathrm{mL}\) of gas (a mixture of \(\mathrm{H}_{2}\) and water vapor) is collected at \(23^{\circ} \mathrm{C}\) and \(748 \mathrm{mmHg} .\) Will \(\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})\) precipitate if electrolysis is carried to this point? (Use 21 mmHg as the vapor pressure of the solution.)

A particular water sample contains 56.9 ppm \(\mathrm{SO}_{4}^{2-}\) and \(176 \mathrm{ppm} \mathrm{HCO}_{3}^{-},\) with \(\mathrm{Ca}^{2+}\) as the only cation. (a) How many parts per million of \(\mathrm{Ca}^{2+}\) does the water contain? (b) How many grams of \(\mathrm{CaO}\) are consumed in removing \(\mathrm{HCO}_{3}^{-}\), from \(602 \mathrm{kg}\) of the water? (c) Show that the \(\mathrm{Ca}^{2+}\) remaining in the water after the treatment described in part (b) can be removed by adding \(\mathrm{Na}_{2} \mathrm{CO}_{3}.\) (d) How many grams of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) are required for the precipitation referred to in part (c)?

An aluminum production cell of the type pictured in Figure \(21-24\) operates at a current of \(1.00 \times 10^{5} \mathrm{A}\) and a voltage of 4.5 V. The cell is \(38 \%\) efficient in using electrical energy to produce chemical change. (The rest of the electrical energy is dissipated as thermal energy in the cell.) (a) What mass of \(\mathrm{Al}\) can be produced by this cell in \(8.00 \mathrm{h} ?\) (b) If the electrical energy required to power this cell is produced by burning coal \((85 \%\) C; heat of combustion of \(C=32.8 \mathrm{kJ} / \mathrm{g}\) ) in a power plant with \(35 \%\) efficiency, what mass of coal must be burned to produce the mass of Al determined in part (a)?

The reaction of borax, calcium fluoride, and concentrated sulfuric acid yields sodium hydrogen sulfate, calcium sulfate, water, and boron trifluoride as products. Write a balanced equation for this reaction.

The dissolution of \(\mathrm{MgCO}_{3}(\mathrm{s})\) in \(\mathrm{NH}_{4}^{+}(\mathrm{aq})\) can be represented as \(\mathrm{MgCO}_{3}(\mathrm{s})+\mathrm{NH}_{4}^{+}(\mathrm{aq}) \rightleftharpoons\) $$ \mathrm{Mg}^{2+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{NH}_{3}(\mathrm{aq}) $$ Calculate the molar solubility of \(\mathrm{MgCO}_{3}\) in each of the following solutions: (a) \(1.00 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq}) ;\) (b) a buffer that is \(1.00 \mathrm{M} \mathrm{NH}_{3}\) and \(1.00 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl} ;\) (c) a buffer that is \(0.100 \mathrm{M} \mathrm{NH}_{3}\) and \(1.00 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}.\)

Show that, in principle, \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) can be converted almost completely to NaOH(aq) by the reaction \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq}) $$