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Chapter 17: Problem 73

For which of these reactions is the equilibrium constant called a solubility product? (a) \(\mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)\) (b) \(3 \mathrm{Ca}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)\) (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) \(\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)\)

Short Answer

Expert verified
The equilibrium constant can be called a solubility product for reaction (d) \(\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)\)

Step by step solution

01

Identify the reactions involving solid substances dissolving into ionic constituents

Analyzing each reaction, it can be noticed that not all of them involve a solid substance dissolving into ions. Some involve ions in the solution reacting with each other. So the reactions involving solid substances initially are (b) \(3 \mathrm{Ca}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)\), (c) \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\), and (d) \(\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)\)
02

Identify the reactions in which a solid is dissolving into its ions in water

The reactions identified in the previous step are checked for whether a solid substance is dissolving into its ions in water or not. Here, (a) is not considered since it already excluded in the previous step. Among these reactions, (b) is not a case of a solid dissolving rather it's being formed through reaction of ions. Hence, the reactions (c) and (d) meet the condition of a substance dissolving into ions.
03

Verification

The remaining reactions (c) and (d) involve a solid in the reaction. However, they need further verification to confirm whether they can be classified under the definition of equilibrium constant known as solubility product. Notice that reaction (c) is an acid-base reaction and the solid CaCO3 is reacting with 2H+ and hence this equilibrium does not signify dissolution into ions in water only. Therefore, among the given reactions, reaction (d) is a true depiction of a solid dissolving into its ions in water and is a classic example where the Ksp, equilibrium constant would be called a solubility product.

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Most popular questions from this chapter

A 5.00 -g quantity of a diprotic acid is dissolved in water and made up to exactly \(250 \mathrm{~mL}\). Calculate the molar mass of the acid if \(25.0 \mathrm{~mL}\) of this solution required \(11.1 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{KOH}\) for neutralization. Assume that both protons of the acid are titrated.

How many grams of \(\mathrm{CaCO}_{3}\) will dissolve in \(3.0 \times\) \(10^{2} \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Acid-base reactions usually go to completion. Confirm this statement by calculating the equilibrium constant for each of the following cases: (a) a strong acid reacting with a strong base, (b) a strong acid reacting with a weak base \(\left(\mathrm{NH}_{3}\right),\) (c) a weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a strong base, \((\mathrm{d})\) a weak acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) reacting with a weak base \(\left(\mathrm{NH}_{3}\right)\) (Hint: Strong acids exist as \(\mathrm{H}^{+}\) ions and strong bases exist as \(\mathrm{OH}^{-}\) ions in solution. You need to look up the \(K_{\mathrm{a}}, K_{\mathrm{b}}\), and \(K_{\mathrm{w}}\) values.)

The molar mass of a certain metal carbonate, \(\mathrm{MCO}_{3}\), can be determined by adding an excess of \(\mathrm{HCl}\) acid to react with the carbonate and then "back-titrating" the remaining acid with \(\mathrm{NaOH}\). (a) Write an equation for these reactions. (b) In a certain experiment, \(20.00 \mathrm{~mL}\) of \(0.0800 \mathrm{M} \mathrm{HCl}\) were added to a \(0.1022-\mathrm{g}\) sample of \(\mathrm{MCO}_{3}\). The excess HCl required \(5.64 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{NaOH}\) for neutralization. Calculate the molar mass of the carbonate and identify \(\mathrm{M}\).

\(\mathrm{Cd}(\mathrm{OH})_{2}\) is an insoluble compound. It dissolves in a \(\mathrm{NaOH}\) solution. Write a balanced ionic equation for this reaction. What type of reaction is this?
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