Chapter 16

(a) Given that \(K_{a}\) for acetic acid is \(1.8 \times 10^{-5}\) and that for hypochlorous acid is \(3.0 \times 10^{-8}\), which is the stronger acid? (b) Which is the stronger base, the acetate ion or the hypochlorite ion? (c) Calculate \(K_{b}\) values for \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) and \(\mathrm{ClO}^{-}\)

Predict whether aqueous solutions of the following compounds are acidic, basic, or neutral: (a) \(\mathrm{NH}_{4} \mathrm{Br}\), (c) \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) (b) \(\mathrm{FeCl}_{3}\) (d) \(\mathrm{KClO}_{4}\), (e) \(\mathrm{NaHC}_{2} \mathrm{O}_{4}\).

An unknown salt is either NaF, \(\mathrm{NaCl}\), or \(\mathrm{NaOCl}\). When \(0.050\) mol of the salt is dissolved in water to form \(0.500 \mathrm{~L}\) of solution, the \(\mathrm{pH}\) of the solution is \(8.08\). What is the identity of the salt?

An unknown salt is either \(\mathrm{KBr}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{KCN}\), or \(\mathrm{K}_{2} \mathrm{CO}_{3}\). If a \(0.100 \mathrm{M}\) solution of the salt is neutral, what is the identity of the salt?

Sorbic acid \(\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{COOH}\right)\) is a weak monoprotic acid with \(K_{a}=1.7 \times 10^{-5} .\) Its salt (potassium sorbate) is added to cheese to inhibit the formation of mold. What is the \(\mathrm{p} \mathrm{H}\) of a solution containing \(11.25 \mathrm{~g}\) of potassium sorbate in \(1.75 \mathrm{~L}\) of solution?

How does the acid strength of an oxyacid depend on (a) the electronegativity of the central atom; (b) the number of nonprotonated oxygen atoms in the molecule?

(a) How does the strength of an acid vary with the polarity and strength of the \(\mathrm{H}-\mathrm{X}\) bond? (b) How does the acidity of the binary acid of an element vary as a function of the electronegativity of the element? How does this relate to the position of the element in the periodic table?

Explain the following observations: (a) \(\mathrm{HNO}_{3}\) is a stronger acid than \(\mathrm{HNO}_{2} ;\) (b) \(\mathrm{H}_{2} \mathrm{~S}\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{O} ;\) (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is a stronger acid than \(\mathrm{HSO}_{4}^{-} ;\) (d) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{SeO}_{4} ;\) (e) \(\mathrm{CCl}_{3} \mathrm{COOH}\) is a stronger acid than \(\mathrm{CH}_{3} \mathrm{COOH}\).

Explain the following observations: (a) \(\mathrm{HCl}\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{~S} ;\) (b) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is a stronger acid than \(\mathrm{H}_{3} \mathrm{AsO}_{4}\); (c) \(\mathrm{HBrO}_{3}\) is a stronger acid than \(\mathrm{HBrO}_{2}\); (d) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) is a stronger acid than \(\mathrm{HC}_{2} \mathrm{O}_{4}{\underline{\phantom{xx}}}^{-} ;(\mathrm{e})\) benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) is a stronger acid than phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\).

Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{BrO}^{-}\) or \(\mathrm{ClO}^{-}\), (b) \(\mathrm{BrO}^{-}\) or \(\mathrm{BrO}_{2}^{-},(\mathrm{c}) \mathrm{HPO}_{4}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\)

Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{NO}_{2}^{-}\), (c) \(\mathrm{HCO}_{3}^{-}\) or \(\mathrm{CO}_{3}^{2-}\). (b) \(\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}\) or \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\)

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) In general, the acidity of binary acids increases from left to right in a given row of the periodic table. (b) In a series of acids that have the same central atom, acid strength increases with the number of hydrogen atoms bonded to the central atom. (c) Hydrotelluric acid \(\left(\mathrm{H}_{2} \mathrm{Te}\right)\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{~S}\) because Te is more electronegative than \(\mathrm{S}\).

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) Acid strength in a series of \(\mathrm{H}-\mathrm{X}\) molecules increases with increasing size of \(X\). (b) For acids of the same general structure but differing electronegativities of the central atoms, acid strength decreases with increasing electronegativity of the central atom. (c) The strongest acid known is HF because fluorine is the most electronegative element.

If a substance is an Arrhenius base, is it necessarily a Brønsted-Lowry base? Is it necessarily a Lewis base? Explain.

If a substance is a Lewis acid, is it necessarily a Brønsted-Lowry acid? Is it necessarily an Arrhenius acid? Explain.

Identify the Lewis acid and Lewis base among the reactants in each of the following reactions: (a) \(\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{\underline{\phantom{xx}}}^{3+}(a q)+3 \mathrm{ClO}_{4}^{-}(a q)\) (b) \(\mathrm{CN}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(g)+\mathrm{BF}_{3}(g) \rightleftharpoons\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NBF}_{3}(s)\) (d) \(\mathrm{HIO}(l q)+\mathrm{NH}_{2}^{-}(l q) \rightleftharpoons \mathrm{NH}_{3}(l q)+\mathrm{IO}^{-}(l q)\) (lq denotes liquid ammonia as solvent)

Identify the Lewis acid and Lewis base in each of the following reactions: (a) \(\mathrm{HNO}_{2}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{NO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{FeBr}_{3}(s)+\mathrm{Br}^{-}(a q) \rightleftharpoons \mathrm{FeBr}_{4}^{-}(a q)\) (c) \(\mathrm{Zn}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)\) (d) \(\mathrm{SO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)\)

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{+}\) or \(\mathrm{Cu}^{2+}\), (b) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\), (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\). Explain.

Which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{ZnBr}_{2}\) or \(\mathrm{CdCl}_{2}\), (b) \(\mathrm{CuCl}\) or \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2},(\mathrm{c}) \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) or \(\mathrm{NiBr}_{2} ?\) Explain.

Indicate whether each of the following statements is correct or incorrect. For those that are incorrect, explain why they are wrong. (a) Every Brønsted-Lowry acid is also a Lewis acid. (b) Every Lewis acid is also a Brønsted-Lowry acid. (c) Conjugate acids of weak bases produce more acidic solutions than conjugate acids of strong bases. (d) \(\mathrm{K}^{+}\) ion is acidic in water because it causes hydrating water molecules to become more acidic. (e) The percent ionization of a weak acid in water increases as the concentration of acid decreases.

Predict whether the equilibrium lies to the right or to the left in the following reactions: (a) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}(a q)+\mathrm{PO}_{4}{\underline{\phantom{xx}}}^{3-}(a q) \rightleftharpoons\) \(\mathrm{NH}_{3}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\) (The ammonium ion is a stronger acid than the hydrogen phosphate ion.) (b) \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons\) \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{HCN}(a q)\) (The cyanide ion is a stronger base than the acetate ion.)

The odor of fish is due primarily to amines, especially methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right) .\) Fish is often served with a wedge of lemon, which contains citric acid. The amine and the acid react forming a product with no odor, thereby making the less-than-fresh fish more appetizing. Using data from Appendix \(D\), calculate the equilibrium constant for the reaction of citric acid with methylamine, if only the first proton of the citric acid \(\left(K_{a 1}\right)\) is important in the neutralization reaction.

Hemoglobin plays a part in a series of equilibria involving protonation- deprotonation and oxygenation-deoxygenation. The overall reaction is approximately as follows: $$ \mathrm{HbH}^{+}(a q)+\mathrm{O}_{2}(a q) \rightleftharpoons \mathrm{HbO}_{2}(a q)+\mathrm{H}^{+}(a q) $$ where \(\mathrm{Hb}\) stands for hemoglobin, and \(\mathrm{HbO}_{2}\) for oxyhemoglobin. (a) The concentration of \(\mathrm{O}_{2}\) is higher in the lungs and lower in the tissues. What effect does high \(\left[\mathrm{O}_{2}\right]\) have on the position of this equilibrium? (b) The normal \(\mathrm{pH}\) of blood is \(7.4\). Is the blood acidic, basic, or neutral? (c) If the blood \(\mathrm{pH}\) is lowered by the presence of large amounts of acidic metabolism products, a condition known as acidosis results. What effect does lowering blood \(\mathrm{pH}\) have on the ability of hemoglobin to transport \(\mathrm{O}_{2}\) ?

Calculate the \(\mathrm{pH}\) of a solution made by adding \(2.50 \mathrm{~g}\) of lithium oxide \(\left(\mathrm{Li}_{2} \mathrm{O}\right)\) to enough water to make \(1.500 \mathrm{~L}\) of solution.

Which of the following solutions has the higher pH? (a) a \(0.1 \mathrm{M}\) solution of a strong acid or a \(0.1 \mathrm{M}\) solution of a weak acid, (b) a \(0.1 \mathrm{M}\) solution of an acid with \(K_{a}=2 \times 10^{-3}\) or one with \(K_{a}=8 \times 10^{-6}\), (c) a 0.1 M solution of a base with \(\mathrm{p} K_{b}=4.5\) or one with \(\mathrm{p} K_{b}=6.5\).

What is the \(\mathrm{pH}\) of a solution that is \(2.5 \times 10^{-9} \mathrm{M}\) in NaOH? Does your answer make sense?

Caproic acid \(\left(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{COOH}\right)\) is found in small amounts in coconut and palm oils and is used in making artificial flavors. A saturated solution of the acid contains \(11 \mathrm{~g} / \mathrm{L}\) and has a pH of 2.94. Calculate \(K_{a}\) for the acid.

A hypothetical acid \(\mathrm{H}_{2} \mathrm{X}\) is both a strong acid and a diprotic acid. (a) Calculate the pH of a \(0.050 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{X}\), assuming that only one proton ionizes peracid molecule. (b) Calculate the \(\mathrm{pH}\) of the solution from part (a), now assuming that both protons of each acid molecule completely ionize. (c) In an experiment it is observed that the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{X}\) is \(1.27 .\) Comment on the relative acid strengths of \(\mathrm{H}_{2} \mathrm{X}\) and \(\mathrm{H} \mathrm{X}^{-}\). (d) Would a solution of the salt \(\mathrm{NaH} \mathrm{X}\) be acidic, basic, or neutral? Explain.

Butyric acid is responsible for the foul smell of rancid butter. The \(\mathrm{pK}_{a}\) of butyric acid is \(4.84\). (a) Calculate the \(\mathrm{pK}_{b}\) for the butyrate ion. (b) Calculate the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of butyric acid. (c) Calculate the pH of a \(0.050 \mathrm{M}\) solution of sodium butyrate.

Arrange the following \(0.10 \mathrm{M}\) solutions in order of increasing acidity (decreasing \(\mathrm{pH}\) ): (i) \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) (ii) \(\mathrm{NaNO}_{3}\), (iii) \(\mathrm{CH}_{3} \mathrm{COONH}_{4}\), (iv) \(\mathrm{NaF}\), (v) \(\mathrm{CH}_{3} \mathrm{COONa}\)

Many moderately large organic molecules containing basic nitrogen atoms are not very soluble in water as neutral molecules, but they are frequently much more soluble as their acid salts. Assuming that \(\mathrm{pH}\) in the stomach is \(2.5\), indicate whether each of the following compounds would be present in the stomach as the neutral base or in the protonated form: nicotine, \(K_{b}=7 \times 10^{-7} ;\) caffeine, \(K_{b}=4 \times 10^{-14} ;\) strychnine, \(K_{b}=1 \times 10^{-6} ;\) quinine, \(K_{b}=1.1 \times 10^{-6}\)

The amino acid glycine \(\left(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}\right)\) can participate in the following equilibria in water: $$ \begin{aligned} \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons & \\ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} & K_{a}=4.3 \times 10^{-3} \\ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons & \\ { }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{OH}^{-} & K_{b}=6.0 \times 10^{-5} \end{aligned} $$ (a) Use the values of \(K_{a}\) and \(K_{b}\) to estimate the equilibrium constant for the intramolecular proton transfer to form a zwitterion: $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-} $$ What assumptions did you need to make? (b) What is the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) aqueous solution of glycine? (c) What would be the predominant form of glycine in a solution with pH 13? With pH 1?

Calculate the number of \(\mathrm{H}^{+}(a q)\) ions in \(1.0 \mathrm{~mL}\) of pure water at \(25^{\circ} \mathrm{C}\).

The volume of an adult's stomach ranges from about \(50 \mathrm{~mL}\) when empty to \(1 \mathrm{~L}\) when full. If the stomach volume is \(400 \mathrm{~mL}\) and its contents have a \(\mathrm{pH}\) of 2 , how many moles of \(\mathrm{H}^{+}\) does the stomach contain? Assuming that all the \(\mathrm{H}^{+}\) comes from \(\mathrm{HCl}\), how many grams of sodium hydrogen carbonate will totally neutralize the stomach acid?

In many reactions the addition of \(\mathrm{AlCl}_{3}\) produces the same effect as the addition of \(\mathrm{H}^{+} .\) (a) Draw a Lewis structure for \(\mathrm{AlCl}_{3}\) in which no atoms carry formal charges, and determine its structure using the VSEPR method. (b) What characteristic is notable about the structure in part (a) that helps us understand the acidic character of \(\mathrm{AlCl}_{3} ?\) (c) Predict the result of the reaction between \(\mathrm{AlCl}_{3}\) and \(\mathrm{NH}_{3}\) in a solvent that does not participate as a reactant. (d) Which acid-base theory is most suitable for discussing the similarities between \(\mathrm{AlCl}_{3}\) and \(\mathrm{H}^{+}\) ?

What is the boiling point of a \(0.10 \mathrm{M}\) solution of \(\mathrm{NaHSO}_{4}\) if the solution has a density of \(1.002 \mathrm{~g} / \mathrm{mL} ?\)

The iodate ion is reduced by sulfite according to the following reaction: $$ \mathrm{IO}_{3}^{-}(a q)+3 \mathrm{SO}_{3}^{2-}(a q) \longrightarrow \mathrm{I}^{-}(a q)+3 \mathrm{SO}_{4}^{2-}(a q) $$ The rate of this reaction is found to be first order in \(\mathrm{IO}_{3}^{-}\), first order in \(\mathrm{SO}_{3}^{2-}\), and first order in \(\mathrm{H}^{+}\). (a) Write the rate law for the reaction. (b) By what factor will the rate of the reaction change if the \(\mathrm{pH}\) is lowered from \(5.00\) to 3.50? Does the reaction proceed faster or slower at the lower pH? (c) By using the concepts discussed in Section 14.6, explain how the reaction can be pH- dependent even though \(\mathrm{H}^{+}\) does not appear in the overall reaction.

(a) Using dissociation constants from Appendix \(\mathrm{D}\), determine the value for the equilibrium constant for each of the following reactions. (Remember that when reactions are added, the corresponding equilibrium constants are multiplied.) (i) \(\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(I)\) (ii) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}(a q)+\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}(a q) \rightleftharpoons \mathrm{NH}_{3}(a q)+\mathrm{HCO}_{3}^{-}(a q)\) (b) We usually use single arrows for reactions when the forward reaction is appreciable (K much greater than 1) or when products escape from the system, so that equilibrium is never established. If we follow this convention, which of these equilibria might be written with a single arrow?

Lactic acid, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\), received its name because it is present in sour milk as a product of bacterial action. It is also responsible for the soreness in muscles after vigorous exercise. (a) The \(\mathrm{pK}_{a}\) of lactic acid is \(3.85\). Compare this with the value for propionic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}, \mathrm{p} K_{a}=4.89\right)\), and explain the differ- ence. (b) Calculate the lactate ion concentration in a \(0.050 \mathrm{M}\) solution of lactic acid. (c) When a solution of sodium lactate, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COONa}\), is mixed with an aqueous copper(II) solution, it is possible to obtain a solid salt of copper(II) lactate as a blue-green hydrate, \(\left(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COO}\right)_{2} \mathrm{Cu} \cdot x \mathrm{H}_{2} \mathrm{O} .\) Elemental analysis of the solid tells us that the solid is \(22.9 \% \mathrm{Cu}\) and \(26.0 \% \mathrm{C}\) by mass. What is the value for \(x\) in the formula for the hydrate? (d) The acid-dissociation constant for the \(\mathrm{Cu}^{2+}(a q)\) ion is \(1.0 \times 10^{-8}\). Based on this value and the acid-dissociation constant of lactic acid, predict whether a solution of copper(II) lactate will be acidic, basic, or neutral. Explain your answer.