Chapter 16

Codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\right)\) is a weak organic base. A \(5.0 \times 10^{-3} \mathrm{M}\) solution of codeine has a pH of \(9.95\). Calculate the value of \(K_{b}\) for this substance. What is the \(\mathrm{p} K_{b}\) for this base?

Although the acid-dissociation constant for phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) is listed in Appendix \(\mathrm{D}\), the base-dissociation constant for the phenolate ion \(\left(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{O}^{-}\right)\)is not. (a) Explain why it is not necessary to list both \(K_{a}\) for phenol and \(K_{b}\) for the phenolate ion. (b) Calculate \(K_{b}\) for the phenolate ion. (c) Is the phenolate ion a weaker or stronger base than ammonia?

(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 \(\mathrm{ClO}^{-}\).

(a) Given that \(K_{b}\) for ammonia is \(1.8 \times 10^{-5}\) and that for hydroxylamine is \(1.1 \times 10^{-8}\), which is the stronger base?

Using data from Appendix \(\mathrm{D}\), calculate \(\left[\mathrm{OH}^{-}\right]\)and \(\mathrm{pH}\) for each of the following solutions: (a) \(0.105 \mathrm{M} \mathrm{NaF}\), (b) \(0.035 \mathrm{MNa}_{2} \mathrm{~S}\), (c) a mixture that is \(0.045 \mathrm{M}\) in \(\mathrm{NaCH}_{3} \mathrm{COO}\) and \(0.055 \mathrm{M}\) in \(\mathrm{Ba}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}\).

Pyridinium bromide \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHBr}\right)\) is a strong electrolyte that dissociates completely into $\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NH}^{+}\( and \)\mathrm{Br}^{-}$. An aqueous solution of pyridinium bromide has a pH of \(2.95 .\) (a) Write out the reaction that leads to this acidic pH. (b) Using Appendix D, calculate the \(K_{a}\) for pyridinium bromide. (c) A solution of pyridinium bromide has a pH of 2.95 . What is the concentration of the pyridinium cation at equilibrium, in units of molarity?

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

Predict whether aqueous solutions of the following substances are acidic, basic, or neutral: (a) \(\mathrm{AlCl}_{3}\), (b) \(\mathrm{NaBr}\), (c) \(\mathrm{NaClO}\), (d) \(\left[\mathrm{CH}_{3} \mathrm{NH}_{3}\right] \mathrm{NO}_{3}\), (e) \(\mathrm{Na}_{2} \mathrm{SO}_{3}\).

An unknown salt is either \(\mathrm{NaF}, \mathrm{NaCl}\), or \(\mathrm{NaOCl}\). When \(0.050 \mathrm{~mol}\) of the salt is dissolved in water to form \(0.500 \mathrm{~L}\) of solution, the pH of the solution is \(8.08\). What is the identity of the salt? \(0.100 \mathrm{M}\) solution of the salt is neutral, what is the identity of the salt?

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 \(\mathrm{CCl}_{3} \mathrm{COOH}\).

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 \(\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\); (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 \(\mathrm{BrO}_{2}^{-}\), (c) \(\mathrm{HPO}_{4}{\underline{\phantom{xx}}}^{2-}\) 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 \(\mathrm{NO}_{2}^{-}\), (b) \(\mathrm{PO}_{4}^{3-}\) or \(\mathrm{AsO}_{4}^{3-}\), (c) \(\mathrm{HCO}_{3}^{-}\)or \(\mathrm{CO}_{3}^{2-}\).

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 \(\mathrm{H}\) - A molecules increases with increasing size of \(A\). (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 \(\mathrm{HF}\) because fluorine is the most electronegative element. Lewis Acids and Bases (Section 16.11)

If a substance is an Arrhenius base, is it necessarily a BronstedLowry base? Is it necessarily a Lewis base?

If a substance is a Lewis acid, is it necessarily a BronstedLowry acid? Is it necessarily an Arrhenius acid?

Identify the Lewis acid and Lewis base among the reactants in each of the following reactions: (a) \(\begin{aligned} \mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) & \rightleftharpoons \\\ \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{\underline{\phantom{xx}}}^{3+}(a q)+3 \mathrm{ClO}_{4}{\underline{\phantom{xx}}}^{-}(a q) \end{aligned}\) (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) \(\mathrm{HIO}(l q)+\mathrm{NH}_{2}^{-}(l q) \rightleftharpoons \mathrm{NH}_{3}(l q)+\mathrm{IO}^{-}(l q)\)

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) \(\mathrm{Zn}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}{\underline{\phantom{xx}}}^{2+}(a q)\) (d) \(\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)\)

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 \(\mathrm{Ga}^{3+}\).

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

Indicate whether each of the following statements is correct or incorrect. (a) Every Brønsted-Lowry acid is also a Lewis acid. (b) Every Lewis acid is also a Bronsted-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.

A solution is made by adding \(0.300 \mathrm{~g} \mathrm{Ca}(\mathrm{OH})_{2}(s), 50.0 \mathrm{~mL}\) of \(1.40 \mathrm{M} \mathrm{HNO}_{3}\), and enough water to make a final volume of \(75.0 \mathrm{~mL}\) Assuming that all of the solid dissolves, what is the \(\mathrm{pH}\) of the final solution?

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.

For solutions of a weak acid, a graph of \(\mathrm{pH}\) versus the logarithm of the initial acid concentration should be a straight line. What is the magnitude of the slope of that line?

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 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.

Benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) and aniline \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)\) are both derivatives of benzene. Benzoic acid is an acid with \(K_{a}=6.3 \times 10^{-5}\) and aniline is a base with \(K_{a}=4.3 \times 10^{-10}\). (a) What are the conjugate base of benzoic acid and the conjugate acid of aniline? (b) Anilinium chloride \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{Cl}\right)\) is a strong electrolyte that dissociates into anilinium ions \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\right)\)and chloride ions. Which will be more acidic, a \(0.10 \mathrm{M}\) solution of benzoic acid or a \(0.10 \mathrm{M}\) solution of anilinium chloride? (c) What is the value of the equilibrium constant for the following equilibrium? $$ \begin{aligned} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(a q)+\mathrm{C}_{6} \mathrm{H}_{5} & \mathrm{NH}_{2}(a q) \rightleftharpoons \\ & \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(a q)+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}+(a q) \end{aligned} $$

What is the pH of a solution that is \(2.5 \times 10^{-9} \mathrm{M}\) in \(\mathrm{NaOH}\) ? Does your answer make sense? What assumption do we normally make that is not valid in this case?

Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is a diprotic acid. By using data in Appendix \(\mathrm{D}\) as needed, determine whether each of the following statements is true: (a) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) can serve as both a BrønstedLowry acid and a Brønsted-Lowry base. (b) \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) is the conjugate base of \(\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\). (c) An aqueous solution of the strong electrolyte \(\mathrm{KHC}_{2} \mathrm{O}_{4}\) will have \(\mathrm{pH}<7\).

Succinic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{4}\right)\), which we will denote \(\mathrm{H}_{2} \mathrm{Suc}\), is a biologically relevant diprotic acid with the structure shown below. It is closely related to tartaric acid and malic acid (Figure 16.1). At \(25^{\circ} \mathrm{C}\), the acid-dissociation constants for succinic acid are \(K_{a 1}=6.9 \times 10^{-5}\) and \(K_{a 2}=2.5 \times 10^{-6}\). (a) Determine the pH of a \(0.32 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{Suc}\) at \(25^{\circ} \mathrm{C}\), assuming that only the first dissociation is relevant. (b) Determine the molar concentration of \(\mathrm{Suc}^{2-}\) in the solution in part (a). (c) Is the assumption you made in part (a) justified by the result from part (b)? (d) Will a solution of the salt NaHSuc be acidic, neutral, or basic?

Butyric acid is responsible for the foul smell of rancid butter. The \(\mathrm{p} K_{a}\) of butyric acid is \(4.84\). (a) Calculate the \(\mathrm{p} K_{b}\) 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) \(\mathrm{CH}_{3} \mathrm{COONa}_{\text {. }}\)

\mathrm{~A} 0.25 \mathrm{M}\( solution of a salt \)\mathrm{NaA}\( has \)\mathrm{pH}=9.29\(. What is the value of \)K_{a}$ for the parent acid HA?

The following observations are made about a diprotic acid \(\mathrm{H}_{2} \mathrm{~A}\) : (i) \(\mathrm{A} 0.10 \mathrm{M}\) solution of \(\mathrm{H}_{2} \mathrm{~A}\) has \(\mathrm{pH}=3.30\). (ii) \(\mathrm{A} 0.10 \mathrm{M}\) solution of the salt NaHA is acidic. Which of the following could be the value of \(\mathrm{p} K_{a 2}\) for \(\mathrm{H}_{2} \mathrm{~A}\) : (i) \(3.22\), (ii) \(5.30\), (iii) 7.47, or (iv) \(9.82 ?\)

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: \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \quad K_{\mathrm{a}}=4.3 \times 10^{-3}\) \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \({ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}+\mathrm{OH} \quad K_{\mathrm{b}}=6.0 \times 10^{-5}\) (a) Use the values of \(K_{a}\) and \(K_{b}\) to estimate the equilibrium constant for the intramolecular proton transfer to form a zwitterion: $$ \mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH} \rightleftharpoons{ }^{+} \mathrm{H}_{3} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COO}^{-} $$

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

How many milliliters of concentrated hydrochloric acid solution ( \(36.0 \% \mathrm{HCl}\) by mass, density \(=1.18 \mathrm{~g} / \mathrm{mL}\) ) are required to produce \(10.0 \mathrm{~L}\) of a solution that has a \(\mathrm{pH}\) of \(2.05\) ?

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 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?

Atmospheric \(\mathrm{CO}_{2}\) levels have risen by nearly \(20 \%\) over the past 40 years from \(315 \mathrm{ppm}\) to \(380 \mathrm{ppm}\). (a) Given that the average \(\mathrm{pH}\) of clean, unpolluted rain today is \(5.4\), determine the \(\mathrm{pH}\) of unpolluted rain 40 years ago. Assume that carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) formed by the reaction of \(\mathrm{CO}_{2}\) and water is the only factor influencing \(\mathrm{pH}\). $$ \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{CO}_{3}(a q) $$ (b) What volume of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\) is dissolved in a 20.0-L bucket of today's rainwater?

At \(50^{\circ} \mathrm{C}\), the ion-product constant for \(\mathrm{H}_{2} \mathrm{O}\) has the value \(K_{w}=5.48 \times 10^{-14}\). (a) What is the pH of pure water at \(50^{\circ} \mathrm{C}\) ? (b) Based on the change in \(K_{w}\) with temperature, predict whether \(\Delta H\) is positive, negative, or zero for the autoionization reaction of water: $$ 2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) $$

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: $$ \mathrm{IO}_{3}^{-}(a q)+3 \mathrm{SO}_{3}^{2-}(a q) \longrightarrow \Gamma(a q)+3 \mathrm{SO}_{4}^{2-}(a q) $$ 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 more quickly or more slowly at the lower \(\mathrm{pH}\) ? (c) By using the concepts discussed in Section 14.6, explain how the reaction can be \(\mathrm{pH}\)-dependent even though \(\mathrm{H}^{+}\)does not appear in the overall reaction.

(a) Using dissociation constants from Appendix D, determine the value for the equilibrium constant for each of the following reactions. (i) \(\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (ii) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{NH}_{3}(a q)+\mathrm{HCO}_{3}^{-}(a q)\) (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?