Chapter 13

Would you expect \(\mathrm{Fe}^{3+}\) or \(\mathrm{Fe}^{2+}\) to be the stronger Lewis acid? Explain.

Use the Lewis acid-base model to explain the following reaction. $$\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}\mathrm{CO}_{3}(a q)$$

A 10.0 -mL sample of an HCl solution has a pH of \(2.000 .\) What volume of water must be added to change the pH to 4.000?

Which of the following represent conjugate acid-base pairs? For those pairs that are not conjugates, write the correct conjugate acid or base for each species in the pair. a. \(\mathrm{H}_{2} \mathrm{O}, \mathrm{OH}^{-}\) b. \(\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{4}^{2-}\) c. \(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) d. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\)

Hemoglobin (abbreviated Hb) is a protein that is responsible for the transport of oxygen in the blood of mammals. Each hemoglobin molecule contains four iron atoms that are the binding sites for \(\mathrm{O}_{2}\) molecules. The oxygen binding is \(\mathrm{pH}\) dependent. The relevant equilibrium reaction is $$\mathrm{HbH}_{4}^{4+}(a q)+4 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4}(a q)+4 \mathrm{H}^{+}(a q)$$ Use Le Châtelier's principle to answer the following. a. What form of hemoglobin, \(\mathrm{HbH}_{4}^{4+}\) or \(\mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4},\) is favored in the lungs? What form is favored in the cells? b. When a person hyperventilates, the concentration of \(\mathrm{CO}_{2}\) in the blood is decreased. How does this affect the oxygenbinding equilibrium? How does breathing into a paper bag help to counteract this effect? (See Exercise 146.) c. When a person has suffered a cardiac arrest, injection of a sodium bicarbonate solution is given. Why is this necessary? (Hint: \(\mathrm{CO}_{2}\) blood levels increase during cardiac arrest.

At \(25^{\circ} \mathrm{C},\) a saturated solution of benzoic acid \(\left(K_{a}=6.4 \times\right.\) \(10^{-5}\) ) has a pH of \(2.80 .\) Calculate the water solubility of benzoic acid in moles per liter.

Calculate the \(\mathrm{pH}\) of an aqueous solution containing \(1.0 \times\) \(10^{-2} M \mathrm{HCl}, 1.0 \times 10^{-2} \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4},\) and \(1.0 \times 10^{-2} \mathrm{M} \mathrm{HCN}\)

Acrylic acid \(\left(\mathrm{CH}_{2}=\mathrm{CHCO}_{2} \mathrm{H}\right)\) is a precursor for many important plastics. \(K_{\mathrm{a}}\) for acrylic acid is \(5.6 \times 10^{-5}\) a. Calculate the \(\mathrm{pH}\) of a \(0.10-M\) solution of acrylic acid. b. Calculate the percent dissociation of a 0.10-M solution of acrylic acid. c. Calculate the \(\mathrm{pH}\) of a \(0.050-M\) solution of sodium acrylate \(\left(\mathrm{NaC}_{3} \mathrm{H}_{3} \mathrm{O}_{2}\right)\)

Classify each of the following as a strong acid, weak acid, strong base, or weak base in aqueous solution. a. \(\mathrm{HNO}_{2}\) b. \(\mathrm{HNO}_{3}\) c. \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) d. \(\mathrm{NaOH}\) e. \(\mathrm{NH}_{3}\) f. HF g. h. \(\mathrm{Ca}(\mathrm{OH})_{2}\) i. \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Quinine \(\left(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2}\right)\) is the most important alkaloid derived from cinchona bark. It is used as an antimalarial drug. For quinine, \(\mathrm{p} K_{\mathrm{b}_{1}}=5.1\) and \(\mathrm{p} K_{\mathrm{b}_{2}}=9.7\left(\mathrm{p} K_{\mathrm{b}}=-\log K_{\mathrm{b}}\right) .\) Only 1 g quinine will dissolve in \(1900.0 \mathrm{mL}\) of solution. Calculate the \(\mathrm{pH}\) of a saturated aqueous solution of quinine. Consider only the reaction \(\mathrm{Q}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{QH}^{+}+\mathrm{OH}^{-}\) described by \(\mathrm{p} K_{\mathrm{b}_{1}},\) where \(\mathrm{Q}=\) quinine.

Codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\right)\) is a derivative of morphine that is used as an analgesic, narcotic, or antitussive. It was once commonly used in cough syrups but is now available only by prescription because of its addictive properties. If the \(\mathrm{pH}\) of a \(1.7 \times 10^{-3}-M\) solution of codeine is \(9.59,\) calculate \(K_{\mathrm{b}}\)

A codeine-containing cough syrup lists codeine sulfate as a major ingredient instead of codeine. The Merck Index gives \(\mathrm{C}_{36} \mathrm{H}_{44} \mathrm{N}_{2} \mathrm{O}_{10} \mathrm{S}\) as the formula for codeine sulfate. Describe the composition of codeine sulfate. (See Exercise \(155 .\) ) Why is codeine sulfate used instead of codeine?

The equilibrium constant \(K_{\mathrm{a}}\) for the reaction $$\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons{\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}}(\mathrm{OH})^{2+}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)$$ is \(6.0 \times 10^{-3}\) a. Calculate the \(\mathrm{pH}\) of a \(0.10-M\) solution of \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) b. Will a \(1.0-M\) solution of iron(II) nitrate have a higher or lower \(\mathrm{pH}\) than a \(1.0-M\) solution of iron(III) nitrate? Explain.

Rank the following 0.10 \(M\) solutions in order of increasing pH. a. HI, HF, NaF, NaI b. \(\mathrm{NH}_{4} \mathrm{Br}, \mathrm{HBr}, \mathrm{KBr}, \mathrm{NH}_{3}\) c. \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{NO}_{3}, \mathrm{NaNO}_{3}, \mathrm{NaOH}, \mathrm{HOC}_{6} \mathrm{H}_{5}, \mathrm{KOC}_{6} \mathrm{H}_{5}\) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}, \mathrm{HNO}_{3}\)

Is an aqueous solution of NaHSO_ acidic, basic, or neutral? What reaction occurs with water? Calculate the pH of a 0.10-M solution of \(\mathrm{NaHSO}_{4}\).

Students are often surprised to learn that organic acids, such as acetic acid, contain - OH groups. Actually, all oxyacids contain hydroxyl groups. Sulfuric acid, usually written as \(\mathrm{H}_{2} \mathrm{SO}_{4}\) has the structural formula \(\mathrm{SO}_{2}(\mathrm{OH})_{2},\) where \(\mathrm{S}\) is the central atom. Identify the acids whose structural formulas are shown below. Why do they behave as acids, while NaOH and KOH are bases? a. \(\mathrm{SO}(\mathrm{OH})_{2}\) b. \(\mathrm{ClO}_{2}(\mathrm{OH})\) c. \(\mathrm{HPO}(\mathrm{OH})_{2}\)

For solutions of the same concentration, as acid strength increases, indicate what happens to each of the following (increases, decreases, or doesn't change). a. \(\left[\mathrm{H}^{+}\right]\) b. \(\mathrm{pH}\) c. \(\left[\mathrm{OH}^{-}\right]\) d. pOH \(\mathbf{e} . K_{\mathrm{a}}\)

Consider a \(0.60-M\) solution of \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3},\) lactic acid \(\left(K_{\mathrm{a}}=\right.\) \(\left.1.4 \times 10^{-4}\right)\) a. Which of the following are major species in the solution? i. \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\) ii. \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}\) iii. \(\mathrm{H}^{+}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) \(\mathbf{v} . \mathrm{OH}^{-}\) b. Complete the following ICE table in terms of \(x,\) the amount (mol/L) of lactic acid that dissociates to reach equilibrium. c. What is the equilibrium concentration for \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-} ?\) d. Calculate the \(p H\) of the solution.

Consider a \(0.67-M\) solution of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\left(K_{\mathrm{b}}=5.6 \times 10^{-4}\right)\) a. Which of the following are major species in the solution? i. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) ii. \(\mathrm{H}^{+}\) iii. OH \(^{-}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) v. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) b. Calculate the \(p\) H of this solution.

Rank the following 0.10 \(M\) solutions in order of increasing pH. a. \(\mathrm{NH}_{3}\) b. KOH c. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) d. KCl e. HCl

Consider \(0.25 \mathrm{M}\) solutions of the following salts: \(\mathrm{NaCl}\), RbOCI, KI, Ba(CIO_{ } _ { 2 } \text { , and } \mathrm { NH } _ { 4 } \mathrm { NO } _ { 3 } \text { . For each salt, indicate } whether the solution is acidic, basic, or neutral.

Calculate the pH of the following solutions: a. \(1.2 \mathrm{M} \mathrm{CaBr}_{2}\) b. \(0.84 M C_{6} H_{5} N H_{3} N O_{3}\left(K_{b} \text { for } C_{6} H_{5} N H_{2}=3.8 \times 10^{-10}\right)\) c. \(0.57 M \mathrm{KC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\left(K_{\mathrm{a}} \text { for } \mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}=6.4 \times 10^{-5}\right)\)

Consider 0.10 \(M\) solutions of the following compounds: \(\mathrm{AlCl}_{3}, \mathrm{NaCN}, \mathrm{KOH}, \mathrm{CsClO}_{4},\) and NaF. Place these solutions in order of increasing \(\mathrm{pH}\).

The pH of \(1.0 \times 10^{-8} M\) hydrochloric acid is not \(8.00 .\) The correct \(\mathrm{pH}\) can be calculated by considering the relationship between the molarities of the three principal ions in the solution \(\left(\mathrm{H}^{+}, \mathrm{Cl}^{-}, \text {and } \mathrm{OH}^{-}\right) .\) These molarities can be calculated from algebraic equations that can be derived from the considerations given below. a. The solution is electrically neutral. b. The hydrochloric acid can be assumed to be \(100 \%\) ionized. c. The product of the molarities of the hydronium ions and the hydroxide ions must equal \(K_{\mathrm{w}}\) Calculate the \(\mathrm{pH}\) of a \(1.0 \times 10^{-8}-M\) HCl solution.

Calculate the \(\mathrm{pH}\) of a \(1.0 \times 10^{-7}-M\) solution of \(\mathrm{NaOH}\) in water.

Calculate \(\left[\mathrm{OH}^{-}\right]\) in a \(3.0 \times 10^{-7}-M\) solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\)

Making use of the assumptions we ordinarily make in calculating the pH of an aqueous solution of a weak acid, calculate the \(\mathrm{pH}\) of a \(1.0 \times 10^{-6}-M\) solution of hypobromous acid (HBrO, \(K_{\mathrm{a}}=2 \times 10^{-9} \mathrm{J} .\) What is wrong with your answer? Why is it wrong? Without trying to solve the problem, explain what has to be included to solve the problem correctly.

Calculate the \(\mathrm{pH}\) of a \(0.200-M\) solution of \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHF}\). Hint: \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NHF}\) is a salt composed of \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NH}^{+}\) and \(\mathrm{F}^{-}\) ions. The principal equilibrium in this solution is the best acid reacting with the best base; the reaction for the principal equilibrium is $$\begin{aligned} \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NH}^{+}(a q)+\mathrm{F}^{-}(a q) & \rightleftharpoons \\ \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}(a q) &+\mathrm{HF}(a q) \quad K=8.2 \times 10^{-3}\end{aligned}$$

What mass of \(\mathrm{NaOH}(s)\) must be added to \(1.0 \mathrm{L}\) of \(0.050 \mathrm{M}\) \(\mathrm{NH}_{3}\) to ensure that the percent ionization of \(\mathrm{NH}_{3}\) is no greater than \(0.0010 \% ?\) Assume no volume change on addition of NaOH.

Consider \(1000 .\) mL of a \(1.00 \times 10^{-4}-M\) solution of a certain acid HA that has a \(K_{\mathrm{a}}\) value equal to \(1.00 \times 10^{-4} .\) How much water was added or removed (by evaporation) so that a solution remains in which \(25.0 \%\) of \(\mathrm{HA}\) is dissociated at equilibrium? Assume that HA is nonvolatile.

Calculate the mass of sodium hydroxide that must be added to \(1.00 \mathrm{L}\) of \(1.00-M \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) to double the \(\mathrm{pH}\) of the solution (assume that the added NaOH does not change the volume of the solution).

Consider the species \(\mathrm{PO}_{4}^{3-}, \mathrm{HPO}_{4}^{2-},\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} .\) Each ion can act as a base in water. Determine the \(K_{\mathrm{b}}\) value for each of these species. Which species is the strongest base?

A \(0.100-\mathrm{g}\) sample of the weak acid HA (molar mass \(=\) \(100.0 \mathrm{g} / \mathrm{mol}\) ) is dissolved in \(500.0 \mathrm{g}\) water. The freezing point of the resulting solution is \(-0.0056^{\circ} \mathrm{C}\). Calculate the value of \(K_{\mathrm{a}}\) for this acid. Assume molality equals molarity in this solution.

A sample containing 0.0500 mole of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is dissolved in enough water to make 1.00 L of solution. This solution contains hydrated \(\mathrm{SO}_{4}^{2-}\) and \(\mathrm{Fe}^{3+}\) ions. The latter behaves as an acid: $$\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q) \rightleftharpoons \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{OH}^{2+}(a q)+\mathrm{H}^{+}(a q)$$ a. Calculate the expected osmotic pressure of this solution at \(25^{\circ} \mathrm{C}\) if the above dissociation is negligible. b. The actual osmotic pressure of the solution is 6.73 atm at \(25^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{a}}\) for the dissociation reaction of \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+} .\) (To do this calculation, you must assume that none of the ions go through the semipermeable membrane. Actually, this is not a great assumption for the tiny \(\mathrm{H}^{+}\) ion.)

A \(2.14-\mathrm{g}\) sample of sodium hypoiodite is dissolved in water to make 1.25 L of solution. The solution \(\mathrm{pH}\) is \(11.32 .\) What is \(K_{\mathrm{b}}\) for the hypoiodite ion?

Isocyanic acid (HNCO) can be prepared by heating sodium cyanate in the presence of solid oxalic acid according to the equation $$2 \mathrm{NaOCN}(s)+\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(s) \longrightarrow 2 \mathrm{HNCO}(l)+\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(s)$$ Upon isolating pure HNCO(I), an aqueous solution of HNCO can be prepared by dissolving the liquid HNCO in water. What is the \(\mathrm{pH}\) of a \(100 .\) -mL solution of HNCO prepared from the reaction of \(10.0 \mathrm{g}\) each of \(\mathrm{NaOCN}\) and \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) assuming all of the HNCO produced is dissolved in solution? \((K_{\mathrm{a}}\) of HNCO \(\left.=1.2 \times 10^{-4} .\right)\)

A certain acid, HA, has a vapor density of \(5.11 \mathrm{g} / \mathrm{L}\) when in the gas phase at a temperature of \(25^{\circ} \mathrm{C}\) and a pressure of 1.00 atm. When 1.50 g of this acid is dissolved in enough water to make 100.0 mL of solution, the \(p\) H is found to be \(1.80 .\) Calculate \(K_{\mathrm{a}}\) for the acid.

An aqueous solution contains a mixture of 0.0500 \(M\) HCOOH \(\left(K_{\mathrm{a}}=1.77 \times 10^{-4}\right)\) and \(0.150 M \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\left(K_{\mathrm{a}}=1.34 \times\right.\) \(10^{-5}\) ). Calculate the \(p\) H of this solution. Because both acids are of comparable strength, the \(\mathrm{H}^{+}\) contribution from both acids must be considered.