Chapter Questions
Define buffer solution.
Define $\mathrm{p} K_{\mathrm{a}}$ for a weak acid and explain the relationship between the value of the $\mathrm{p} K_{\mathrm{a}}$ and the strength of the acid. Do the same for $\mathrm{p} K_{\mathrm{b}}$ and a weak base.
Which of the following has the greatest buffer capacity? (a) $0.40 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$,(b) $0.40 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 0.60 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$(c) $0.30 M$ $\mathrm{CH}_{3} \mathrm{COONa} / 0.60 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$
The $\mathrm{p} K_{\mathrm{b}}$ s for the bases $\mathrm{X}^{-}, \mathrm{Y}^{-},$ and $\mathrm{Z}^{-}$ are $2.72,8.66,$ and $4.57,$ respectively. Arrange the following acids in order of increasing strength: HX, HY, HZ.
Specify which of these systems can be classified as a buffer system:(a) $\mathrm{KCl} / \mathrm{HCl}$,(b) $\mathrm{NH}_{3} / \mathrm{NH}_{4} \mathrm{NO}_{3}$,(c) $\mathrm{Na}_{2} \mathrm{HPO}_{4} / \mathrm{NaH}_{2} \mathrm{PO}_{4}$.
Specify which of these systems can be classified as a buffer system:(a) $\mathrm{KNO}_{2} / \mathrm{HNO}_{2}$,(b) $\mathrm{KHSO}_{4} / \mathrm{H}_{2} \mathrm{SO}_{4}$(c) HCOOK/HCOOH.
The $\mathrm{pH}$ of a bicarbonate-carbonic acid buffer is $8.00 .$ Calculate the ratio of the concentration of carbonic acid to that of the bicarbonate ion.
Calculate the $\mathrm{pH}$ of these two buffer solutions:(a) $2.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 2.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$,(b) $0.20 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COONa} / 0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$. Which is the more effective buffer? Why?
Calculate the $\mathrm{pH}$ of the buffer system $0.15 \mathrm{M}$ $\mathrm{NH}_{3} / 0.35 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$
What is the $\mathrm{pH}$ of the buffer $0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4} / 0.15 \mathrm{M}$$\mathrm{KH}_{2} \mathrm{PO}_{4} ?$
The $\mathrm{pH}$ of a sodium acetate-acetic acid buffer is $4.50 .$ Calculate the ratio $\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right] /\left[\mathrm{CH}_{3} \mathrm{COOH}\right]$.
The pH of blood plasma is $7.40 .$ Assuming the principal buffer system is $\mathrm{HCO}_{3}^{-} / \mathrm{H}_{2} \mathrm{CO}_{3},$ calculate the ratio $\left[\mathrm{HCO}_{3}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right]$. Is this buffer more effective against an added acid or an added base?
Calculate the $\mathrm{pH}$ of $1.00 \mathrm{~L}$ of the buffer $0.80 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{NH}_{2} / 1.00 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}$ before and after the ad-dition of (a) $0.070 \mathrm{~mol} \mathrm{NaOH}$ and (b) $0.11 \mathrm{~mol} \mathrm{HCl}$. (See Table 16.5 for $K_{\mathrm{a}}$ value.)
Calculate the $\mathrm{pH}$ of $1.00 \mathrm{~L}$ of the buffer $1.00 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COONa} / 1.00 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ before and after the addition of (a) $0.080 \mathrm{~mol} \mathrm{NaOH}$ and (b) 0.12 mol $\mathrm{HCl}$. (Assume that there is no change in volume.)
A diprotic acid, $\mathrm{H}_{2} \mathrm{~A},$ has the following ionization constants: $K_{\mathrm{a}_{\mathrm{1}}}=1.1 \times 10^{-3}$ and $K_{\mathrm{a}2}=2.5 \times 10^{-6}$ To make up a buffer solution of $\mathrm{pH} 5.80$, which combination would you choose: $\mathrm{NaHA} / \mathrm{H}_{2} \mathrm{~A}$ or $\mathrm{Na}_{2} \mathrm{~A} /$NaHA?
A student wishes to prepare a buffer solution at $\mathrm{pH}=$ $8.60 .$ Which of these weak acids should she choose and why: HA $\left(K_{\mathrm{a}}=2.7 \times 10^{-3}\right), \mathrm{HB}\left(K_{\mathrm{a}}=4.4 \times\right.$ $10^{-6}$ ), or $\mathrm{HC}\left(K_{\mathrm{a}}=2.6 \times 10^{-9}\right) ?$
The diagrams shown here contain one or more of the compounds: $\mathrm{H}_{2} \mathrm{~A}, \mathrm{NaHA},$ and $\mathrm{Na}_{2} \mathrm{~A},$ where $\mathrm{H}_{2} \mathrm{~A}$ is a weak diprotic acid. (1) Which of the solutions can act as buffer solutions? (2) Which solution is the most effective buffer solution? Water molecules and $\mathrm{Na}^{+}$ ions have been omitted for clarity.
The diagrams shown here represent solutions containing a weak acid HA $\left(\mathrm{p} K_{\mathrm{a}}=5.00\right)$ and its sodium salt NaA. (1) Calculate the $\mathrm{pH}$ of the solutions. (2) What is the $\mathrm{pH}$ after the addition of $0.1 \mathrm{~mol} \mathrm{H}^{+}$ ions to solution (a)? (3) What is the pH after the addition of 0.1 mol $\mathrm{OH}^{-}$ ions to solution (d)? Treat each sphere as $0.1 \mathrm{~mol}$.
A 0.2688 -g sample of a monoprotic acid neutralizes $16.4 \mathrm{~mL}$ of $0.08133 \mathrm{M}$ KOH solution. Calculate the molar mass of the acid.
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.
Calculate the $\mathrm{pH}$ at the equivalence point for these titrations:(a) $0.10 M \mathrm{HCl}$ versus $0.10 \mathrm{M} \mathrm{NH}_{3}$,(b) $0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ versus $0.10 \mathrm{M} \mathrm{NaOH}$.
A sample of $0.1276 \mathrm{~g}$ of an unknown monoprotic acid was dissolved in $25.0 \mathrm{~mL}$ of water and titrated with $0.0633 M \mathrm{NaOH}$ solution. The volume of base required to reach the equivalence point was $18.4 \mathrm{~mL}$. (a) Calculate the molar mass of the acid. (b) After $10.0 \mathrm{~mL}$ of base had been added to the titration, the $\mathrm{pH}$ was determined to be 5.87 . What is the $K_{\mathrm{a}}$ of the unknown acid?
The diagrams shown here represent solutions at different stages in the titration of a weak acid HA with $\mathrm{NaOH}$. Identify the solution that corresponds to (1) the initial stage before the addition of $\mathrm{NaOH}$, (2) halfway to the equivalence point, (3) the equivalence point, (4) beyond the equivalence point. Is the pH greater than, less than, or equal to 7 at the equivalence point? Water molecules and $\mathrm{Na}^{+}$ ions have been omitted for clarity.
The diagrams shown here represent solutions at various stages in the titration of a weak base $\mathrm{B}$ (such as $\mathrm{NH}_{3}$ ) with $\mathrm{HCl}$. Identify the solution that corresponds to (1) the initial stage before the addition of $\mathrm{HCl}$, (2) halfway to the equivalence point, (3) the equivalence point, (4) beyond the equivalence point. Is the pH greater than, less than, or equal to 7 at the equivalence point? Water molecules and $\mathrm{Cl}^{-}$ ions have been omitted for clarity.
Explain how an acid-base indicator works in a titration.
What are the criteria for choosing an indicator for a particular acid-base titration?
The amount of indicator used in an acid-base titration must be small. Why?
A student carried out an acid-base titration by adding $\mathrm{NaOH}$ solution from a buret to an Erlenmeyer flask containing $\mathrm{HCl}$ solution and using phenolphthalein as indicator. At the equivalence point, he observed a faint reddish-pink color. However, after a few minutes, the solution gradually turned colorless. What do you suppose happened?
Referring to Table 17.1 , specify which indicator or indicators you would use for the following titrations:(a) HCOOH versus $\mathrm{NaOH}$,(b) HCl versus KOH,(c) $\mathrm{HNO}_{3}$ versus $\mathrm{NH}_{3}$.
The ionization constant $K_{\mathrm{a}}$ of an indicator HIn is $1.0 \times$ $10^{-6} .$ The color of the nonionized form is red and that of the ionized form is yellow. What is the color of this indicator in a solution whose $\mathrm{pH}$ is $4.00 ?$ (Hint: The color of an indicator can be estimated by considering the ratio [HIn]/[ In $^{-}$ ]. If the ratio is equal to or greater than $10,$ the color will be that of the nonionized form. If the ratio is equal to or smaller than $0.1,$ the color will be that of the ionized form.)
Define solubility, molar solubility, and solubility product. Explain the difference between solubility and the solubility product of a slightly soluble substance such as $\mathrm{BaSO}_{4}$.
Why do we usually not quote the $K_{\mathrm{sp}}$ values for soluble ionic compounds?
Write balanced equations and solubility product expressions for the solubility equilibria of these compounds:(a) $\mathrm{CuBr}$(b) $\mathrm{ZnC}_{2} \mathrm{O}_{4}$(c) $\mathrm{Ag}_{2} \mathrm{CrO}_{4}$(d) $\mathrm{Hg}_{2} \mathrm{Cl}_{2}$(e) $\mathrm{AuCl}_{3}$(f) $\mathrm{Mn}_{3}\left(\mathrm{PO}_{4}\right)_{2}$.
Write the solubility product expression for the ionic compound $\mathrm{A}_{x} \mathrm{~B}_{y}$
How can we predict whether a precipitate will form when two solutions are mixed?
Silver chloride has a larger $K_{\mathrm{sp}}$ than silver carbonate (see Table 17.2). Does this mean that the former also has a larger molar solubility than the latter?
Calculate the concentration of ions in these saturated solutions:(a) $\left[\mathrm{I}^{-}\right]$ in AgI solution with $\left[\mathrm{Ag}^{+}\right]=9.1 \times 10^{-9} \mathrm{M}$(b) $\left[\mathrm{Al}^{3+}\right]$ in $\mathrm{Al}(\mathrm{OH})_{3}$ with $\left[\mathrm{OH}^{-}\right]=2.9 \times 10^{-9} \mathrm{M}$
From the solubility data given, calculate the solubility products for these compounds:(a) $\operatorname{SrF}_{2}, 7.3 \times 10^{-2} \mathrm{~g} / \mathrm{L}$(b) $\mathrm{Ag}_{3} \mathrm{PO}_{4}, 6.7 \times 10^{-3} \mathrm{~g} / \mathrm{L}$
The molar solubility of $\mathrm{MnCO}_{3}$ is $4.2 \times 10^{-6} \mathrm{M}$. What is $K_{\mathrm{sp}}$ for this compound?
Using data from Table $17.2,$ calculate the molar solubility of calcium phosphate, which is a component of bones.
The solubility of an ionic compound $\mathrm{M}_{2} \mathrm{X}_{3}$ (molar mass $=288 \mathrm{~g}$ ) is $3.6 \times 10^{-17} \mathrm{~g} / \mathrm{L}$. What is $K_{\mathrm{sp}}$ for the compound?
Using data from Table $17.2,$ calculate the solubility of $\mathrm{CaF}_{2}$ in $\mathrm{g} / \mathrm{L}$.
What is the $\mathrm{pH}$ of a saturated zinc hydroxide solution?
The pH of a saturated solution of a metal hydroxide $\mathrm{MOH}$ is $9.68 .$ Calculate the $K_{\mathrm{sp}}$ for the compound.
A sample of $20.0 \mathrm{~mL}$ of $0.10 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$ is added to $50.0 \mathrm{~mL}$ of $0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .$ Will $\mathrm{BaCO}_{3}$ precipitate?
A volume of $75 \mathrm{~mL}$ of $0.060 \mathrm{M} \mathrm{NaF}$ is mixed with $25 \mathrm{~mL}$ of $0.15 \mathrm{M} \mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2} .$ Calculate the concentrations in the final solution of $\mathrm{NO}_{3}^{-}, \mathrm{Na}^{+}, \mathrm{Sr}^{2+},$ and $\mathrm{F}^{-}$. $\left(K_{\mathrm{sp}}\right.$ for $\left.\mathrm{SrF}_{2}=2.0 \times 10^{-10} .\right)$
How does a common ion affect solubility? Use Le Châtelier's principle to explain the decrease in solubility of $\mathrm{CaCO}_{3}$ in a $\mathrm{Na}_{2} \mathrm{CO}_{3}$ solution.
The molar solubility of $\mathrm{AgCl}$ in $6.5 \times 10^{-3} \mathrm{M} \mathrm{AgNO}_{3}$is $2.5 \times 10^{-8} M$. In deriving $K_{\mathrm{sp}}$ from these data, which of these assumptions are reasonable?(a) $K_{\mathrm{sp}}$ is the same as solubility.(b) $K_{\mathrm{sp}}$ of $\mathrm{AgCl}$ is the same in $6.5 \times 10^{-3} \mathrm{M} \mathrm{AgNO}_{3}$as in pure water.(c) Solubility of $\mathrm{AgCl}$ is independent of the concentration of $\mathrm{AgNO}_{3}$(d) $\left[\mathrm{Ag}^{+}\right]$ in solution does not change significantly on the addition of $\mathrm{AgCl}$ to $6.5 \times 10^{-3} \mathrm{M} \mathrm{AgNO}_{3}$.(e) $\left[\mathrm{Ag}^{+}\right]$ in solution after the addition of $\mathrm{AgCl}$ to $6.5 \times 10^{-3} \mathrm{M} \mathrm{AgNO}_{3}$ is the same as it would be in pure water.
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} ?$
The solubility product of $\mathrm{PbBr}_{2}$ is $8.9 \times 10^{-6} .$ Determine the molar solubility (a) in pure water, (b) in $0.20 M$ KBr solution, (c) in $0.20 M \mathrm{~Pb}\left(\mathrm{NO}_{3}\right)_{2}$ solution.
Calculate the molar solubility of $\mathrm{AgCl}$ in a solution made by dissolving $10.0 \mathrm{~g}$ of $\mathrm{CaCl}_{2}$ in enough water to make up a $1.00 \mathrm{~L}$ solution.
Calculate the molar solubility of $\mathrm{BaSO}_{4}$ (a) in water and (b) in a solution containing $1.0 M \mathrm{SO}_{4}^{2-}$ ions.
Explain the formation of complexes in Table 17.4 in terms of Lewis acid-base theory.
Give an example to illustrate the general effect of complex ion formation on solubility.
Write the formation constant expressions for these complex ions:(a) $\mathrm{Zn}(\mathrm{OH})_{4}^{2-}$(b) $\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}$(c) $\mathrm{HgI}_{4}^{2-}$.
Explain, with balanced ionic equations, why (a) $\mathrm{CuI}_{2}$ dissolves in ammonia solution, (b) AgBr dissolves in NaCN solution, $\begin{array}{llll}\text { (c) } & \mathrm{Hg}_{2} \mathrm{Cl}_{2} & \text { dissolves } & \text { in } & \mathrm{KCl}\end{array}$ solution.
If $2.50 \mathrm{~g}$ of $\mathrm{CuSO}_{4}$ are dissolved in $9.0 \times 10^{2} \mathrm{~mL}$ of $0.30 M \mathrm{NH}_{3},$ what are the concentrations of $\mathrm{Cu}^{2+}$ $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+},$ and $\mathrm{NH}_{3}$ at equilibrium?
Calculate the concentrations of $\mathrm{Cd}^{2+}, \mathrm{Cd}(\mathrm{CN})_{4}^{2-},$ and $\mathrm{CN}^{-}$ at equilibrium when $0.50 \mathrm{~g}$ of $\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}$ dissolves in $5.0 \times 10^{2} \mathrm{~mL}$ of $0.50 \mathrm{M} \mathrm{NaCN}$.
If $\mathrm{NaOH}$ is added to $0.010 \mathrm{M} \mathrm{Al}^{3+}$, which will be the predominant species at equilibrium: $\mathrm{Al}(\mathrm{OH})_{3}$ or $\mathrm{Al}(\mathrm{OH})_{4}^{-} ?$ The $\mathrm{pH}$ of the solution is $14.00 .\left[K_{\mathrm{f}}\right.$ for $\left.\mathrm{Al}(\mathrm{OH})_{4}^{-}=2.0 \times 10^{33} .\right]$
Calculate the molar solubility of AgI in a $1.0 \mathrm{M} \mathrm{NH}_{3}$ solution. (Hint: You need to consider two different types of equilibria.)
Outline the general principle of qualitative analysis.
Give two examples of metal ions in each group ( 1 through 5 ) in the qualitative analysis scheme.
In a group 1 analysis, a student obtained a precipitate containing both $\mathrm{AgCl}$ and $\mathrm{PbCl}_{2}$. Suggest one reagent that would enable her to separate $\operatorname{AgCl}(s)$ from $\mathrm{PbCl}_{2}(s)$
In a group 1 analysis, a student adds hydrochloric acid to the unknown solution to make $\left[\mathrm{Cl}^{-}\right]=0.15 \mathrm{M}$. Some $\mathrm{PbCl}_{2}$ precipitates. Calculate the concentration of $\mathrm{Pb}^{2+}$ remaining in solution.
Both $\mathrm{KCl}$ and $\mathrm{NH}_{4} \mathrm{Cl}$ are white solids. Suggest one reagent that would enable you to distinguish between these two compounds.
Describe a simple test that would enable you to distinguish between $\mathrm{AgNO}_{3}(s)$ and $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(s)$
A quantity of $0.560 \mathrm{~g}$ of $\mathrm{KOH}$ is added to $25.0 \mathrm{~mL}$ of $1.00 M \mathrm{HCl}$. Excess $\mathrm{Na}_{2} \mathrm{CO}_{3}$ is then added to the solution. What mass (in grams) of $\mathrm{CO}_{2}$ is formed?
A volume of $25.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{HCl}$ is titrated against a $0.100 M \mathrm{NH}_{3}$ solution added to it from a buret. Calculate the $\mathrm{pH}$ values of the solution (a) after $10.0 \mathrm{~mL}$ of $\mathrm{NH}_{3}$ solution have been added, $(\mathrm{b})$ after $25.0 \mathrm{~mL}$ of $\mathrm{NH}_{3}$ solution have been added, (c) after $35.0 \mathrm{~mL}$ of $\mathrm{NH}_{3}$ solution have been added.
The buffer range is defined by the equation $\mathrm{pH}=$ $\mathrm{p} K_{\mathrm{a}} \pm 1 .$ Calculate the range of the ratio [conjugate base $]$ / [acid] that corresponds to this equation.
The $\mathrm{p} K_{\mathrm{a}}$ of the indicator methyl orange is $3.46 .$ Over what pH range does this indicator change from $90 \%$ HIn to $90 \% \mathrm{In}^{-} ?$
Sketch the titration curve of a weak acid versus a strong base such as that shown in Figure $17.5 .$ On your graph indicate the volume of base used at the equivalence point and also at the half-equivalence point, that is, the point at which half of the base has been added. Show how you can measure the $\mathrm{pH}$ of the solution at the half-equivalence point. Using Equation (17.3), explain how you can determine the $\mathrm{p} K_{\mathrm{a}}$ of the acid by this procedure.
A 200 -mL volume of $\mathrm{NaOH}$ solution was added to $400 \mathrm{~mL}$ of a $2.00 \mathrm{M} \mathrm{HNO}_{2}$ solution. The $\mathrm{pH}$ of the mixed solution was 1.50 units greater than that of the original acid solution. Calculate the molarity of the $\mathrm{NaOH}$ solution.
The $\mathrm{p} K_{\mathrm{a}}$ of butyric acid (HBut) is $4.7 .$ Calculate $K_{\mathrm{b}}$ for the butyrate ion (But $^{-}$ ).
A solution is made by mixing exactly $500 \mathrm{~mL}$ of 0.167 $M \mathrm{NaOH}$ with exactly $500 \mathrm{~mL} 0.100 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COOH}$. Calculate the equilibrium concentrations of $\mathrm{H}^{+}, \mathrm{CH}_{3} \mathrm{COOH}, \mathrm{CH}_{3} \mathrm{COO}^{-}, \mathrm{OH}^{-},$ and $\mathrm{Na}^{+}$.
$\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?
Calculate the $\mathrm{pH}$ of the $0.20 \mathrm{M} \mathrm{NH}_{3} / 0.20 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$ buffer. What is the $\mathrm{pH}$ of the buffer after the addition of $10.0 \mathrm{~mL}$ of $0.10 \mathrm{M} \mathrm{HCl}$ to $65.0 \mathrm{~mL}$ of the buffer?
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) $\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)$
A student mixes $50.0 \mathrm{~mL}$ of $1.00 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}$ with $86.4 \mathrm{~mL}$ of $0.494 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} .$ Calculate the mass of $\mathrm{BaSO}_{4}$ formed and the $\mathrm{pH}$ of the mixed solution.
A 2.0 - $L$ kettle contains 116 g of calcium carbonate as boiler scale. How many times would the kettle have to be completely filled with distilled water to remove all of the deposit at $25^{\circ} \mathrm{C} ?$
Equal volumes of $0.12 \mathrm{M} \mathrm{AgNO}_{3}$ and $0.14 \mathrm{M} \mathrm{ZnCl}_{2}$solution are mixed. Calculate the equilibrium concentrations of $\mathrm{Ag}^{+}, \mathrm{Cl}^{-}, \mathrm{Zn}^{2+},$ and $\mathrm{NO}_{3}^{-}$
Calculate the solubility (in grams per liter) of $\mathrm{Ag}_{2} \mathrm{CO}_{3}$
Find the approximate $\mathrm{pH}$ range suitable for the separation of $\mathrm{Fe}^{3+}$ and $\mathrm{Zn}^{2+}$ by precipitation of $\mathrm{Fe}(\mathrm{OH})_{3}$ from a solution that is initially $0.010 M$ in $\mathrm{Fe}^{3+}$ and $\mathrm{Zn}^{2+}$
Which of these ionic compounds will be more soluble in acid solution than in water: (a) $\mathrm{BaSO}_{4},$ (b) $\mathrm{PbCl}_{2}$, (c) $\mathrm{Fe}(\mathrm{OH})_{3},$ (d) $\mathrm{CaCO}_{3}$ ? Explain. (Hint: For each salt, determine any possible reaction between the anion and $\mathrm{H}^{+}$ ions. $.$
Which of these substances will be more soluble in acid solution than in pure water: (a) $\mathrm{CuI},$ (b) $\mathrm{Ag}_{2} \mathrm{SO}_{4}$, (c) $\mathrm{Zn}(\mathrm{OH})_{2},$ (d) $\mathrm{BaC}_{2} \mathrm{O}_{4},$ (e) $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ ? Explain. (Hint: For each salt, determine any possible reaction between the anion and $\mathrm{H}^{+}$ ions.
What is the $\mathrm{pH}$ of a saturated solution of aluminum hydroxide?
The molar solubility of $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}$ in a $0.10 \mathrm{M} \mathrm{NaIO}_{3}$solution is $2.4 \times 10^{-11} \mathrm{~mol} / \mathrm{L}$. What is $K_{\mathrm{sp}}$ for $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2} ?$
The solubility product of $\mathrm{Mg}(\mathrm{OH})_{2}$ is $1.2 \times 10^{-11}$ What minimum $\mathrm{OH}^{-}$ concentration must be attained (for example, by adding $\mathrm{NaOH}$ ) to make the $\mathrm{Mg}^{2+}$ concentration in a solution of $\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ less than $1.0 \times 10^{-10} M ?$
Calculate whether a precipitate will form if $2.00 \mathrm{~mL}$ of $0.60 M \mathrm{NH}_{3}$ are added to $1.0 \mathrm{~L}$ of $1.0 \times 10^{-3} \mathrm{M}$ $\mathrm{FeSO}_{4}$
Both $\mathrm{Ag}^{+}$ and $\mathrm{Zn}^{2+}$ form complex ions with $\mathrm{NH}_{3}$. Write balanced equations for the reactions. However, $\mathrm{Zn}(\mathrm{OH})_{2}$ is soluble in $6 \mathrm{M} \mathrm{NaOH},$ and $\mathrm{AgOH}$ is not. Explain.
When a KI solution was added to a solution of mercury(II) chloride, a precipitate [mercury(II) iodide] was formed. A student plotted the mass of the precipitate formed versus the volume of the KI solution added and obtained the graph shown here. Explain the appearance of the graph.
Barium is a toxic substance that can cause serious deterioration of the heart's function. In a barium enema procedure, a patient drinks an aqueous suspension of $20 \mathrm{~g} \mathrm{BaSO}_{4}$. If this substance were to equilibrate with the $5.0 \mathrm{~L}$ of the blood in the patient's body, how many grams of $\mathrm{BaSO}_{4}$ will dissolve in the blood? For a good estimate, we may assume that the temperature is $25^{\circ} \mathrm{C}$. Why is $\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$ not chosen for this procedure?
The $\mathrm{p} K_{\mathrm{a}}$ of phenolphthalein is $9.10 .$ Over what $\mathrm{pH}$ range does this indicator change from $95 \%$ HIn to $95 \% \mathrm{In}^{-} ?$
Look up the $K_{\mathrm{sp}}$ values for $\mathrm{BaSO}_{4}$ and $\mathrm{SrSO}_{4}$ in Table 17.2. Calculate $\left[\mathrm{Ba}^{2+}\right],\left[\mathrm{Sr}^{2+}\right]$, and $\left[\mathrm{SO}_{4}^{2-}\right]$ in a solution that is saturated with both compounds.
Solid NaI is slowly added to a solution that is $0.010 M$ in $\mathrm{Cu}^{+}$ and $0.010 \mathrm{M}$ in $\mathrm{Ag}^{+}$.(a) Which compound will begin to precipitate first?(b) Calculate $\left[\mathrm{Ag}^{+}\right]$ when CuI just begins to precipitate. (c) What percentage of $\mathrm{Ag}^{+}$ remains in solution at this point?
Radiochemical techniques are useful in estimating the solubility product of many compounds. In one experiment, $50.0 \mathrm{~mL}$ of a $0.010 \mathrm{M} \mathrm{AgNO}_{3}$ solution containing a silver isotope with a radioactivity of 74,025 counts per min per $\mathrm{mL}$ were mixed with $100 \mathrm{~mL}$ of a $0.030 \mathrm{M} \mathrm{NaIO}_{3}$ solution. The mixed solution was diluted to $500 \mathrm{~mL}$ and filtered to remove all of the $\mathrm{AgIO}_{3}$ precipitate. The remaining solution was found to have a radioactivity of 44.4 counts per min per $\mathrm{mL}$. What is the $K_{\mathrm{sp}}$ of $\mathrm{AgIO}_{3} ?$
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 -g sample of $\mathrm{MCO}_{3}$. The excess $\mathrm{HCl}$ required $5.64 \mathrm{~mL}$ of $0.1000 \mathrm{M}$ $\mathrm{NaOH}$ for neutralization. Calculate the molar mass of the carbonate and identify $\mathrm{M}$.
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. $)$
Calculate $x$, the number of molecules of water in oxalic acid hydrate, $\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},$ from the following data: $5.00 \mathrm{~g}$ of the compound is made up to exactly $250 \mathrm{~mL}$ solution and $25.0 \mathrm{~mL}$ of this solution requires $15.9 \mathrm{~mL}$ of $0.500 \mathrm{M} \mathrm{NaOH}$ solution for neutralization.
Describe how you would prepare $1 \mathrm{~L}$ of the buffer $0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ by (a) mixinga solution of $\mathrm{CH}_{3} \mathrm{COOH}$ with a solution of $\mathrm{CH}_{3} \mathrm{COONa},$ (b) reacting a solution of $\mathrm{CH}_{3} \mathrm{COOH}$ with a solution of $\mathrm{NaOH}$, and (c) reacting a solution of $\mathrm{CH}_{3} \mathrm{COONa}$ with a solution of $\mathrm{HCl}$.
What reagents would you employ to separate these pairs of ions in solution:(a) $\mathrm{Na}^{+}$ and $\mathrm{Ba}^{2+}$,(b) $\mathrm{K}^{+}$ and $\mathrm{Pb}^{2+},$ (c) $\mathrm{Zn}^{2+}$ and $\mathrm{Hg}^{2+} ?$
$\mathrm{CaSO}_{4}\left(K_{\mathrm{sp}}=2.4 \times 10^{-5}\right)$ has a larger $K_{\mathrm{sp}}$ value than that of $\mathrm{Ag}_{2} \mathrm{SO}_{4}\left(K_{\mathrm{sp}}=1.4 \times 10^{-5}\right) .$ Does it follow that $\mathrm{CaSO}_{4}$ also has greater solubility $(\mathrm{g} / \mathrm{L}) ?$
How many milliliters of $1.0 \mathrm{M} \mathrm{NaOH}$ must be added to $200 \mathrm{~mL}$ of $0.10 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}$ to make a buffer solution with a pH of $7.50 ?$
The maximum allowable concentration of $\mathrm{Pb}^{2+}$ ions in drinking water is $0.05 \mathrm{ppm}$ (that is, $0.05 \mathrm{~g}$ of $\mathrm{Pb}^{2+}$ in 1 million $g$ of water). Is this guideline exceeded if an underground water supply is at equilibrium with the mineral anglesite, $\mathrm{PbSO}_{4}\left(K_{\mathrm{sp}}=1.6 \times 10^{-8}\right) ?$
Which of these solutions has the highest $\left[\mathrm{H}^{+}\right]$ :(a) $0.10 \mathrm{M} \mathrm{HF},$(b) $0.10 \mathrm{M} \mathrm{HF}$ in $0.10 \mathrm{M} \mathrm{NaF}$, or(c) $0.10 \mathrm{M} \mathrm{HF}$ in $0.10 \mathrm{M} \mathrm{SbF}_{5}$ ? (Hint: $\mathrm{SbF}_{5}$ reacts with $\mathrm{F}^{-}$ to form the complex ion $\mathrm{SbF}_{6}^{-}$.)
Distribution curves show how the fractions of nonionized acid and its conjugate base vary as a function of $\mathrm{pH}$ of the medium. Plot distribution curves for $\mathrm{CH}_{3} \mathrm{COOH}$ and its conjugate base $\mathrm{CH}_{3} \mathrm{COO}^{-}$ in solution. Your graph should show fraction as the $y$ axis and $\mathrm{pH}$ as the $x$ axis. What are the fractions and $\mathrm{pH}$ at the point these two curves intersect?
Water containing $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ ions is called hard water and is unsuitable for some household and industrial use because these ions react with soap to form insoluble salts, or curds. One way to remove the $\mathrm{Ca}^{2+}$ ions from hard water is by adding washing soda $\left(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot 10 \mathrm{H}_{2} \mathrm{O}\right) .$ (a) The molar solubility of $\mathrm{CaCO}_{3}$ is $9.3 \times 10^{-5} M$. What is its molar solubility in a $0.050 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}$ solution? (b) Why are $\mathrm{Mg}^{2+}$ ions not removed by this procedure? (c) The $\mathrm{Mg}^{2+}$ ions are removed as $\mathrm{Mg}(\mathrm{OH})_{2}$ by adding slaked lime $\left[\mathrm{Ca}(\mathrm{OH})_{2}\right]$ to the water to produce a saturated solution. Calculate the $\mathrm{pH}$ of a saturated $\mathrm{Ca}(\mathrm{OH})_{2}$ solution. (d) What is the concentration of $\mathrm{Mg}^{2+}$ ions at this $\mathrm{pH}$ ? (e) In general, which ion $\left(\mathrm{Ca}^{2+}\right.$ or $\mathrm{Mg}^{2+}$ ) would you remove first? Why?
(a) Referring to Figure $17.6,$ describe how you would determine the $\mathrm{p} K_{\mathrm{b}}$ of the base. (b) Derive an analogous Henderson-Hasselbalch equation relating pOH to $\mathrm{p} K_{\mathrm{b}}$ of a weak base $\mathrm{B}$ and its conjugate acid $\mathrm{HB}^{+}$. Sketch a titration curve showing the variation of the $\mathrm{pOH}$ of the base solution versus the volume of a strong acid added from a buret. Describe how you would determine the $\mathrm{p} K_{\mathrm{b}}$ from this curve.
A $25.0-\mathrm{mL}$ of $0.20 \mathrm{M}$ HF solution is titrated with a $0.20 \mathrm{M} \mathrm{NaOH}$ solution. Calculate the volume of $\mathrm{NaOH}$ solution added when the $\mathrm{pH}$ of the solution is (a) $2.85,$ (b) $3.15,$ (c) $11.89 .$ Ignore salt hydrolysis.
One of the most commonly used antibiotics is penicillin G (benzylpenicillinic acid), which has the following structure: It is a weak monoprotic acid:$$\mathrm{HP} \rightleftharpoons \mathrm{H}^{+}+\mathrm{P}^{-} \quad K_{\mathrm{a}}=1.64 \times 10^{-3}$$in which HP denotes the parent acid and $\mathrm{P}^{-}$ the conjugate base. Penicillin $\mathrm{G}$ is produced by growing molds in fermentation tanks at $25^{\circ} \mathrm{C}$ and a pH range of 4.5 to $5.0 .$ The crude form of this antibiotic is obtained by extracting the fermentation broth with an organic solvent in which the acid is soluble. (a) Identify the acidic hydrogen atom. (b) In one stage of purification, the organic extract of the crude penicillin $\mathrm{G}$ is treated with a buffer solution at $\mathrm{pH}=6.50$. What is the ratio of the conjugate base of penicillin $\mathrm{G}$ to the acid at this pH? Would you expect the conjugate base to be more soluble in water than the acid? (c) Penicillin G is not suitable for oral administration, but the sodium salt (NaP) is because it is soluble. Calculate the $\mathrm{pH}$ of a $0.12 \mathrm{M}$ NaP solution formed when a tablet containing the salt is dissolved in a glass of water.
Amino acids are the building blocks of proteins. These compounds contain at least one amino group and one carboxyl group. Consider glycine, whose structure is shown in Figure $11.18 .$ Depending on the $\mathrm{pH}$ of the solution, glycine can exist in one of three possible forms: Predict the predominant form of glycine at $\mathrm{pH} 1.0$ $7.0,$ and $12.0 .$ The $\mathrm{p} K_{\mathrm{a}}$ of the carboxyl group is 2.3 and that of the ammonium group is 9.6. [Hint: Use Equation (17.3).]
One way to distinguish a buffer solution with an acid solution is by dilution. (a) Consider a buffer solution made of $0.500 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ and $0.500 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COONa}$. Calculate its $\mathrm{pH}$ and the $\mathrm{pH}$ after it has been diluted 10 -fold. (b) Compare the result in(a) with the pHs of a $0.500 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ solution before and after it has been diluted 10 -fold.
A sample of $0.96 \mathrm{~L}$ of $\mathrm{HCl}$ at $372 \mathrm{mmHg}$ and $22^{\circ} \mathrm{C}$ is bubbled into $0.034 \mathrm{~L}$ of $0.57 \mathrm{M} \mathrm{NH}_{3}$. What is the $\mathrm{pH}$ of the resulting solution? Assume the volume of solution remains constant and that the HCl is totally dissolved in the solution.
Histidine is one of the 20 amino acids found in proteins. Shown here is a fully protonated histidine molecule where the numbers denote the $\mathrm{p} K_{\mathrm{a}}$ values of the acidic groups. (a) Show stepwise ionization of histidine in solution. (Hint: The $\mathrm{H}^{+}$ ion will first come off from the strongest acid group followed by the next strongest acid group and so on.)(b) A dipolar ion is one in which the species has an equal number of positive and negative charges. Identify the dipolar ion in (a).(c) The pH at which the dipolar ion predominates is called the isoelectric point, denoted by pI. The
A 1.0-L saturated silver carbonate solution at $5^{\circ} \mathrm{C}$ is treated with enough hydrochloric acid to decompose the compound. The carbon dioxide generated is collected in a $19-\mathrm{mL}$ vial and exerts a pressure of $114 \mathrm{mmHg}$ at $25^{\circ} \mathrm{C}$. What is the $K_{\mathrm{sp}}$ of $\mathrm{Ag}_{2} \mathrm{CO}_{3}$ at $5^{\circ} \mathrm{C} ?$
The titration curve shown here represents the titration of a weak diprotic acid $\left(\mathrm{H}_{2} \mathrm{~A}\right)$ versus $\mathrm{NaOH}$. (a) Label the major species present at the marked points. (b) Estimate the $\mathrm{p} K_{\mathrm{a}_{1}}$ and $\mathrm{pK}_{\mathrm{a}_{2}}$ values of the acid.