Ionic Equilibria in Aqueous Systems

Amino acids [general formula  ${\mathbf{\text{NH}}}_{\mathbf{\text{2}}}\mathbf{\text{CH(R)COOH]}}$can be considered polypro tic acids. In many cases, the  R group contains additional amine and carboxyl groups.

(a) Can an amino acid dissolved in pure water have a protonated $\mathbf{\text{COOH}}$ group and an unprotonated ${\mathbf{\text{NH}}}_{\mathbf{\text{2}}}$group  

$\mathbf{(}{\mathbf{\text{K}}}_{\mathbf{\text{X}}}{\mathbf{\text{of COOH group =4.47×10}}}^{\mathbf{\text{-3}}}{\mathbf{\text{;K}}}_{\mathbf{\text{b}}}{\mathbf{\text{ of NH}}}_{\mathbf{\text{2}}}{\mathbf{\text{ group =6.03×10}}}^{\mathbf{\text{-3}}}\mathbf{\text{y?}}$

Use glycine, ${\mathbf{\text{NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{COOH}}$ , to explain why.

(b) Calculate  ${\mathbf{\text{[}}}^{\mathbf{\text{+}}}{\mathbf{\text{NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{COO}}}^{\mathbf{\text{-}}}{\mathbf{\text{y}}}^{\mathbf{\text{+}}}{\mathbf{\text{NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}\mathbf{\text{COOH] at pH 5.5.}}$

(c) The R group of lysine is ${\mathbf{\text{-CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{NH}}}_{\mathbf{\text{2}}}{\mathbf{\text{ (p K}}}_{\mathbf{\text{b}}}\mathbf{\text{= 3.47)}}$Draw the structure of lysine at  .$\mathbf{\text{pH}}$ physiological  $\mathbf{\text{pH (-7), and pH 13.}}$

(d) The$\mathbf{R}$ group of glutamic acid ${\mathbf{\text{-CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}\mathbf{\text{COOH}}\mathbf{(}{\mathbf{\text{pK}}}_{\mathbf{\text{a}}}\mathbf{\text{=}}\mathbf{\text{ 4.07).}}$of the forms of glutamic acid that are shown below, which predominates at  ,$\mathbf{\text{(1)}}$$\mathbf{\text{pH1}}$(2) $\mathbf{\text{physaiological pHH(-7),}}$

 and (3) $\mathbf{\text{pH13?}}$

Tris (hydroxymethyl)aminomethane [${\left({\text{HOCH}}_{\text{2}}\right)}_{\mathbf{\text{3}}}{\mathbf{\text{CNH}}}_{\mathbf{\text{2}}}\mathbf{\text{,}}$ known as TRIS] is a weak base used in biochemical experiments to make buffer solutions in the $\mathbf{pH}$ range of 7 to 9. A certain TRIS buffer has a  $\mathbf{pH}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{8}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{25}\mathbf{ }\mathbf{°}\mathbf{C}$ and a $\mathbf{pH}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{7}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{37}\mathbf{ }\mathbf{°}\mathbf{C}$. Why does the pH pH change with temperature?

Cadmium ion in solution is analyzed by precipitation as the sulfide, a yellow compound used as a pigment in everything from artists' oil paints to glass and rubber. Calculate the molar solubility of cadmium sulfide at $\mathbf{25}\mathbf{ }\mathbf{°}\mathbf{C}$.

Phosphate systems form essential buffers in organisms. Calculate the pH of a buffer made by dissolving  $\mathbf{0}\mathbf{.}\mathbf{80}\mathbf{ }\mathbf{mol}\mathbf{of}\mathbf{NaOH}\mathbf{in}\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{ }\mathbf{Lof}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{M}\mathbf{ }\mathbf{ }{\mathbf{H}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}\mathbf{.}$

It is possible to detect  NH₃ gas over ${\mathbf{\text{10}}}^{\mathbf{\text{ - 2}}}{\mathbf{\text{ M NH}}}_{\mathbf{\text{3}}}$. To what must be raised to form detectable ${\mathbf{\text{NH}}}_{\mathbf{\text{3}}}$ ?

Manganese (II) sulfide is one of the compounds found in the nodules on the ocean floor that may eventually be a primary source of many transition metals. The solubility of $\mathbf{MnS}\mathbf{is}\mathbf{4}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{100}\mathbf{ }\mathbf{mL}$ solution. Estimate the K_sp of  $\mathbf{\text{MnS}}$.

The typical pH of blood is $\mathbf{\text{7.40 }}\mathbf{\pm }\mathbf{\text{ 0.05,}}$ which is influenced by the ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{CO}}}_{\mathbf{\text{3}}}\mathbf{\text{/HC}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{ - }}}$ buffer system in part.

(a) Given that the K_a value for carbonic acid is  $\mathbf{25}\mathbf{ }\mathbf{°}\mathbf{C}$ what applies to blood ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{CO}}}_{\mathbf{\text{3}}}\mathbf{\text{/HC}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{ - }}}$ In normal blood, what is the ratio?

(b) Acidosis is a condition in which the blood is overly acidic. What is the  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{CO}}}_{\mathbf{\text{3}}}\mathbf{\text{/HC}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{ - }}}$ ratio in a patient with a  $\mathbf{\text{pH is 7.20}}$  in their blood?

A bioengineer preparing cells for cloning bathes a small piece of rat epithelial tissue in a TRIS buffer (see Problem $\mathbf{19}\mathbf{.}\mathbf{108}$ ). The buffer is made by dissolving $\mathbf{43}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{g}$ of TRIS $\left({\text{pK}}_{\text{3}}\text{ = 5.91}\right)$ in enough  $\mathbf{0}.\mathbf{095}\mathbf{M}\mathbf{HCl}$ to make $\mathbf{\text{1.00 L}}$ of solution. What is the molarity of TRIS and the pH of the buffer?

Sketch a qualitative curve for the titration of ethylenediamine

${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{NCH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{NH}}}_{\mathbf{\text{2}}}\mathbf{\text{, with 0.1 M HCl.}}$ 

An environmental technician collects a sample of rainwater. Back in the lab, her  meter isn't working, so she uses indicator solutions to estimate the . A piece of litmus paper turns red, indicating acidity, so she divides the sample into thirds and obtains the following results: thymol blue turns yellow; bromophenol blue turns green; and methyl red turns red. Estimate the  of the rainwater.

$\mathbf{A}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{050}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{S}$ solution contains  $\mathbf{0}\mathbf{.}\mathbf{15}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{NiCl}}_{\mathbf{2}}$ and $\mathbf{0}\mathbf{.}\mathbf{35}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{Hg}{\left({\mathrm{NO}}_3\right)}_{\mathbf{2}}$. What data-custom-editor="chemistry" $\mathbf{pH}$ is required to precipitate the maximum amount of $\mathbf{HgS}$ but none of the $\mathbf{Ni}\mathbf{ }\mathbf{S}$? (See Appendix C.)

Quantitative analysis of  ${\mathbf{Cl}}^{\mathbf{-}}$ion is often performed by a titration with silver nitrate, using sodium chromate as an indicator. As standardized ${\mathbf{AgNO}}_{\mathbf{3}}$is added, both white $\mathbf{AgCl}$ and red ${\mathbf{Ag}}_{\mathbf{2}}{\mathbf{CrO}}_{\mathbf{4}}$ precipitate, but so long as some ${\mathbf{Cl}}^{\mathbf{-}}$remains, the ${\mathbf{Ag}}_{\mathbf{2}}{\mathbf{CrO}}_{\mathbf{4}}$redissolves as the mixture is stirred. When the red color is permanent, the equivalence point has been reached.

(a) Calculate the equilibrium constant for the reaction

data-custom-editor="chemistry" $\mathbf{2}\mathbf{AgCl}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{Cr}{{\mathbf{O}}_{\mathbf{4}}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{Ag}}_{\mathbf{2}}{\mathbf{CrO}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{C}{\mathbf{l}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$

(b) Explain why the silver chromate redissolves.

(c) If $\mathbf{25}\mathbf{.}\mathbf{00}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}$ of $\mathbf{0}\mathbf{.}\mathbf{1000}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{NaCl}$is mixed with $\mathbf{25}\mathbf{.}\mathbf{00}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}$of $\mathbf{0}\mathbf{.}\mathbf{1000}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{AgNO}}_{\mathbf{3}}$, what is the concentration of ${\mathbf{Ag}}^{\mathbf{+}}$remaining in solution? Is this sufficient to precipitate any silver chromate?

An eco-botanist separates the components of a tropical bark extract by chromatography. She discovers a large proportion of quinidine, a dextrorotatory isomer of quinine used for control of arrhythmic heartbeat. Quinidine has two basic nitrogen’s $(K_{b1}=4.0\times {10}^{-6}$and ${\mathbf{K}}_{\mathbf{b}\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}$). To measure the concentration, she carries out a titration. Because of the low solubility of quinidine, she first protonates both nitrogen’s with excess  and titrates the acidified solution with standardized base. A $\mathbf{33}\mathbf{.}\mathbf{85}$-mg sample of quinidine $\mathbf{(}\mathbf{M}\mathbf{=}\mathbf{324}\mathbf{.}\mathbf{41}\mathbf{g}\mathbf{/}\mathbf{mol}\mathbf{)}$is acidified with $\mathbf{6}\mathbf{.}\mathbf{55}\mathbf{mL}$ of $\mathbf{0}\mathbf{.}\mathbf{150}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{HCl}$.

(a) How many milliliters of $\mathbf{0}\mathbf{.}\mathbf{0133}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{NaOH}$are needed to titrate the excess $\mathbf{HCl}$?

(b) How many additional milliliters of titrant are needed to reach the first equivalence point of quinidine dihydrochloride?

(c) What is the  at the first equivalence point?

 student wants to dissolve the maximum amount of ${\mathbf{\text{CaF}}}_{\mathbf{2}}$  $\mathbf{\left(}{\mathbf{\text{K}}}_{\mathbf{\text{sp}}}{\mathbf{\text{=3.2×10}}}^{\mathbf{\text{-11}}}\mathbf{\right)}$ to make$\mathbf{\text{1 L}}$  of aqueous solution.

(a) Into which of the following solvents should she dissolve the salt?

 $\begin{array}{ll}\mathbf{\text{ (I) Pure water }}& \mathbf{\text{ (II) }}\mathbf{0}\mathbf{.01}\mathbf{M}\mathbf{\text{HF}}\end{array}$

(III) $\mathbf{0}\mathbf{.01}\mathbf{\text{\hspace{0.17em}M\hspace{0.17em}\hspace{0.17em}NaOH}}$  (IV)$\mathbf{0}\mathbf{.01}\mathbf{\text{\hspace{0.17em}M\hspace{0.17em}\hspace{0.17em}HCl}}$  (V)  $\mathbf{0}\mathbf{.01}\mathit{M}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}Ca}}{\mathbf{\left(}\mathbf{\text{OH}}\mathbf{\right)}}_{\mathbf{2}}$

(b) Which would dissolve the least amount of salt?

Environmental engineers use alkalinity as a measure of the capacity of carbonate buffering systems in water samples:

Alkalinity  $\mathbf{\text{(mol/L)=}}\mathbf{\left[}{\mathbf{\text{HCO}}}_{\mathbf{\text{3}}}^{\mathbf{\text{-}}}\mathbf{\right]}\mathbf{\text{+2}}\mathbf{\left[}{{\mathbf{\text{CO}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{2-}}}\mathbf{\right]}\mathbf{\text{+}}\mathbf{\left[}{\mathbf{\text{OH}}}^{\mathbf{\text{-}}}\mathbf{\right]}\mathbf{\text{-}}\mathbf{\left[}{\mathbf{\text{H}}}^{\mathbf{\text{+}}}\mathbf{\right]}$

Find the alkalinity of a water sample that has a   $\mathbf{\text{pH}}$of  , ${{\mathbf{\text{26.0 mg/L CO}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{2-}}}$$\mathbf{\text{9.5,}}$and.${{\mathbf{\text{65.0 mg/L HCO}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{-}}}$

Human blood contains one buffer system based on phosphate species and one on carbonate species. Assuming that blood has a normal  of  , what are the principal phosphate and carbonate species present? What is the ratio of the two phosphate species? (In the presence of the dissolved ions and other species in blood,${\text{K}}_{\text{a1}}$ of ${\mathbf{\text{H}}}_{\mathbf{\text{3}}}{\mathbf{\text{PO}}}_{\mathbf{\text{4}}}{\mathbf{\text{=1.3×10}}}^{\mathbf{\text{-2}}}{\mathbf{\text{, K}}}_{\mathbf{\text{a2}}}{\mathbf{\text{=2.3×10}}}^{\mathbf{\text{-7}}}\mathbf{\text{,}}$and ${\mathbf{\text{K}}}_{\mathbf{\text{a3}}}{\mathbf{\text{=6×10}}}^{\mathbf{\text{-12}}}{\mathbf{\text{, K}}}_{\mathbf{\text{al}}}$of  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{CO}}}_{\mathbf{\text{3}}}{\mathbf{\text{=8×10}}}^{\mathbf{\text{-7}}}$ and ${\mathbf{\text{K}}}_{\mathbf{\text{a2}}}{\mathbf{\text{=1.6×10}}}^{\mathbf{\text{-10}}}\mathbf{\text{.}}\mathbf{)}$

Litmus is an organic dye extracted from lichens. It is red below$\mathbf{\text{pH 4.5}}$ and blue above $\mathbf{\text{pH 8.3}}$. One drop of either$\mathbf{\text{0.1 M HCl ( pH1}}$) or a$\mathbf{\text{pH3}}$ buffer changes blue litmus paper to red, but a drop of $\mathbf{\text{0.001 M HCl}}$(also$\mathbf{\text{pH3}}$) does not. Explain.

Instrumental acid-base titrations use a pH  meter to monitor the changes in pH  and volume. The equivalence point is found from the volume at which the curve has the steepest slope. 

(a) Use Figure 19.7  to calculate the slope $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}$  for all pairs of adjacent points and to calculate the average volume ${\mathbf{\text{(V}}}_{\mathbf{\text{avg}}}\mathbf{\text{)}}$  for each interval.

(b)Plot $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}$ vs. ${\mathbf{\text{V}}}_{\mathbf{\text{avg}}}$  to find the steepest slope, and thus the volume at the equivalence point. (For example, the first pair of points gives $\mathbf{\Delta pH}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{22}\mathbf{,}\mathbf{\Delta V}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{mL}$; hence, $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{022}{\mathbf{mL}}^{\mathbf{-}\mathbf{1}}$ , and ${\mathbf{\text{V}}}_{\mathbf{\text{avg}}}\mathbf{\text{ = 5.00 mL}}$).

A  $\mathbf{500}\mathbf{ }\mathbf{ml}$ solution consists of  $\mathbf{0}\mathbf{.}\mathbf{050}\mathbf{ }\mathbf{mol}$ of solid NaOH  and  $\mathbf{0}\mathbf{.}\mathbf{130}\mathbf{ }\mathbf{mol}$ of hypochlorous acid $(\mathrm{HClO};K_a=3.0\times {10}^{-8})$  dissolved in water.

(a) Aside from water, what is the concentration of each species that is present?

(b) What is the  pH of the solution?

(c) What is the  pH after adding $\mathbf{0}\mathbf{.}\mathbf{005}\mathbf{ }\mathbf{mol}\mathbf{.}$ of  HCl to the flask?

Calcium ion present in water supplies is easily precipitated as calcite $\left({\text{CaCO}}_{\text{3}}\right)$:

 ${\mathbf{\text{Ca}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq) + C}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{2 - }}}\mathbf{\text{(aq)}}\mathbf{\rightleftharpoons }{\mathbf{\text{CaCO}}}_{\mathbf{\text{3}}}\mathbf{\text{(s)}}$. Because the K_sp  decreases with temperature, heating hard water forms a calcite "scale," which clogs pipes and water heaters. Find the solubility of calcite in water

(a) At $\mathbf{10}\mathbf{°}\mathbf{C}\left(K_{\mathrm{sp}}=4.4\times {10}^{-9}\right)$  and 

(b) At  $\mathbf{30}\mathbf{°}\mathbf{C}\left(K_{\mathrm{sp}}=3.1\times {10}^{-9}\right)$.

Muscle physiologists study the accumulation of lactic acid $\left[{\text{CH}}_3\text{CH}\left(\text{OH}\right)\text{COOH}\right]$ during exercise. Food chemists study its occurrence in sour milk, beer, wine, and fruit. Industrial microbiologists study its formation by various bacterial species from carbohydrates. A biochemist prepares a lactic acid-lactate buffer by mixing  $\mathbf{225}\mathbf{ }\mathbf{ml}$ of $\mathbf{0}\mathbf{.}\mathbf{85}\mathbf{ }\mathbf{M}$  lactic acid  $\left(K_a=1.38\times {10}^{-4}\right)$ with $\mathbf{435}\mathbf{ }\mathbf{mL}$ of  $\mathbf{0}\mathbf{.}\mathbf{68}\mathbf{ }\mathbf{M}$ sodium lactate. What is the buffer  ?

The Henderson-Hasselbalch equation gives a relationship for obtaining the pH  of a buffer solution consisting of HA  and  A. Derive an analogous relationship for obtaining the pOH of a buffer solution consisting of B and BH⁺?

The acid-base indicator ethyl orange turns from red to yellow over the pH  range 3.4  to 4.8 . Estimate Ka for ethyl orange.

Tooth enamel consists of hydroxyapatite, ${\mathbf{Ca}}_{\mathbf{5}}{\left({\mathrm{PO}}_4\right)}_{\mathbf{3}}\mathbf{OH}$ ${\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{37}}$. Fluoride ion added to drinking water reacts with   ${\mathbf{\text{Ca}}}_{\mathbf{\text{5}}}{\left({\text{PO}}_{\text{4}}\right)}_{\mathbf{\text{3}}}\mathbf{\text{OH}}$ to form the more tooth decay–resistant fluoroapatite Fluoridated water has dramatically decreased cavities among children. Calculate the solubility of ${\mathbf{\text{Ca}}}_{\mathbf{\text{5}}}{\left({\text{PO}}_{\text{4}}\right)}_{\mathbf{\text{3}}}{\mathbf{\text{OH and of Ca}}}_{\mathbf{\text{5}}}{\left({\text{PO}}_{\text{4}}\right)}_{\mathbf{\text{3}}}\mathbf{\text{F}}$  in water.

Does any solid ${\mathbf{\text{Ba(IO}}}_{\mathbf{\text{3}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$ form when  $\mathbf{7}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{mg}$ of  ${\mathbf{BaCL}}_{\mathbf{2}}$ is dissolved in $\mathbf{500}\mathbf{ }\mathbf{ml}$ of ${\mathbf{\text{0.023 M NaIO}}}_{\mathbf{\text{3}}}$ ?

Calculate the molar solubility of ${\mathbf{Hg}}_{\mathbf{2}}{\mathbf{C}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{4}}\mathbf{ }\mathbf{ }(K_{\mathrm{sp}}=1.75\times {10}^{-13})$ in  $\mathbf{0}\mathbf{.}\mathbf{13}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{Hg}{\left({\mathrm{NO}}_3\right)}_{\mathbf{2}}$.

1. The solubility of  $\text{Ag(I)}$ in aqueous solutions containing different concentrations of${\mathbf{\text{Cl}}}^{\mathbf{\text{ - }}}$is based on the following equilibria:

${\text{Ag}}^{\text{ + }}{\text{(aq) + Cl}}^{\text{ - }}\text{(aq)}\to \text{AgCl(s)} {\text{K}}_{\text{sp}}{\text{=1.8×10}}^{-10}$

${\text{Ag}}^{\text{ + }}{\text{(aq) + 2Cl}}^{\text{ - }}\text{(aq)}\rightleftharpoons {\text{AgCl}}_{\text{2}}^{\text{ - }}\text{(aq)} {\text{K=1.8×10}}^5$

When solid $\text{AgCl}$is shaken with a solution containing ${\text{Cl}}^{\text{ - }}\text{,Ag(I)}$is present as both ${\text{Ag}}^{\text{ + }}$and ${\text{AgCl}}_{\text{2}}^{\text{ - }}$. The solubility of $\text{AgCl}$ is the sum of the concentrations of ${\text{Ag}}^{\text{ + }}$and ${\text{AgCl}}_{\text{2}}^{\text{ - }}$.

(a) Show that $\left[{\text{Ag}}^{\text{ + }}\right]$in solution is given by

$\left[{\text{Ag}}^{\text{ + }}\right]{\text{ = 1.8×10}}^{-10}\text{/}\left[{\text{Cl}}^{\text{ - }}\right]$

and that $\left[{\text{AgCl}}_{\text{2}}^{\text{ - }}\right]$in solution is given by

$\left[{\text{AgCl}}_{\text{2}}^{\text{ - }}\right]\text{ = }\left({\text{3.2×10}}^{-5}\right)\left(\left[{\text{Cl}}^{\text{ - }}\right]\right)$

 (b) Find the $\left[{\text{Cl}}^{\text{ - }}\right]$at which $\left[{\text{Ag}}^{\text{ + }}\right]\text{ = }\left[\text{AgC}{{\text{l}}_{\text{2}}}^{\text{ - }}\right]$

(c) Explain the shape of a plot of $\text{AgCl}$ solubility vs. $\left[{\text{Cl}}^{\text{ - }}\right]$.

(d) Find the solubility of $\text{AgCl}$ at the $\left[{\text{Cl}}^{\text{ - }}\right]$ of part (b), which is the minimum solubility of $\text{AgCl}$in the presence of ${\text{Cl}}^{\text{ - }}$.

EDTA binds metal ions to form complex ions (see Problem ), so it is used to determine the concentrations of metal ions in solution: 

${\text{M}}^{\text{n + }}{\text{(aq) + EDTA}}^{\text{4 - }}\text{(aq)}\to {\text{MEDTA}}^{\text{n - 4}}\text{(aq)}$

A $\text{50.0 - mL}$ sample of ${\text{0.048 M Co}}^{\text{2 + }}$is titrated with ${\text{0.050 M EDTA}}^{\text{4 - }}$.Find ${\text{[Co}}^{\text{2 + }}\text{]}$ and ${\text{[EDTA}}^{\text{4 - }}\text{]}$ after.

1. $\text{25.0 mL}$ and
2. $\text{75.0 mL}$of ${\text{EDTA}}^{\text{4 - }}$are added (${\text{log K}}_{\text{f}}$ of ${\text{CoEDTA}}^{\text{2 - }}\text{ = 16.31}$).
   

Some kidney stones form by the precipitation of calcium oxalate monohydrate $\left({\mathrm{CaC}}_2{O}_4\times H_{2}O,K_{\mathrm{sp}}=2.3\times {10}^{-9}\right)$. The  of urine varies from $\mathbf{5}\mathbf{.}\mathbf{5}$ to $\mathbf{7}\mathbf{.}\mathbf{0}$, and the average $\left[{\mathrm{Ca}}^{2+}\right]$in urine is $\mathbf{2}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{M}$.

(a) If the [oxalic acid] in urine is $\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{13}}\mathbf{ }\mathbf{M}$, will kidney stones form at  $\mathbf{pH}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{5}$?

(b) at $\mathbf{pH}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{0}$?

(c) Vegetarians have a urine  above $\mathbf{7}$. Are they more or less likely to form kidney stones?

A biochemist needs a medium for acid-producing bacteria. The pH of the medium must not change by more than $\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{pH}$ units for every $\mathbf{0}\mathbf{.}\mathbf{0010}\mathbf{mol}$ of  ${\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}$generated by the organisms per litre of medium. A buffer consisting of $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{HA}$ and $\mathbf{0}\mathbf{.}\mathbf{10}{\mathbf{MA}}^{\mathbf{-}}$ is included in the medium to control its $\mathbf{pH}$. What volume of this buffer must be included in $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{L}$ of medium?

A $\mathbf{35}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{mL}$ solution of  $\mathbf{0}\mathbf{.}\mathbf{2500}\mathbf{\text{M }}\mathbf{HF}$is titrated with a standardized  $\mathbf{0}\mathbf{.}\mathbf{1532}\mathbf{ }\mathbf{M}$ solution of   $\mathbf{\text{NaoH}}$at ${\mathbf{25}}^{\mathbf{\circ }}\mathit{C}$. 

(a) What is the $\mathbf{pH}$ of the $\mathbf{HF}$ solution before titrant is added? 

(b) How many millilitres of titrant are required to reach the equivalence point? 

(c) What is the  $\mathbf{pH}$ at $\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{mL}$  before the equivalence point? 

(d) What is the $\mathbf{pH}$  at the equivalence point? 

(e) What is the  $\mathbf{pH}$ at $\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{ }\mathbf{mL}$  after the equivalence point?

Because of the toxicity of mercury compounds, mercury $\mathbf{\text{(I)}}$chloride is used in antibacterial salves. The mercury $\mathbf{\text{(I)}}$ ion  ${\mathbf{(}\mathbf{Hg}}_{\mathbf{2}}^{\mathbf{2}\mathbf{+}}\mathbf{)}$ consists of two bounds  ions. 

(a) What is the empirical formula of mercury $\mathbf{\text{(I)}}$chloride?

(b) Calculate ${\mathbf{(}\mathbf{Hg}}_{\mathbf{2}}^{\mathbf{2}\mathbf{+}}\mathbf{)}$ in a saturated solution of mercury $\mathbf{(}\mathbf{I}\mathbf{)}$chloride $\mathbf{(}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{18}}\mathbf{)}$. 

(c) A seawater sample contains  $\mathbf{0}\mathbf{.}\mathbf{20}\mathbf{ }\mathbf{\text{lb}}$of $\mathbf{\text{NaCL}}$ per gallon. Find ${\mathbf{[}\mathbf{Hg}}_{\mathbf{2}}^{\mathbf{2}\mathbf{+}}\mathbf{]}$ if the seawater is saturated with mercury $\mathbf{\text{(I)}}$chloride. 

(d) How many grams of mercury $\mathbf{\text{(I)}}$chloride is needed to saturate $\mathbf{4900}\mathbf{ }{\mathbf{km}}^{\mathbf{3}}$of pure water (the volume of Lake Michigan)? 

(e) How many grams of mercury $\mathbf{\text{(I)}}$chloride is needed to saturate $\mathbf{4900}\mathbf{ }{\mathbf{km}}^{\mathbf{3}}$ of seawater?

A lake that has a surface area of  $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{acres}\mathbf{(}\mathbf{1}\mathbf{ }\mathbf{acre}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{840}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }{\mathbf{yd}}^{\mathbf{2}}\mathbf{)}$ receives $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{in}\mathbf{.}$ of rain of $\mathbf{pH}\mathbf{ }\mathbf{4}\mathbf{.}\mathbf{20}$. (Assume that the acidity of the rain is due to a strong, monoprotic acid.) 

(a) How many moles of ${\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}$ are in the rain falling on the lake? 

(b) If the lake is unbuffered $\mathbf{(}\mathbf{pH}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{00}\mathbf{)}$and its average depth is $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{ft}$ before the rain, find the $\mathbf{\text{pH}}$ after the rain has been mixed with lake water. (Ignore runoff from the surrounding land.) 

(c) If the lake contains hydrogen carbonate ions ${\mathbf{(}\mathbf{HCO}}_{\mathbf{3}}^{\mathbf{-}}\mathbf{)}$, what mass of ${\mathbf{(}\mathbf{HCO}}_{\mathbf{3}}^{\mathbf{-}}\mathbf{)}$would neutralize the acid in the rain?

A $\mathbf{35}\mathbf{ }\mathbf{\text{mL}}$ solution of  $\mathbf{0}\mathbf{.}\mathbf{075}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{CaCl}}_{\mathbf{2}}$is mixed with $\mathbf{25}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{mL}$ of $\mathbf{0}\mathbf{.}\mathbf{090}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{BaCl}}_{\mathbf{2}}$. 

(a) If aqueous $\mathbf{KF}$ is added, which fluoride precipitates first? 

(b) Describe how the metal ions can be separated using $\mathbf{KF}$ to form the fluorides.

(c) Calculate the fluoride ion concentration that will accomplish the separation.

Even before the industrial age, rainwater was slightly acidic due to dissolved ${\mathbf{\text{CO}}}_{\mathbf{2}}$. Use the following data to calculate $\mathbf{\text{pH}}$ of unpolluted rainwater at ${\mathbf{\text{25}}}^{\mathbf{\circ }}\mathbf{\text{C}}\mathbf{:}\mathbf{vol}\mathbf{\%}$in air of ${\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{033}\mathbf{ }\mathbf{vol}\mathbf{\%}$; solubility of ${\mathbf{\text{CO}}}_{\mathbf{2}}$ in pure water at ${\mathbf{\text{25}}}^{\mathbf{\circ }}\mathbf{\text{C}}$and $\mathbf{1}\mathbf{atm}\mathbf{=}\mathbf{88}\mathbf{ }\mathbf{mL}\mathbf{ }{\mathbf{CO}}_{\mathbf{2}}\mathbf{/}\mathbf{100}\mathbf{ }\mathbf{mL}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{;}\mathbf{ }{\mathbf{K}}_{\mathbf{a}\mathbf{1}}$ of ${\mathbf{H}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}$.

Seawater at the surface has a $\mathbf{\text{pH}}$ of about $\mathbf{\text{85}}$.

(a) Which of the following species has the highest concentration at this $\mathbf{pH}\mathbf{:}{\mathbf{H}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\mathbf{;}\mathbf{HC}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{-}}\mathbf{;}\mathbf{C}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}$ ? Explain.

(b) What are the concentration ratios $\left[C{O_3}^{2-}\right]\mathbf{/}\left[\mathrm{HC}{O_3}^{-}\right]$ and data-custom-editor="chemistry" $\left[\mathrm{HC}{O_3}^{-}\right]\mathbf{/}\left[H_2{\mathrm{CO}}_3\right]$ at this $\mathbf{\text{pH}}$?

(c) In the deep sea, light levels are low, and the $\mathbf{\text{pH}}$ is around $\mathbf{\text{7.5}}$. Suggest a reason for the lower $\mathbf{\text{pH}}$ at the greater ocean depth. (Hint: Consider the presence or absence of plant and animal life, and the effects on carbon dioxide concentrations.)

Ethylenediaminetetraacetic acid (abbreviated ${\mathbf{H}}_{\mathbf{4}}\mathbf{EDTA}$) is a tetraprotic acid. Its salts are used to treat toxic metal poisoning by forming soluble complex ions that are then excreted. Because ${\mathbf{EDTA}}^{\mathbf{4}\mathbf{-}}$also binds essential calcium ions, it is often administered as the calcium disodium salt. For example, when ${\mathbf{Na}}_{\mathbf{2}}\mathbf{Ca}$ (EDTA) is given to a patient ${\mathbf{\left[}\mathbf{Ca}\mathbf{\right(}\mathbf{EDTA}\mathbf{\left)}\mathbf{\right]}}^{\mathbf{2}\mathbf{-}}$, the  ions react with circulating  ions and the metal ions are exchanged:

$\begin{array}{l}{\mathbf{\left[}\mathbf{Ca}\mathbf{\right(}\mathbf{EDTA}\mathbf{\left)}\mathbf{\right]}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{P}{\mathbf{b}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\\ {\mathbf{\left[}\mathbf{Pb}\mathbf{\right(}\mathbf{EDTA}\mathbf{\left)}\mathbf{\right]}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{a}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{ }{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\end{array}$

A child has a dangerous blood lead level of $\mathbf{120}\mathbf{\mu g}\mathbf{/}\mathbf{100}\mathbf{mL}$. If the child is administered $\mathbf{100}\mathbf{ }\mathbf{mL}$ of $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{M}\mathbf{ }{\mathbf{NaNa}}_{\mathbf{2}}$ (EDTA), assuming the exchange reaction and excretion process are  $\mathbf{100}\mathbf{\%}$efficient, what is the final concentration of ${\mathbf{Pb}}^{\mathbf{2}\mathbf{+}}$in  $\mathbf{\mu g}\mathbf{/}\mathbf{100}\mathbf{mL}$ blood? (Total blood volume is $\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{L}$.)

Buffers that are based on 3-morpholinopropanesulfonic acid (MOPS) are often used in RNA analysis. The useful pH range of a MOPS buffer is $\mathbf{6}\mathbf{.}\mathbf{5}$ to $\mathbf{7}\mathbf{.}\mathbf{9}$. Estimate the ${\mathbf{K}}_{\mathbf{a}}$of MOPS.

 $\mathbf{\text{NaCl}}$is purified by adding $\mathbf{\text{HCl}}$ to a saturated solution of $\mathbf{NaCl}\mathbf{(}\mathbf{317}\mathbf{g}\mathbf{/}\mathbf{L}\mathbf{)}$. When $\mathbf{28}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{mL}$of $\mathbf{8}\mathbf{.}\mathbf{65}\mathbf{ }\mathbf{M}\mathbf{ }\mathbf{HCl}$ is added to $\mathbf{0}\mathbf{.}\mathbf{100}\mathbf{\text{ L}}$ of saturated solution, what mass (g) of pure $\mathbf{NaCl}$ precipitates?

Scenes A to D represent tiny portions of  $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{\text{M}}$ aqueous solutions of a weak acid HA (red and blue; ${\mathbf{K}}_{\mathbf{a}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}$), its conjugate base  ${\mathbf{A}}^{\mathbf{-}}$(red), or a mixture of the two (only these species are shown):

(a) Which scene(s) show(s) a buffer?

(b) What is the $\mathbf{pH}$ of each solution?

(c) Arrange the scenes in sequence, assuming that they represent stages in a weak acid-strong base titration.

(d) Which scene represents the titration at its equivalence point?

Scenes A to C represent aqueous solutions of the slightly soluble salt MZ (only the ions of this salt are shown):

$\mathbf{MZ}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{M}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{Z}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$

 (a) Which scene represents the solution just after solid MZ is stirred thoroughly in distilled water?

(b) If each sphere represents $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{M}$ of ions, what is the ${\mathbf{K}}_{\mathbf{sp}}$ of MZ?

(c) Which scene represents the solution after ${\mathbf{Na}}_{\mathbf{2}}\mathbf{Z}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$is added?

(d) If ${\mathbf{Z}}^{\mathbf{2}\mathbf{-}}$is $\mathbf{C}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{2}\mathbf{-}}$, which scene represents the solution after the  has been lowered?