Ionic Equilibria in Aqueous Systems

The indicator ethyl red has ${\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$. Over what approximate  pH range does it change colour?

The indicator cresol red has ${\mathit{K}}_{\mathbf{\text{a}}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}$. Over what approximate pH range does it change color?

How does the titration curve of a monoprotic acid differ from that of a diprotic acid?

Why is the centre of the buffer region of a weak acid–strong base titration significant?

Explain how strong acid–strong base, weak acid–strong base, and weak base–strong acid titrations using the same concentrations differ in terms of (a) the initial pH and (b) the pH at the equivalence point. (The component in italics is in the flask.)

The scenes below depict the relative concentrations of  ${\mathbf{\text{H}}}_{\mathbf{\text{3}}}{\mathbf{\text{PO}}}_{\mathbf{\text{4}}}{\mathbf{\text{,H}}}_{\mathbf{\text{2}}}\mathbf{\text{P}}{{\mathbf{\text{O}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{ - }}}$, and $\mathbf{\text{HP}}{{\mathbf{\text{O}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2 - }}}$  during a titration with aqueous  $\mathbf{\text{NaOH}}$, but they are out of order. (Phosphate groups are purple, hydrogens are blue, and ${\mathbf{\text{Na}}}^{\mathbf{\text{ + }}}$ ions and water molecules are not shown.) 

(a) List the scenes in the correct order. 

(b) What is the pH  in the correctly ordered second scene (see Appendix C)? 

(c) If it requires $\mathbf{10}\mathbf{.00}\mathbf{\text{ mL}}$  of the   solution to reach this scene, how much more is needed to reach the last scene?

What is the difference between the endpoint of titration and the equivalence point? Is the equivalence point always reached first? Explain.

Why doesn’t the addition of an acid-base indicator affect the pH of the test solution?

What species are in the buffer region of a weak acid–strong base titration? How are they different from the species at the equivalence point? How are they different from the species in the buffer region of a weak base–strong acid titration?

Use Figure 19.5 to find an indicator for these titrations:

(a) $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{HCl}}$ with $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{NaOH}}$.

(b) $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{HCOOH}}$  (Appendix C) with $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{NaOH}}$.

Use Figure 19.5 to find an indicator for these titrations:

(a)  $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }{\mathbf{\text{M CH}}}_{\mathbf{3}}{\mathbf{\text{NH}}}_{\mathbf{2}}$ (Appendix C) with $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{\text{MHCl}}$.

(b)  $\mathbf{\text{0.50 M}}$ HI with $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathbf{\text{M KOH}}$.

Use Figure 19.5 to find an indicator for these titrations:

(a) $\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{\text{M}}{\mathbf{\left(}{\mathbf{\text{CH}}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}\mathbf{\text{NH\#000A64}}$ (Appendix C) with $\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{HBr}}$.

(b) $\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{KOH}}$ with $\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }{\mathbf{\text{HNO}}}_{\mathbf{3}}$.

Find the pH of the equivalence point(s) and the volume (mL) of $\mathbf{0}\mathbf{.}\mathbf{0588}\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{KOH}}$ needed to reach it in titrations of

(a) $\mathbf{23}\mathbf{.}\mathbf{4}\mathbf{ }\mathbf{\text{mL}}$ of $\mathbf{0}\mathbf{.}\mathbf{0390}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }\mathbf{\text{HNO}}\mathbf{2}$

(b) $\mathbf{17}\mathbf{.}\mathbf{3}\mathbf{ }\mathbf{\text{mL}}$ of $\mathbf{0}\mathbf{.}\mathbf{130}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }{\mathbf{\text{H}}}_{\mathbf{2}}{\mathbf{\text{CO}}}_{\mathbf{3}}$ (two equivalence points)

Find the pH of the equivalence point(s) and the volume (mL) of  needed to reach it in titrations of

(a) $\mathbf{65}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{\text{mL}}$ of $\mathbf{0}\mathbf{.}\mathbf{234}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }{\mathbf{\text{NH}}}_{\mathbf{3}}$

(b) $\mathbf{21}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{\text{mL}}$ of $\mathbf{1}\mathbf{.}\mathbf{11}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }{\mathbf{\text{CH}}}_{\mathbf{3}}{\mathbf{\text{NH}}}_{\mathbf{2}}$.

19.62 The molar solubility of ${\mathbf{\text{M}}}_{\mathbf{2}}\mathbf{\text{X}}$ is $\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{ }\mathbf{\text{M}}$. What is the molarity of each ion? How do you set up the calculation to find ${\mathbf{K}}_{\mathbf{\text{sp}}}$? What assumption must you make about the dissociation of ${\mathbf{\text{M}}}_{\mathbf{2}}\mathbf{\text{X}}$ into ions? Why is the calculated ${\mathbf{K}}_{\mathbf{\text{sp}}}$ higher than the actual value?

Why does  affect the solubility of ${\mathbf{\text{BaF}}}_{\mathbf{\text{2}}}$but not of ${\mathbf{\text{BaCl}}}_{\mathbf{\text{2}}}$? 

In a gaseous equilibrium, the reverse reaction occurs when ${\mathbf{\text{Q}}}_{\mathbf{\text{c}}}{\mathbf{\text{ > K}}}_{\mathbf{\text{c}}}$. What occurs in aqueous solution when ${\mathbf{\text{Q}}}_{\mathbf{\text{sp}}}{\mathbf{\text{ > K}}}_{\mathbf{\text{sp}}}$?

Find the pH and volume (mL) of $\mathbf{0}\mathbf{.}\mathbf{447}\mathbf{ }\mathbf{\text{M}}\mathbf{ }\mathbf{ }{\mathbf{\text{HNO}}}_{\mathbf{3}}$ needed to reach the equivalence point(s) in titrations of

(a) $\mathbf{2}\mathbf{.}\mathbf{65}\mathbf{ }\mathbf{\text{L}}$ of $\mathbf{0}\mathbf{.}\mathbf{0750}\mathbf{ }\mathbf{\text{M}}$ pyridine $({\text{C}}_5{\text{H}}_5 \text{N})$ 

(b) $\mathbf{0}\mathbf{.}\mathbf{188}\mathbf{ }\mathbf{\text{L}}$ of $\mathbf{0}\mathbf{.}\mathbf{250}\mathbf{ }\mathbf{\text{M}}$ ethylenediamine $\left({\text{H}}_2{\text{NCH}}_2{\text{CH}}_2{\text{NH}}_2\right)$

A list of ${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}$ values like that in Appendix C can be used to compare the solubility of silver chloride directly with that of silver bromide but not with that of silver chromate. Explain.

What is $\left[{\mathrm{Ag}}^{+}\right]$when 25.0 mL each of 0.044 M ${\mathrm{AgNO}}_3$and 0.57 M ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3$are mixed [${\text{K}}_{\text{f}}$ of $\mathrm{Ag}{\left({\mathrm{S}}_2{\mathrm{O}}_3\right)}_2^{3-}=4.7\times {10}^{13}$]?

Find the solubility of $\mathbf{Cr}{\left(\mathbf{OH}\right)}_{\mathbf{3}}$in a buffer of pH 13.0 [ ${\text{K}}_{\text{sp}}$ of ${\text{Cr(OH)}}_{\text{3}}{\text{ = 6.3×10}}^{-31}$ ;  ${\text{K}}_{\text{f}}$ of $\text{Cr(OH}{{\text{)}}_{\text{4}}}^{\text{ - }}{\text{ = 8.0×10}}^{29}$].

Find the solubility of $\mathbf{Agl}$ in ${\mathbf{\text{2.5 M NH}}}_{\mathbf{\text{3}}}$ [${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}$ of $\mathbf{\text{Agl}}\mathbf{ }\mathbf{\text{ = }}\mathbf{ }{\mathbf{\text{8.3×10}}}^{\mathbf{\text{ - 17}}}$; ${\mathbf{\text{K}}}_{\mathbf{\text{f}}}$ of ${\mathbf{\text{Ag(NH}}}_{\mathbf{\text{3}}}{{\mathbf{\text{)}}}_{\mathbf{\text{2}}}}^{\mathbf{\text{ + }}}{\mathbf{\text{ = 1.7×10}}}^{\mathbf{\text{7}}}$].

Write the ion-product expressions for

$\left(\text{a}\right)\mathbf{\text{ lead(II)iodide; }}\left(\text{b}\right)\mathbf{\text{ strontium sulfate; }}\left(\text{c}\right)\mathbf{\text{ cadmium sulfide.}}$

The solubility of silver carbonate is $\mathbf{\text{0.032 M}}$ at $\mathbf{\text{20°C.}}$Calculate its$\mathbf{\text{Ksp.}}$

The solubility of zinc oxalate is$\mathbf{7}\mathbf{.}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{M}\mathbf{\text{ at 18 °C.}}$Calculate its${\mathit{K}}_{\mathbf{sp}}$.

The solubility of silver dichromate at $\mathbf{15}\mathbf{ }\mathbf{°}\mathbf{C}$ is $\mathbf{8}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{100}\mathbf{ }\mathbf{mL}$ solution. Calculate its ${\mathit{K}}_{\mathbf{s}\mathbf{p}}$.

The solubility of calcium sulphate at ${\mathbf{\text{30 }}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$  is  $\mathbf{\text{0.209 g/100 mL}}$ solution. Calculate its ${\mathbf{K}}_{\mathbf{sp}}$.

Find the molar solubility of ${\mathbf{SrCO}}_{\mathbf{3}}\mathbf{(}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{)}$  in 

(a) pure water and 

(b)  $\mathbf{0}\mathbf{.}\mathbf{13}\mathbf{MSr}\mathbf{(}{\mathbf{NO}}_{\mathbf{3}}{\mathbf{)}}_{\mathbf{2}}$.

When$\mathbf{\text{0.84}}$  g of  ${\mathbf{\text{ZnCl}}}_{\mathbf{\text{2}}}$ is dissolved in 245 mL of 0.150 M  , $\mathbf{\text{NaCN}}$what are $\mathbf{\left[}{\mathbf{\text{Zn}}}^{\mathbf{\text{2+}}}\mathbf{\right]}$ , $\mathbf{\left[}{{\mathbf{\text{Zn(CN)}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2-}}}\mathbf{\right]}$ , and  [ $\mathbf{\left[}{\mathbf{\text{CN}}}^{\mathbf{\text{-}}}\mathbf{\right]}$ ${\mathbf{\text{K}}}_{\mathbf{\text{f}}}$of ${{\mathbf{\text{Zn(CN)}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2-}}}{\mathbf{\text{=4.2×10}}}^{\mathbf{\text{19}}}$]?

Find the molar solubility of  ${\mathbf{BaCrO}}_{\mathbf{4}}\mathbf{(}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{)}$ in 

(a) pure water and 

(b) $\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{M}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{CrO}}_{\mathbf{4}}$ .

Calculate the molar solubility of${\mathbf{\text{Ca(IO}}}_{\mathbf{\text{3}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$in 

(a) ${\mathbf{\text{0.060 M Ca(NO}}}_{\mathbf{\text{3}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$ and 

(b) ${\mathbf{\text{0.060 M NaIO}}}_{\mathbf{\text{3}}}$. (See Appendix C.)

Calculate the molar solubility of ${\mathbf{\text{Ag}}}_{\mathbf{\text{2}}}{\mathbf{\text{SO}}}_{\mathbf{\text{4}}}$ in 

(a)  ${\mathbf{\text{0.22 M AgNO}}}_{\mathbf{\text{3}}}$and 

(b) ${\mathbf{\text{0.22 M Na}}}_{\mathbf{\text{2}}}{\mathbf{\text{SO}}}_{\mathbf{\text{4}}}$. (See Appendix C.)

Which compound in each pair is more soluble in water? 

(a) Magnesium hydroxide or nickel (II) hydroxide 

(b) Lead (II) sulphide or copper (II) sulphide 

(c) Silver sulphate or magnesium fluoride

Which compound in each pair is more soluble in water? 

(a) Strontium sulphate or barium chromate 

(b) Calcium carbonate or copper (II) carbonate 

(c) Barium iodate or silver chromate

Which compound in each pair is more soluble in water? 

(a) Barium sulphate or calcium sulphate 

(b) Calcium phosphate or magnesium phosphate 

(c) Silver chloride or lead (II) sulfate

Which compound in each pair is more soluble in water? 

(a) Manganese (II) hydroxide or calcium iodate 

(b) Strontium carbonate or cadmium sulfide 

(c) Silver cyanide or copper (I) iodide

Write equations to show whether the solubility of either of the following is affected by pH: 

(a)  $\mathbf{\text{AgCl}}$; 

(b)  ${\mathbf{\text{SrCO}}}_{\mathbf{\text{3}}}$.

Question: Write equations to show whether the solubility of either of the following is affected by  : 

(a)$\mathbf{CuBr}$; 

(b)${\mathbf{\text{Ca}}}_{\mathbf{\text{3}}}{\mathbf{\text{(PO}}}_{\mathbf{\text{4}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$.

Write equations to show whether the solubility of either of the following is affected by pH: 

(a) Fe(OH)₂ ; 

(b) CuS.

Does any solid ${\mathbf{\text{Cu(OH)}}}_{\mathbf{2}}$form when $\mathbf{\text{0.075 g}}$ of $\mathbf{\text{KOH}}$ is dissolved in  of $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{M}\mathbf{Cu}\mathbf{(}{\mathbf{NO}}_{\mathbf{3}}{\mathbf{)}}_{\mathbf{2}}$ ?

Does any solid ${\mathbf{\text{PbCl}}}_{\mathbf{\text{2}}}$form when $\mathbf{\text{3.5 mg}}$ of $\mathbf{NaCl}$ is dissolved in $\mathbf{\text{0.250 L}}$ of ${\mathbf{\text{0.12 M Pb(NO}}}_{\mathbf{\text{3}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$?

Does any solid ${\mathbf{\text{Ag}}}_{\mathbf{\text{2}}}{\mathbf{\text{CrO}}}_{\mathbf{\text{4}}}$ form when  $\mathbf{2}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{g}$ of  ${\mathbf{\text{AgNO}}}_{\mathbf{3}}$ is dissolved in  $\mathbf{\text{15.0 mL}}$ of $\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{M}{\mathbf{K}}_{\mathbf{2}}{\mathbf{CrO}}_{\mathbf{4}}$?

When blood is donated, sodium oxalate solution is used to precipitate ${\mathbf{\text{Ca}}}^{\mathbf{\text{2 + }}}$, which triggers clotting. A  $\mathbf{\text{104 mL}}$ sample of blood contains $\mathbf{9}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{g}{\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}\mathbf{/}\mathbf{mL}$. A technologist treats the sample with $\mathbf{\text{100.0 mL}}$  of  ${\mathbf{\text{0.1550 M Na}}}_{\mathbf{\text{2}}}{\mathbf{\text{C}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{4}}}$. Calculate ${\mathbf{\text{[Ca}}}^{\mathbf{\text{2 + }}}\mathbf{\text{]}}$  after the treatment. (See Appendix C for K_sp of ${\mathbf{\text{CaC}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{4}}}\mathbf{·}{\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$.)

How can a metal cation be at the centre of a complex anion?

Write equations to show the stepwise reaction of ${\mathbf{\text{Cd(H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O)}}}_{\mathbf{\text{4}}}^{\mathbf{\text{2 + }}}$  in an aqueous solution of  $\mathbf{\text{KI}}$ to form ${\mathbf{\text{CdI}}}_{\mathbf{\text{4}}}^{\mathbf{\text{2 - }}}$. Show that ${\mathbf{K}}_{\mathbf{f}\mathbf{\left(}\mathbf{overall}\mathbf{\right)}}\mathbf{=}{\mathbf{K}}_{\mathbf{f}\mathbf{1}}\mathbf{\times }{\mathbf{K}}_{\mathbf{f}\mathbf{2}}\mathbf{\times }{\mathbf{K}}_{\mathbf{f}\mathbf{3}}\mathbf{\times }{\mathbf{K}}_{\mathbf{f}\mathbf{4}}$ .

Consider the dissolution of $\mathbf{\text{PbS}}$ in water:

 $\mathbf{PbS}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{Pb}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{HS}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{OH}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}$

Adding aqueous $\mathbf{\text{NaOH}}$  causes more $\mathbf{\text{PbS}}$ to dissolve. Does this violate Le Chatelier’s principle? Explain.

Write a balanced equation for the reaction of ${\mathbf{\text{Hg(H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O)}}}_{\mathbf{\text{4}}}^{\mathbf{\text{2 + }}}$ in aqueous  $\mathbf{\text{KCN}}$.

Write a balanced equation for the reaction of ${\mathbf{\text{Zn(H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O)}}}_{\mathbf{\text{4}}}^{\mathbf{\text{2 + }}}$ in aqueous  $\mathbf{\text{NaCN}}$.

Write a balanced equation for the reaction of $\mathbf{\text{Al}}{{\mathbf{\left(}{\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}\mathbf{\right)}}_{\mathbf{\text{6}}}}^{\mathbf{\text{3 + }}}$in aqueous $\mathbf{KF}$.

As an FDA physiologist, you need 0.700 L of formic acid–formate buffer with a pH of 3.74. 

(a) What is the required buffer-component concentration ratio? 

(b) How do you prepare this solution from stock solutions of  $\mathbf{\text{1.0 M HCOOH}}$and  data-custom-editor="chemistry" $\mathbf{\text{1.0 M NaOH}}$? 

(c) What is the final concentration of  data-custom-editor="chemistry" $\mathbf{\text{HCOOH}}$in this solution?