16.2: Equilibria of Other Reaction Classes (Exercises)
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15.1: Precipitation and Dissolution
Q15.1.1
Complete the changes in concentrations for each of the following reactions:
\(\begin{alignat}{3}
&\ce{AgI}(s)⟶&&\ce{Ag+}(aq)\,+\,&&\ce{I-}(aq)\\
& &&x &&\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{CaCO3}(s)⟶&&\ce{Ca^2+}(aq)\,+\,&&\ce{CO3^2-}(aq)\\
& &&\underline{\hspace{45px}} &&x
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Mg(OH)2}(s)⟶&&\ce{Mg^2+}(aq)\,+\,&&\ce{2OH-}(aq)\\
& &&x &&\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Mg3(PO4)2}(s)⟶&&\ce{3Mg^2+}(aq)\,+\,&&\ce{2PO4^3-}(aq)\\
& && &&x\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Ca5(PO4)3OH}(s)⟶&&\ce{5Ca^2+}(aq)\,+\,&&\ce{3PO4^3-}(aq)\,+\,&&\ce{OH-}(aq)\\
& &&\underline{\hspace{45px}} &&\underline{\hspace{45px}} &&x
\end{alignat}\)
S15.1.1
\(\begin{alignat}{3}
&\ce{AgI}(s)⟶&&\ce{Ag+}(aq)\,+\,&&\ce{I-}(aq)\\
& &&x &&\underline{x}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{CaCO3}(s)⟶&&\ce{Ca^2+}(aq)\,+\,&&\ce{CO3^2-}(aq)\\
& &&\underline{x} &&x
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Mg(OH)2}(s)⟶&&\ce{Mg^2+}(aq)\,+\,&&\ce{2OH-}(aq)\\
& &&x &&\underline{2x}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Mg3(PO4)2}(s)⟶&&\ce{3Mg^2+}(aq)\,+\,&&\ce{2PO4^3-}(aq)\\
& &&\underline{3x} &&2x
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Ca5(PO4)3OH}(s)⟶&&\ce{5Ca^2+}(aq)\,+\,&&\ce{3PO4^3-}(aq)\,+\,&&\ce{OH-}(aq)\\
& &&\underline{5x} &&\underline{3x} &&x
\end{alignat}\)
Q15.1.2
Complete the changes in concentrations for each of the following reactions:
\(\begin{alignat}{3}
&\ce{BaSO4}(s)⟶&&\ce{Ba^2+}(aq)\,+\,&&\ce{SO4^2-}(aq)\\
& &&x &&\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Ag2SO4}(s)⟶&&\ce{2Ag+}(aq)\,+\,&&\ce{SO4^2-}(aq)\\
& &&\underline{\hspace{45px}} &&x
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Al(OH)3}(s)⟶&&\ce{Al^3+}(aq)\,+\,&&\ce{3OH-}(aq)\\
& &&x &&\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Pb(OH)Cl}(s)⟶&&\ce{Pb^2+}(aq)\,+\,&&\ce{OH-}(aq)\,+\,&&\ce{Cl-}(aq)\\
& &&\underline{\hspace{45px}} &&x &&\underline{\hspace{45px}}
\end{alignat}\)
\(\begin{alignat}{3}
&\ce{Ca3(AsO4)2}(s)⟶&&\ce{3Ca^2+}(aq)\,+\,&&\ce{2AsO4^3-}(aq)\\
& &&3x &&\underline{\hspace{45px}}
\end{alignat}\)
Q15.1.3
How do the concentrations of Ag + and \(\ce{CrO4^2-}\) in a saturated solution above 1.0 g of solid Ag 2 CrO 4 change when 100 g of solid Ag 2 CrO 4 is added to the system? Explain.
S15.1.3
There is no change. A solid has an activity of 1 whether there is a little or a lot.
Q15.1.4
How do the concentrations of Pb 2+ and S 2– change when K 2 S is added to a saturated solution of PbS?
Q15.1.5
What additional information do we need to answer the following question: How is the equilibrium of solid silver bromide with a saturated solution of its ions affected when the temperature is raised?
S15.1.5
The solubility of silver bromide at the new temperature must be known. Normally the solubility increases and some of the solid silver bromide will dissolve.
Q15.1.6
Which of the following slightly soluble compounds has a solubility greater than that calculated from its solubility product because of hydrolysis of the anion present: CoSO 3 , CuI, PbCO 3 , PbCl 2 , Tl 2 S, KClO 4 ?
Q15.1.7
Which of the following slightly soluble compounds has a solubility greater than that calculated from its solubility product because of hydrolysis of the anion present: AgCl, BaSO 4 , CaF 2 , Hg 2 I 2 , MnCO 3 , ZnS, PbS?
S15.1.7
CaF 2 , MnCO 3 , and ZnS
Q15.1.8
Write the ionic equation for dissolution and the solubility product ( K sp ) expression for each of the following slightly soluble ionic compounds:
- PbCl 2
- Ag 2 S
- Sr 3 (PO 4 ) 2
- SrSO 4
Q15.1.9
Write the ionic equation for the dissolution and the K sp expression for each of the following slightly soluble ionic compounds:
- LaF 3
- CaCO 3
- Ag 2 SO 4
- Pb(OH) 2
Q15.1.10
- \(\ce{LaF3}(s)⇌\ce{La^3+}(aq)+\ce{3F-}(aq) \hspace{20px} K_\ce{sp}=\ce{[La^3+][F- ]^3};\)
- \(\ce{CaCO3}(s)⇌\ce{Ca^2+}(aq)+\ce{CO3^2-}(aq) \hspace{20px} K_\ce{sp}=\ce{[Ca^2+][CO3^2- ]};\)
- \(\ce{Ag2SO4}(s)⇌\ce{2Ag+}(aq)+\ce{SO4^2-}(aq) \hspace{20px} K_\ce{sp}=\ce{[Ag+]^2[SO4^2- ]};\)
- \(\ce{Pb(OH)2}(s)⇌\ce{Pb^2+}(aq)+\ce{2OH-}(aq) \hspace{20px} K_\ce{sp}=\ce{[Pb^2+][OH- ]^2}\)
Q15.1.11
The Handbook of Chemistry and Physics gives solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.
- BaSiF 6 , 0.026 g/100 mL (contains \(\ce{SiF6^2-}\) ions)
- Ce(IO 3 ) 4 , 1.5 × 10 –2 g/100 mL
- Gd 2 (SO 4 ) 3 , 3.98 g/100 mL
- (NH 4 ) 2 PtBr 6 , 0.59 g/100 mL (contains \(\ce{PtBr6^2-}\) ions)
Q15.1.12
The Handbook of Chemistry and Physics gives solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.
- BaSeO 4 , 0.0118 g/100 mL
- Ba(BrO 3 ) 2 •H 2 O, 0.30 g/100 mL
- NH 4 MgAsO 4 •6H 2 O, 0.038 g/100 mL
- La 2 (MoO 4 ) 3 , 0.00179 g/100 mL
S15.1.12
(a)1.77 × 10 –7 ; 1.6 × 10 –6 ; 2.2 × 10 –9 ; 7.91 × 10 –22
Q15.1.13
Use solubility products and predict which of the following salts is the most soluble, in terms of moles per liter, in pure water: CaF 2 , Hg 2 Cl 2 , PbI 2 , or Sn(OH) 2 .
Q15.1.14
Assuming that no equilibria other than dissolution are involved, calculate the molar solubility of each of the following from its solubility product:
- KHC 4 H 4 O 6
- PbI 2
- Ag 4 [Fe(CN) 6 ], a salt containing the \(\ce{Fe(CN)4-}\) ion
- Hg 2 I 2
S15.1.15
2 × 10 –2 M ; 1.3 × 10 –3 M ; 2.27 × 10 –9 M ; 2.2 × 10 –10 M
Q15.1.16
Assuming that no equilibria other than dissolution are involved, calculate the molar solubility of each of the following from its solubility product:
- Ag 2 SO 4
- PbBr 2
- AgI
- CaC 2 O 4 •H 2 O
Q15.1.X
Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that changes in the initial concentrations of the common ions can be neglected.
- AgCl( s ) in 0.025 M NaCl
- CaF 2 ( s ) in 0.00133 M KF
- Ag 2 SO 4 ( s ) in 0.500 L of a solution containing 19.50 g of K 2 SO 4
- Zn(OH) 2 ( s ) in a solution buffered at a pH of 11.45
S15.1.X
7.2 × 10 −9 M = [Ag + ], [Cl − ] = 0.025 M
Check: \(\dfrac{7.2×10^{−9}\:M}{0.025\:M}×100\%=2.9×10^{−5}\%\), an insignificant change;
2.2 × 10 −5 M = [Ca 2+ ], [F − ] = 0.0013 M
Check: \(\dfrac{2.25×10^{−5}\:M}{0.00133\:M}×100\%=1.69\%\). This value is less than 5% and can be ignored.
0.2238 M = \(\ce{[SO4^2- ]}\); [Ag + ] = 2.30 × 10 –9 M
Check: \(\dfrac{1.15×10^{−9}}{0.2238}×100\%=5.14×10^{−7}\); the condition is satisfied.
[OH – ] = 2.8 × 10 –3 M ; 5.7 × 10 −12 M = [Zn 2+ ]
Check: \(\dfrac{5.7×10^{−12}}{2.8×10^{−3}}×100\%=2.0×10^{−7}\%\); x is less than 5% of [OH – ] and is, therefore, negligible.
Q15.1.X
Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that changes in the initial concentrations of the common ions can be neglected.
- TlCl( s ) in 1.250 M HCl
- PbI 2 ( s ) in 0.0355 M CaI 2
- Ag 2 CrO 4 ( s ) in 0.225 L of a solution containing 0.856 g of K 2 CrO 4
- Cd(OH) 2 ( s ) in a solution buffered at a pH of 10.995
Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that it is not appropriate to neglect the changes in the initial concentrations of the common ions.
- TlCl( s ) in 0.025 M TlNO 3
- BaF 2 ( s ) in 0.0313 M KF
- MgC 2 O 4 in 2.250 L of a solution containing 8.156 g of Mg(NO 3 ) 2
- Ca(OH) 2 ( s ) in an unbuffered solution initially with a pH of 12.700
S15.1.X
- [Cl – ] = 7.6 × 10 −3 M
Check: \(\dfrac{7.6×10^{−3}}{0.025}×100\%=30\%\)
This value is too large to drop x . Therefore solve by using the quadratic equation:
- [Ti + ] = 3.1 × 10 –2 M
- [Cl – ] = 6.1 × 10 –3
- [Ba 2+ ] = 1.7 × 10 –3 M
Check: \(\dfrac{1.7×10^{−3}}{0.0313}×100\%=5.5\%\)
This value is too large to drop x, and the entire equation must be solved.
- [Ba 2+ ] = 1.6 × 10 –3 M
- [F – ] = 0.0329 M ;
- Mg(NO 3 ) 2 = 0.02444 M
\(\ce{[C2O4^2- ]}=3.5×10^{−3}\)
Check: \(\dfrac{3.5×10^{−3}}{0.02444}×100\%=14\%\)
This value is greater than 5%, so the quadratic equation must be used:
- \(\ce{[C2O4^2- ]}=3.5×10^{−3}\:M\)
- [Mg 2+ ] = 0.0275 M
- [OH – ] = 0.0501 M
- [Ca 2+ ] = 3.15 × 10 –3
Check: \(\dfrac{3.15×10^{−3}}{0.050}×100\%=6.28\%\)
This value is greater than 5%, so a more exact method, such as successive approximations, must be used.
- [Ca 2+ ] = 2.8 × 10 –3 M
- [OH – ] = 0.053 × 10 –2 M
Q15.1.X
Explain why the changes in concentrations of the common ions in Exercise cannot be neglected.
S15.1.X
The changes in concentration are greater than 5% and thus exceed the maximum value for disregarding the change.
Q15.1.X
Calculate the solubility of aluminum hydroxide, Al(OH) 3 , in a solution buffered at pH 11.00.
Q15.1.X
Refer to Appendix J for solubility products for calcium salts. Determine which of the calcium salts listed is most soluble in moles per liter and which is most soluble in grams per liter.
S15.1.X
CaSO 4 ∙2H 2 O is the most soluble Ca salt in mol/L, and it is also the most soluble Ca salt in g/L.
Q15.1.X
Most barium compounds are very poisonous; however, barium sulfate is often administered internally as an aid in the X-ray examination of the lower intestinal tract. This use of BaSO 4 is possible because of its low solubility. Calculate the molar solubility of BaSO 4 and the mass of barium present in 1.00 L of water saturated with BaSO 4 .
Q15.1.X
Public Health Service standards for drinking water set a maximum of 250 mg/L (2.60 × 10 –3 M ) of \(\ce{SO4^2-}\) because of its cathartic action (it is a laxative). Does natural water that is saturated with CaSO 4 (“gyp” water) as a result or passing through soil containing gypsum, CaSO 4 •2H 2 O, meet these standards? What is \(\ce{SO4^2-}\) in such water?
S15.1.X
4.9 × 10 –3 M = \(\ce{[SO4^2- ]}\) = [Ca 2+ ]; Since this concentration is higher than 2.60 × 10 –3 M , “gyp” water does not meet the standards.
Q15.1.X
Perform the following calculations:
- Calculate [Ag + ] in a saturated aqueous solution of AgBr.
- What will [Ag + ] be when enough KBr has been added to make [Br – ] = 0.050 M ?
- What will [Br – ] be when enough AgNO 3 has been added to make [Ag + ] = 0.020 M ?
The solubility product of CaSO 4 •2H 2 O is 2.4 × 10 –5 . What mass of this salt will dissolve in 1.0 L of 0.010 M \(\ce{SO4^2-}\)?
S15.1.X
Mass (CaSO 4 •2H 2 O) = 0.34 g/L
Q15.1.X
Assuming that no equilibria other than dissolution are involved, calculate the concentrations of ions in a saturated solution of each of the following (see Table E3 for solubility products).
- TlCl
- BaF 2
- Ag 2 CrO 4
- CaC 2 O 4 •H 2 O
- the mineral anglesite, PbSO 4
Q15.1.X
Assuming that no equilibria other than dissolution are involved, calculate the concentrations of ions in a saturated solution of each of the following (see Table E3 for solubility products).
- AgI
- Ag 2 SO 4
- Mn(OH) 2
- Sr(OH) 2 •8H 2 O
- the mineral brucite, Mg(OH) 2
S15.1.X
[Ag + ] = [I – ] = 1.2 × 10 –8 M ; [Ag + ] = 2.86 × 10 –2 M , \(\ce{[SO4^2- ]}\) = 1.43 × 10 –2 M ; [Mn 2+ ] = 2.2 × 10 –5 M , [OH – ] = 4.5 × 10 –5 M ; [Sr 2+ ] = 4.3 × 10 –2 M , [OH – ] = 8.6 × 10 –2 M ; [Mg 2+ ] = 1.6 × 10 –4 M , [OH – ] = 3.1 × 10 –4 M .
Q15.1.X
The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K sp for each of the slightly soluble solids indicated:
- AgBr: [Ag + ] = 5.7 × 10 –7 M , [Br – ] = 5.7 × 10 –7 M
- CaCO 3 : [Ca 2+ ] = 5.3 × 10 –3 M , \(\ce{[CO3^2- ]}\) = 9.0 × 10 –7 M
- PbF 2 : [Pb 2+ ] = 2.1 × 10 –3 M , [F – ] = 4.2 × 10 –3 M
- Ag 2 CrO 4 : [Ag + ] = 5.3 × 10 –5 M , 3.2 × 10 –3 M
- InF 3 : [In 3+ ] = 2.3 × 10 –3 M , [F – ] = 7.0 × 10 –3 M
Q15.1.X
The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K sp for each of the slightly soluble solids indicated:
- TlCl: [Tl + ] = 1.21 × 10 –2 M , [Cl – ] = 1.2 × 10 –2 M
- Ce(IO 3 ) 4 : [Ce 4+ ] = 1.8 × 10 –4 M , \(\ce{[IO3- ]}\) = 2.6 × 10 –13 M
- Gd 2 (SO 4 ) 3 : [Gd 3+ ] = 0.132 M , \(\ce{[SO4^2- ]}\) = 0.198 M
- Ag 2 SO 4 : [Ag + ] = 2.40 × 10 –2 M , \(\ce{[SO4^2- ]}\) = 2.05 × 10 –2 M
- BaSO 4 : [Ba 2+ ] = 0.500 M , \(\ce{[SO4^2- ]}\) = 2.16 × 10 –10 M
S15.1.X
2.0 × 10 –4 ; 5.1 × 10 –17 ; 1.35 × 10 –4 ; 1.18 × 10 –5 ; 1.08 × 10 –10
Q15.1.X
Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Table E3 for K sp values.)
- KClO 4 : [K + ] = 0.01 M , \(\ce{[ClO4- ]}\) = 0.01 M
- K 2 PtCl 6 : [K + ] = 0.01 M , \(\ce{[PtCl6^2- ]}\) = 0.01 M
- PbI 2 : [Pb 2+ ] = 0.003 M , [I – ] = 1.3 × 10 –3 M
- Ag 2 S: [Ag + ] = 1 × 10 –10 M , [S 2– ] = 1 × 10 –13 M
Q15.1.X
Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Table E3 for K sp values.)
- CaCO 3 : [Ca 2+ ] = 0.003 M , \(\ce{[CO3^2- ]}\) = 0.003 M
- Co(OH) 2 : [Co 2+ ] = 0.01 M , [OH – ] = 1 × 10 –7 M
- CaHPO 4 : [Ca 2+ ] = 0.01 M , \(\ce{[HPO4^2- ]}\) = 2 × 10 –6 M
- Pb 3 (PO 4 ) 2 : [Pb 2+ ] = 0.01 M , \(\ce{[PO4^3- ]}\) = 1 × 10 –13 M
S15.1.X
- CaCO 3 does precipitate.
- The compound does not precipitate.
- The compound does not precipitate.
- The compound precipitates.
Q15.1.X
Calculate the concentration of Tl + when TlCl just begins to precipitate from a solution that is 0.0250 M in Cl – .
Q15.1.X
Calculate the concentration of sulfate ion when BaSO 4 just begins to precipitate from a solution that is 0.0758 M in Ba 2+ .
S15.1.X
1.42 × 10 −9 M
Q15.1.X
Calculate the concentration of Sr 2+ when SrF 2 starts to precipitate from a solution that is 0.0025 M in F – .
Q15.1.X
Calculate the concentration of \(\ce{PO4^3-}\) when Ag 3 PO 4 starts to precipitate from a solution that is 0.0125 M in Ag + .
S15.1.X
9.2 × 10 −13 M
Q15.1.X
Calculate the concentration of F – required to begin precipitation of CaF 2 in a solution that is 0.010 M in Ca 2+ .
Q15.1.X
Calculate the concentration of Ag + required to begin precipitation of Ag 2 CO 3 in a solution that is 2.50 × 10 –6 M in \(\ce{CO3^2-}\).
S15.1.X
[Ag + ] = 1.8 × 10 –3 M
Q15.1.X
What [Ag + ] is required to reduce \(\ce{[CO3^2- ]}\) to 8.2 × 10 –4 M by precipitation of Ag 2 CO 3 ?
Q15.1.X
What [F – ] is required to reduce [Ca 2+ ] to 1.0 × 10 –4 M by precipitation of CaF 2 ?
S15.1.X
6.2 × 10 –4
Q15.1.X
A volume of 0.800 L of a 2 × 10 –4 - M Ba(NO 3 ) 2 solution is added to 0.200 L of 5 × 10 –4 M Li 2 SO 4 . Does BaSO 4 precipitate? Explain your answer.
Q15.1.X
Perform these calculations for nickel(II) carbonate.
- With what volume of water must a precipitate containing NiCO 3 be washed to dissolve 0.100 g of this compound? Assume that the wash water becomes saturated with NiCO 3 ( K sp = 1.36 × 10 –7 ).
- If the NiCO 3 were a contaminant in a sample of CoCO 3 ( K sp = 1.0 × 10 –12 ), what mass of CoCO 3 would have been lost? Keep in mind that both NiCO 3 and CoCO 3 dissolve in the same solution.
S15.1.X
2.28 L; 7.3 × 10 –7 g
Q15.1.X
Iron concentrations greater than 5.4 × 10 –6 M in water used for laundry purposes can cause staining. What [OH – ] is required to reduce [Fe 2+ ] to this level by precipitation of Fe(OH) 2 ?
Q15.1.X
A solution is 0.010 M in both Cu 2+ and Cd 2+ . What percentage of Cd 2+ remains in the solution when 99.9% of the Cu 2+ has been precipitated as CuS by adding sulfide?
S15.1.X
100% of it is dissolved
Q15.1.X
A solution is 0.15 M in both Pb 2+ and Ag + . If Cl – is added to this solution, what is [Ag + ] when PbCl 2 begins to precipitate?
Q15.1.X
What reagent might be used to separate the ions in each of the following mixtures, which are 0.1 M with respect to each ion? In some cases it may be necessary to control the pH. (Hint: Consider the K sp values given in Appendix J .)
- \(\ce{Hg2^2+}\) and Cu 2+
- \(\ce{SO4^2-}\) and Cl –
- Hg 2+ and Co 2+
- Zn 2+ and Sr 2+
- Ba 2+ and Mg 2+
- \(\ce{CO3^2-}\) and OH –
S15.1.X
- \(\ce{Hg2^2+}\) and Cu 2+ : Add \(\ce{SO4^2-}\).
- \(\ce{SO4^2-}\) and Cl – : Add Ba 2+ .
- Hg 2+ and Co 2+ : Add S 2– .
- Zn 2+ an Sr 2+ : Add OH – until [OH – ] = 0.050 M .
- Ba 2+ and Mg 2+ : Add \(\ce{SO4^2-}\).
- \(\ce{CO3^2-}\) and OH – : Add Ba 2+ .
Q15.1.X
A solution contains 1.0 × 10 –5 mol of KBr and 0.10 mol of KCl per liter. AgNO 3 is gradually added to this solution. Which forms first, solid AgBr or solid AgCl?
Q15.1.X
A solution contains 1.0 × 10 –2 mol of KI and 0.10 mol of KCl per liter. AgNO 3 is gradually added to this solution. Which forms first, solid AgI or solid AgCl?
S15.1.X
AgI will precipitate first.
Q15.1.X
The calcium ions in human blood serum are necessary for coagulation. Potassium oxalate, K 2 C 2 O 4 , is used as an anticoagulant when a blood sample is drawn for laboratory tests because it removes the calcium as a precipitate of CaC 2 O 4 •H 2 O. It is necessary to remove all but 1.0% of the Ca 2+ in serum in order to prevent coagulation. If normal blood serum with a buffered pH of 7.40 contains 9.5 mg of Ca 2+ per 100 mL of serum, what mass of K 2 C 2 O 4 is required to prevent the coagulation of a 10 mL blood sample that is 55% serum by volume? (All volumes are accurate to two significant figures. Note that the volume of serum in a 10-mL blood sample is 5.5 mL. Assume that the K sp value for CaC 2 O 4 in serum is the same as in water.)
Q15.1.X
About 50% of urinary calculi (kidney stones) consist of calcium phosphate, Ca 3 (PO 4 ) 2 . The normal mid range calcium content excreted in the urine is 0.10 g of Ca 2+ per day. The normal mid range amount of urine passed may be taken as 1.4 L per day. What is the maximum concentration of phosphate ion that urine can contain before a calculus begins to form?
S15.1.X
4 × 10 −9 M
Q15.1.X
The pH of normal urine is 6.30, and the total phosphate concentration (\(\ce{[PO4^3- ]}\) + \(\ce{[HPO4^2- ]}\) + \(\ce{[H2PO4- ]}\) + [H 3 PO 4 ]) is 0.020 M . What is the minimum concentration of Ca 2+ necessary to induce kidney stone formation? (See Exercise for additional information.)
Q15.1.X
Magnesium metal (a component of alloys used in aircraft and a reducing agent used in the production of uranium, titanium, and other active metals) is isolated from sea water by the following sequence of reactions:
\(\ce{Mg^2+}(aq)+\ce{Ca(OH)2}(aq)⟶\ce{Mg(OH)2}(s)+\ce{Ca^2+}(aq)\)
\(\ce{Mg(OH)2}(s)+\ce{2HCl}(aq)⟶\ce{MgCl2}(s)+\ce{2H2O}(l)\)
\(\ce{MgCl2}(l)\xrightarrow{\ce{electrolysis}}\ce{Mg}(s)+\ce{Cl2}(g)\)
Sea water has a density of 1.026 g/cm 3 and contains 1272 parts per million of magnesium as Mg 2+ ( aq ) by mass. What mass, in kilograms, of Ca(OH) 2 is required to precipitate 99.9% of the magnesium in 1.00 × 10 3 L of sea water?
S15.1.X
3.99 kg
Q15.1.X
Hydrogen sulfide is bubbled into a solution that is 0.10 M in both Pb 2+ and Fe 2+ and 0.30 M in HCl. After the solution has come to equilibrium it is saturated with H 2 S ([H 2 S] = 0.10 M ). What concentrations of Pb 2+ and Fe 2+ remain in the solution? For a saturated solution of H 2 S we can use the equilibrium:
\(\ce{H2S}(aq)+\ce{2H2O}(l)⇌\ce{2H3O+}(aq)+\ce{S^2-}(aq) \hspace{20px} K=1.0×10^{−26}\)
(Hint: The \(\ce{[H3O+]}\) changes as metal sulfides precipitate.)
Q15.1.X
Perform the following calculations involving concentrations of iodate ions:
- The iodate ion concentration of a saturated solution of La(IO 3 ) 3 was found to be 3.1 × 10 –3 mol/L. Find the K sp .
- Find the concentration of iodate ions in a saturated solution of Cu(IO 3 ) 2 ( K sp = 7.4 × 10 –8 ).
S15.1.X
3.1 × 10 –11 ; [Cu 2+ ] = 2.6 × 10 –3 ; \(\ce{[IO3- ]}\) = 5.3 × 10 –3
Q15.1.X
Calculate the molar solubility of AgBr in 0.035 M NaBr ( K sp = 5 × 10 –13 ).
Q15.1.X
How many grams of Pb(OH) 2 will dissolve in 500 mL of a 0.050- M PbCl 2 solution ( K sp = 1.2 × 10 –15 )?
S15.1.X
1.8 × 10 –5 g Pb(OH) 2
Q15.1.X
Use the simulation from the earlier Link to Learning to complete the following exercise:. Using 0.01 g CaF 2 , give the K sp values found in a 0.2- M solution of each of the salts. Discuss why the values change as you change soluble salts.
Q15.1.X
How many grams of Milk of Magnesia, Mg(OH) 2 ( s ) (58.3 g/mol), would be soluble in 200 mL of water. K sp = 7.1 × 10 –12 . Include the ionic reaction and the expression for K sp in your answer. ( K w = 1 × 10 –14 = [H 3 O + ][OH – ])
S15.1.X
\[\ce{Mg(OH)2}(s)⇌\ce{Mg^2+}+\ce{2OH-} \]
\[K_\ce{sp}=\ce{[Mg^2+][OH- ]^2}\]
\[1.14 × 10 −3 g Mg(OH) 2\]
Q15.1.X
Two hypothetical salts, LM 2 and LQ, have the same molar solubility in H 2 O. If K sp for LM 2 is 3.20 × 10 –5 , what is the K sp value for LQ?
Q15.1.X
Which of the following carbonates will form first? Which of the following will form last? Explain.
- \(\ce{MgCO3} \hspace{20px} K_\ce{sp}=3.5×10^{−8}\)
- \(\ce{CaCO3} \hspace{20px} K_\ce{sp}=4.2×10^{−7}\)
- \(\ce{SrCO3} \hspace{20px} K_\ce{sp}=3.9×10^{−9}\)
- \(\ce{BaCO3} \hspace{20px} K_\ce{sp}=4.4×10^{−5}\)
- \(\ce{MnCO3} \hspace{20px} K_\ce{sp}=5.1×10^{−9}\)
S15.1.X
SrCO 3 will form first, since it has the smallest K sp value it is the least soluble. BaCO 3 will be the last to precipitate, it has the largest K sp value.
Q15.1.X
How many grams of Zn(CN) 2 ( s ) (117.44 g/mol) would be soluble in 100 mL of H 2 O? Include the balanced reaction and the expression for K sp in your answer. The K sp value for Zn(CN) 2 ( s ) is 3.0 × 10 –16 .
15.2: Lewis Acids and Bases
Q15.2.X
Under what circumstances, if any, does a sample of solid AgCl completely dissolve in pure water?
S15.2.X
when the amount of solid is so small that a saturated solution is not produced
Q15.2.X
Explain why the addition of NH 3 or HNO 3 to a saturated solution of Ag 2 CO 3 in contact with solid Ag 2 CO 3 increases the solubility of the solid.
Q15.2.X
Calculate the cadmium ion concentration, [Cd 2+ ], in a solution prepared by mixing 0.100 L of 0.0100 M Cd(NO 3 ) 2 with 1.150 L of 0.100 NH 3 ( aq ).
S15.2.X
2.35 × 10 –4 M
Q15.2.X
Explain why addition of NH 3 or HNO 3 to a saturated solution of Cu(OH) 2 in contact with solid Cu(OH) 2 increases the solubility of the solid.
S15.2.X
Sometimes equilibria for complex ions are described in terms of dissociation constants, K d . For the complex ion \(\ce{AlF6^3-}\) the dissociation reaction is:
\[\ce{AlF6^3- ⇌ Al^3+ + 6F-}\) and \(K_\ce{d}=\ce{\dfrac{[Al^3+][F- ]^6}{[AlF6^3- ]}}=2×10^{−24}\]
Q15.2.X
Calculate the value of the formation constant, K f , for \(\ce{AlF6^3-}\).
S15.2.X
5 × 10 23
Q15.2.X
Using the value of the formation constant for the complex ion \(\ce{Co(NH3)6^2+}\), calculate the dissociation constant.
Q15.2.X
Using the dissociation constant, K d = 7.8 × 10 –18 , calculate the equilibrium concentrations of Cd 2+ and CN – in a 0.250- M solution of \(\ce{Cd(CN)4^2-}\).
S15.2.X
[Cd 2+ ] = 9.5 × 10 –5 M ; [CN – ] = 3.8 × 10 –4 M
Q15.2.X
Using the dissociation constant, K d = 3.4 × 10 –15 , calculate the equilibrium concentrations of Zn 2+ and OH – in a 0.0465- M solution of \(\ce{Zn(OH)4^2-}\).
Q15.2.X
Using the dissociation constant, K d = 2.2 × 10 –34 , calculate the equilibrium concentrations of Co 3+ and NH 3 in a 0.500- M solution of \(\ce{Co(NH3)6^3+}\).
S15.2.X
[Co 3+ ] = 3.0 × 10 –6 M ; [NH 3 ] = 1.8 × 10 –5 M
Q15.2.X
Using the dissociation constant, K d = 1 × 10 –44 , calculate the equilibrium concentrations of Fe 3+ and CN – in a 0.333 M solution of \(\ce{Fe(CN)6^3-}\).
Q15.2.X
Calculate the mass of potassium cyanide ion that must be added to 100 mL of solution to dissolve 2.0 × 10 –2 mol of silver cyanide, AgCN.
S15.2.X
1.3 g
Q15.2.X
Calculate the minimum concentration of ammonia needed in 1.0 L of solution to dissolve 3.0 × 10 –3 mol of silver bromide.
Q15.2.X
A roll of 35-mm black and white photographic film contains about 0.27 g of unexposed AgBr before developing. What mass of Na 2 S 2 O 3 •5H 2 O (sodium thiosulfate pentahydrate or hypo) in 1.0 L of developer is required to dissolve the AgBr as \(\ce{Ag(S2O3)2^3-}\) ( K f = 4.7 × 10 13 )?
S15.2.X
0.80 g
Q15.2.X
We have seen an introductory definition of an acid: An acid is a compound that reacts with water and increases the amount of hydronium ion present. In the chapter on acids and bases, we saw two more definitions of acids: a compound that donates a proton (a hydrogen ion, H + ) to another compound is called a Brønsted-Lowry acid, and a Lewis acid is any species that can accept a pair of electrons. Explain why the introductory definition is a macroscopic definition, while the Brønsted-Lowry definition and the Lewis definition are microscopic definitions.
Q15.2.X
Write the Lewis structures of the reactants and product of each of the following equations, and identify the Lewis acid and the Lewis base in each:
- \(\ce{CO2 + OH- ⟶ HCO3-}\)
- \(\ce{B(OH)3 + OH- ⟶ B(OH)4-}\)
- \(\ce{I- + I2 ⟶ I3-}\)
- \(\ce{AlCl3 + Cl- ⟶ AlCl4-}\) (use Al-Cl single bonds)
- \(\ce{O^2- + SO3 ⟶ SO4^2-}\)
S15.2.X
(a)
;
(b)
;
(c)
;
(d)
;
(e)
Q15.2.X
Write the Lewis structures of the reactants and product of each of the following equations, and identify the Lewis acid and the Lewis base in each:
- \(\ce{CS2 + SH- ⟶ HCS3-}\)
- \(\ce{BF3 + F- ⟶ BF4-}\)
- \(\ce{I- + SnI2 ⟶ SnI3-}\)
- \(\ce{Al(OH)3 + OH- ⟶ Al(OH)4-}\)
- \(\ce{F- + SO3 ⟶ SFO3-}\)
Q15.2.X
Using Lewis structures, write balanced equations for the following reactions:
- \(\ce{HCl}(g)+\ce{PH3}(g)⟶\)
- \(\ce{H3O+ + CH3- ⟶}\)
- \(\ce{CaO + SO3 ⟶}\)
- \(\ce{NH4+ + C2H5O- ⟶}\)
S15.2.X
(a)
;
\(\ce{H3O+ + CH3- ⟶ CH4 + H2O}\)
;
\(\ce{CaO + SO3 ⟶ CaSO4}\)
;
\(\ce{NH4+ + C2H5O- ⟶ C2H5OH + NH3}\)
Q15.2.X
Calculate \(\ce{[HgCl4^2- ]}\) in a solution prepared by adding 0.0200 mol of NaCl to 0.250 L of a 0.100- M HgCl 2 solution.
Q15.2.X
In a titration of cyanide ion, 28.72 mL of 0.0100 M AgNO 3 is added before precipitation begins. [The reaction of Ag + with CN – goes to completion, producing the \(\ce{Ag(CN)2-}\) complex.] Precipitation of solid AgCN takes place when excess Ag + is added to the solution, above the amount needed to complete the formation of \(\ce{Ag(CN)2-}\). How many grams of NaCN were in the original sample?
S15.2.X
0.0281 g
Q15.2.X
What are the concentrations of Ag + , CN – , and \(\ce{Ag(CN)2-}\) in a saturated solution of AgCN?
Q15.2.X
In dilute aqueous solution HF acts as a weak acid. However, pure liquid HF (boiling point = 19.5 °C) is a strong acid. In liquid HF, HNO 3 acts like a base and accepts protons. The acidity of liquid HF can be increased by adding one of several inorganic fluorides that are Lewis acids and accept F – ion (for example, BF 3 or SbF 5 ). Write balanced chemical equations for the reaction of pure HNO 3 with pure HF and of pure HF with BF 3 .
S15.2.X
\(\ce{HNO3}(l)+\ce{HF}(l)⟶\ce{H2NO3+}+\ce{F-}\); \(\ce{HF}(l)+\ce{BF3}(g)⟶\ce{H+}+\ce{BF4}\)
Q15.2.X
The simplest amino acid is glycine, H 2 NCH 2 CO 2 H. The common feature of amino acids is that they contain the functional groups: an amine group, –NH 2 , and a carboxylic acid group, –CO 2 H. An amino acid can function as either an acid or a base. For glycine, the acid strength of the carboxyl group is about the same as that of acetic acid, CH 3 CO 2 H, and the base strength of the amino group is slightly greater than that of ammonia, NH 3 .
Q15.2.X
Write the Lewis structures of the ions that form when glycine is dissolved in 1 M HCl and in 1 M KOH.
Q15.2.X
Write the Lewis structure of glycine when this amino acid is dissolved in water. (Hint: Consider the relative base strengths of the –NH 2 and \(\ce{−CO2-}\) groups.)
Q15.2.X
Boric acid, H 3 BO 3 , is not a Brønsted-Lowry acid but a Lewis acid.
- Write an equation for its reaction with water.
- Predict the shape of the anion thus formed.
- What is the hybridization on the boron consistent with the shape you have predicted?
S15.2.X
\(\ce{H3BO3 + H2O ⟶ H4BO4- + H+}\); The electronic and molecular shapes are the same—both tetrahedral. The tetrahedral structure is consistent with sp 3 hybridization.
15.3: Multiple Equilibria
Q15.3.1
A saturated solution of a slightly soluble electrolyte in contact with some of the solid electrolyte is said to be a system in equilibrium. Explain. Why is such a system called a heterogeneous equilibrium?
Q15.3.2
Calculate the equilibrium concentration of Ni 2+ in a 1.0- M solution [Ni(NH 3 ) 6 ](NO 3 ) 2 .
S15.3.2
0.014 M
Q15.3.3
Calculate the equilibrium concentration of Zn 2+ in a 0.30- M solution of \(\ce{Zn(CN)4^2-}\).
Q15.3.4
Calculate the equilibrium concentration of Cu 2+ in a solution initially with 0.050 M Cu 2+ and 1.00 M NH 3 .
S15.3.2
1.0 × 10 –13 M
Q15.3.5
Calculate the equilibrium concentration of Zn 2+ in a solution initially with 0.150 M Zn 2+ and 2.50 M CN – .
Q15.3.6
Calculate the Fe 3+ equilibrium concentration when 0.0888 mole of K 3 [Fe(CN) 6 ] is added to a solution with 0.0.00010 M CN – .
S15.3.2
9 × 10 −22 M
Q15.3.7
Calculate the Co 2+ equilibrium concentration when 0.100 mole of [Co(NH 3 ) 6 ](NO 3 ) 2 is added to a solution with 0.025 M NH 3 . Assume the volume is 1.00 L.
Q15.3.8
The equilibrium constant for the reaction \(\ce{Hg^2+}(aq)+\ce{2Cl-}(aq)⇌\ce{HgCl2}(aq)\) is 1.6 × 10 13 . Is HgCl 2 a strong electrolyte or a weak electrolyte? What are the concentrations of Hg 2+ and Cl – in a 0.015- M solution of HgCl 2 ?
S15.3.2
6.2 × 10 –6 M = [Hg 2+ ]; 1.2 × 10 –5 M = [Cl – ]; The substance is a weak electrolyte because very little of the initial 0.015 M HgCl 2 dissolved.
Q15.3.9
Calculate the molar solubility of Sn(OH) 2 in a buffer solution containing equal concentrations of NH 3 and \(\ce{NH4+}\).
Q15.3.X
Calculate the molar solubility of Al(OH) 3 in a buffer solution with 0.100 M NH 3 and 0.400 M \(\ce{NH4+}\).
S15.3.2
[OH − ] = 4.5 × 10 −5 ; [Al 3+ ] = 2.1 × 10 –20 (molar solubility)
Q15.3.10
What is the molar solubility of CaF 2 in a 0.100- M solution of HF? K a for HF = 7.2 × 10 –4 .
Q15.3.X
What is the molar solubility of BaSO 4 in a 0.250- M solution of NaHSO 4 ? K a for \(\ce{HSO4-}\) = 1.2 × 10 –2 .
S15.3.2
- \(\ce{[SO4^2- ]}=0.049\:M\)
- [Ba 2+ ] = 2.2 × 10 –9 (molar solubility)
Q15.3.X
What is the molar solubility of Tl(OH) 3 in a 0.10- M solution of NH 3 ?
Q15.3.X
What is the molar solubility of Pb(OH) 2 in a 0.138- M solution of CH 3 NH 2 ?
S15.3.2
- [OH – ] = 7.6 × 10 −3 M
- [Pb 2+ ] = 4.8 × 10 –12 (molar solubility)
Q15.3.X
A solution of 0.075 M CoBr 2 is saturated with H 2 S ([H 2 S] = 0.10 M ). What is the minimum pH at which CoS begins to precipitate?
\(\ce{CoS}(s)⇌\ce{Co^2+}(aq)+\ce{S^2-}(aq) \hspace{20px} K_\ce{sp}=4.5×10^{−27}\)
\(\ce{H2S}(aq)+\ce{2H2O}(l)⇌\ce{2H3O+}(aq)+\ce{S^2-}(aq) \hspace{20px} K=1.0×10^{−26}\)
A 0.125- M solution of Mn(NO 3 ) 2 is saturated with H 2 S ([H 2 S] = 0.10 M ). At what pH does MnS begin to precipitate?
\(\ce{MnS}(s)⇌\ce{Mn^2+}(aq)+\ce{S^2-}(aq) \hspace{20px} K_\ce{sp}=4.3×10^{−22}\)
\(\ce{H2S}(aq)+\ce{2H2O}(l)⇌\ce{2H3O+}(aq)+\ce{S^2-}(aq) \hspace{20px} K=1.0×10^{−26}\)
S15.3.2
3.27
Q15.3.X
Calculate the molar solubility of BaF 2 in a buffer solution containing 0.20 M HF and 0.20 M NaF.
Q15.3.X
Calculate the molar solubility of CdCO 3 in a buffer solution containing 0.115 M Na 2 CO 3 and 0.120 M NaHCO 3
S15.3.2
- \(\ce{[CO3^2- ]}=0.115\:M\)
- [Cd 2+ ] = 3 × 10 −12 M
Q15.3.X
To a 0.10- M solution of Pb(NO 3 ) 2 is added enough HF( g ) to make [HF] = 0.10 M .
- Does PbF 2 precipitate from this solution? Show the calculations that support your conclusion.
- What is the minimum pH at which PbF 2 precipitates?
Calculate the concentration of Cd 2+ resulting from the dissolution of CdCO 3 in a solution that is 0.010 M in H 2 CO 3 .
S15.3.2
1 × 10 −5 M
Q15.3.X
Both AgCl and AgI dissolve in NH 3 .
- What mass of AgI dissolves in 1.0 L of 1.0 M NH 3 ?
- What mass of AgCl dissolves in 1.0 L of 1.0 M NH 3 ?
Calculate the volume of 1.50 M CH 3 CO 2 H required to dissolve a precipitate composed of 350 mg each of CaCO 3 , SrCO 3 , and BaCO 3 .
S15.3.2
0.0102 L (10.2 mL)
Q15.3.X
Even though Ca(OH) 2 is an inexpensive base, its limited solubility restricts its use. What is the pH of a saturated solution of Ca(OH) 2 ?
Q15.3.X
What mass of NaCN must be added to 1 L of 0.010 M Mg(NO 3 ) 2 in order to produce the first trace of Mg(OH) 2 ?
S15.3.2
5 × 10 −3 g
Q15.3.X
Magnesium hydroxide and magnesium citrate function as mild laxatives when they reach the small intestine. Why do magnesium hydroxide and magnesium citrate, two very different substances, have the same effect in your small intestine. (Hint: The contents of the small intestine are basic.)
Q15.3.X
The following question is taken from a Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.
Solve the following problem:
\(\ce{MgF2}(s)⇌\ce{Mg^2+}(aq)+\ce{2F-}(aq)\)
In a saturated solution of MgF 2 at 18 °C, the concentration of Mg 2+ is 1.21 × 10 –3 M . The equilibrium is represented by the preceding equation.
- Write the expression for the solubility-product constant, K sp , and calculate its value at 18 °C.
- Calculate the equilibrium concentration of Mg 2+ in 1.000 L of saturated MgF 2 solution at 18 °C to which 0.100 mol of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible.
- Predict whether a precipitate of MgF 2 will form when 100.0 mL of a 3.00 × 10 –3 - M solution of Mg(NO 3 ) 2 is mixed with 200.0 mL of a 2.00 × 10 –3 - M solution of NaF at 18 °C. Show the calculations to support your prediction.
- At 27 °C the concentration of Mg 2+ in a saturated solution of MgF 2 is 1.17 × 10 –3 M . Is the dissolving of MgF 2 in water an endothermic or an exothermic process? Give an explanation to support your conclusion.
S15.3.2
K sp = [Mg 2+ ][F – ] 2 = (1.21 × 10 –3 )(2 × 1.21 × 10 –3 ) 2 = 7.09 × 10 –9 ; 7.09 × 10 –7 M
Determine the concentration of Mg 2+ and F – that will be present in the final volume. Compare the value of the ion product [Mg 2+ ][F – ] 2 with K sp . If this value is larger than K sp , precipitation will occur. 0.1000 L × 3.00 × 10 –3 M Mg(NO 3 ) 2 = 0.3000 L × M Mg(NO 3 ) 2 M Mg(NO 3 ) 2 = 1.00 × 10 –3 M 0.2000 L × 2.00 × 10 –3 M NaF = 0.3000 L × M NaF M NaF = 1.33 × 10 –3 M ion product = (1.00 × 10 –3 )(1.33 × 10 –3 ) 2 = 1.77 × 10 –9 This value is smaller than K sp , so no precipitation will occur. MgF 2 is less soluble at 27 °C than at 18 °C. Because added heat acts like an added reagent, when it appears on the product side, the Le Chatelier’s principle states that the equilibrium will shift to the reactants’ side to counter the stress. Consequently, less reagent will dissolve. This situation is found in our case. Therefore, the reaction is exothermic.
Q15.3.X
Which of the following compounds, when dissolved in a 0.01- M solution of HClO 4 , has a solubility greater than in pure water: CuCl, CaCO 3 , MnS, PbBr 2 , CaF 2 ? Explain your answer.
Q15.3.X
Which of the following compounds, when dissolved in a 0.01- M solution of HClO 4 , has a solubility greater than in pure water: AgBr, BaF 2 , Ca 3 (PO 4 ) 3 , ZnS, PbI 2 ? Explain your answer.
BaF 2 , Ca 3 (PO 4 ) 2 , ZnS; each is a salt of a weak acid, and the \(\ce{[H3O+]}\) from perchloric acid reduces the equilibrium concentration of the anion, thereby increasing the concentration of the cations
Q15.3.X
What is the effect on the amount of solid Mg(OH) 2 that dissolves and the concentrations of Mg 2+ and OH – when each of the following are added to a mixture of solid Mg(OH) 2 and water at equilibrium?
- MgCl 2
- KOH
- HClO 4
- NaNO 3
- Mg(OH) 2
Q15.3.X
What is the effect on the amount of CaHPO 4 that dissolves and the concentrations of Ca 2+ and \(\ce{HPO4-}\) when each of the following are added to a mixture of solid CaHPO 4 and water at equilibrium?
- CaCl 2
- HCl
- KClO 4
- NaOH
- CaHPO 4
S15.3.X
Effect on amount of solid CaHPO 4 , [Ca 2+ ], [OH – ]: increase, increase, decrease; decrease, increase, decrease; no effect, no effect, no effect; decrease, increase, decrease; increase, no effect, no effect
Q15.3.X
Identify all chemical species present in an aqueous solution of Ca 3 (PO 4 ) 2 and list these species in decreasing order of their concentrations. (Hint: Remember that the \(\ce{PO4^3-}\) ion is a weak base.)
Q15.3.X
A volume of 50 mL of 1.8 M NH 3 is mixed with an equal volume of a solution containing 0.95 g of MgCl 2 . What mass of NH 4 Cl must be added to the resulting solution to prevent the precipitation of Mg(OH) 2 ?
S15.3.X
7.1 g