Chemistry An Atoms First Approach

Steven S. Zumdahl, Susan A. Zumdahl

Chapter 15

Solubility and Complex lon Equilibria - all with Video Answers

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Chapter Questions

Problem 1

Which of the following will affect the total amount of solute that can dissolve in a given amount of solvent?
a. The solution is stirred.
b. The solute is ground to fine particles before dissolving.
c. The temperature changes.

Stephanie L

Stephanie L

Numerade Educator

Problem 2

Devise as many ways as you can to experimentally determine the $K_{\mathrm{sp}}$ value of a solid. Explain why each of these would work.

Sisi Gao

Numerade Educator

Problem 3

You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a $K_{\mathrm{sp}}$ value of zero in water at $25^{\circ} \mathrm{C}$. What does this mean?

David Collins

Numerade Educator

Problem 4

A friend tells you: "The constant $K_{\mathrm{sp}}$ of a salt is called the solubility product constant and is calculated from the concentrations of ions in the solution. Thus, if salt A dissolves to a greater extent than salt $\mathbf{B}$, salt $\mathbf{A}$ must have a higher $K_{\mathrm{sp}}$ than salt $\mathbf{B}$." Do you agree with your friend? Explain.

Ly Tran

Numerade Educator

Problem 5

Explain the following phenomenon: You have a test tube with an aqueous solution of silver nitrate as shown in test tube 1 below. A few drops of aqueous sodium chromate solution was added with the end result shown in test tube $2 .$ A few drops of aqueous sodium chloride solution was then added with the end result shown in test tube 3.
Use the $K_{\mathrm{sp}}$ values in the book to support your explanation, and include the balanced equations. Also, list the ions that are present in solution in each test tube.

David Collins

Numerade Educator

Problem 6

What happens to the $K_{\mathrm{sp}}$ value of a solid as the temperature of the solution changes? Consider both increasing and decreasing temperatures, and explain your answer.

Ly Tran

Numerade Educator

Problem 7

Which is more likely to dissolve in an acidic solution, silver sulfide or silver chloride? Why?

David Collins

Numerade Educator

Problem 8

For which of the following is the $K_{\mathrm{sp}}$ value of the ionic compound the largest? The smallest? Explain your answer.

Aadit Sharma

Numerade Educator

Problem 9

$\mathrm{Ag}_{2} \mathrm{S}(s)$ has a larger molar solubility than CuS even though $\mathrm{Ag}_{2} \mathrm{S}$ has the smaller $K_{\mathrm{sp}}$ value. Explain how this is possible.

David Collins

Numerade Educator

Problem 10

Solubility is an equilibrium position, whereas $K_{\mathrm{sp}}$ is an equilibrium constant. Explain the difference.

Sisi Gao

Numerade Educator

Problem 11

The salts in Table $15-1,$ with the possible exception of the hydroxide salts, generally have one of the following mathematical relationships between the $K_{\mathrm{sp}}$ value and the molar solubility $s$.
i. $K_{\mathrm{sp}}=s^{2}$
ii. $K_{\mathrm{sp}}=4 s^{3}$
iii. $K_{\mathrm{sp}}=27 s^{4}$
iv. $K_{\mathrm{sp}}=108 s^{5}$
For each mathematical relationship, give an example of a salt in Table $15-1$ that exhibits that relationship.

David Collins

Numerade Educator

Problem 12

When $\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)$ is added to a solution containing a metal ion and a precipitate forms, the precipitate generally could be one of two possibilities. What are the two possibilities?

Ly Tran

Numerade Educator

Problem 13

The common ion effect for ionic solids (salts) is to significantly decrease the solubility of the ionic compound in water. Explain the common ion effect.

David Collins

Numerade Educator

Problem 14

Sulfide precipitates are generally grouped as sulfides insoluble in acidic solution and sulfides insoluble in basic solution. Explain why there is a difference between the two groups of sulfide precipitates.

Ly Tran

Numerade Educator

Problem 15

List some ways one can increase the solubility of a salt in water.

David Collins

Numerade Educator

Problem 16

The stepwise formation constants for a complex ion usually have values much greater than $1 .$ What is the significance of this?

Rashmi Sinha

Numerade Educator

Problem 17

Silver chloride dissolves readily in $2 M \mathrm{NH}_{3}$ but is quite insoluble in $2 M \mathrm{NH}_{4} \mathrm{NO}_{3} .$ Explain.

David Collins

Numerade Educator

Problem 18

If a solution contains either $\mathrm{Pb}^{2+}(a q)$ or $\mathrm{Ag}^{+}(a q),$ how can temperature be manipulated to help identify the ion in solution?

Sisi Gao

Numerade Educator

Problem 19

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids.
a. $\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}$
b. $\mathrm{Al}(\mathrm{OH})_{3}$
c. $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$

Stephanie L

Numerade Educator

Problem 20

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids.
a. $\mathrm{Ag}_{2} \mathrm{CO}_{3}$
b. $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}$
c. $\mathrm{BaF}_{2}$

Ly Tran

Numerade Educator

Problem 21

Use the following data to calculate the $K_{\mathrm{sp}}$ value for each solid.
a. The solubility of $\mathrm{CaC}_{2} \mathrm{O}_{4}$ is $4.8 \times 10^{-5} \mathrm{mol} / \mathrm{L}$
b. The solubility of $\mathrm{BiI}_{3}$ is $1.32 \times 10^{-5} \mathrm{mol} / \mathrm{L}$

Stephanie L

Numerade Educator

Problem 22

Use the following data to calculate the $K_{\mathrm{sp}}$ value for each solid.
a. The solubility of $\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ is $6.2 \times 10^{-12} \mathrm{mol} / \mathrm{L}$.
b. The solubility of $\mathrm{Li}_{2} \mathrm{CO}_{3}$ is $7.4 \times 10^{-2} \mathrm{mol} / \mathrm{L}$.

Ly Tran

Numerade Educator

Problem 23

Approximately 0.14 g nickel(II) hydroxide, $\mathrm{Ni}(\mathrm{OH})_{2}(s),$ dissolves per liter of water at $20^{\circ} \mathrm{C}$. Calculate $K_{\mathrm{sp}}$ for $\mathrm{Ni}(\mathrm{OH})_{2}(s)$ at this temperature.

David Collins

Numerade Educator

Problem 24

The solubility of the ionic compound $\mathrm{M}_{2} \mathrm{X}_{3},$ having a molar mass of $288 \mathrm{g} / \mathrm{mol},$ is $3.60 \times 10^{-7} \mathrm{g} / \mathrm{L} .$ Calculate the $K_{\mathrm{sp}}$ of the compound.

Ly Tran

Numerade Educator

Problem 25

The concentration of $\mathrm{Pb}^{2+}$ in a solution saturated with $\mathrm{PbBr}_{2}(s)$ is $2.14 \times 10^{-2} \mathrm{M} .$ Calculate $K_{\mathrm{sp}}$ for $\mathrm{PbBr}_{2}$.

David Collins

Numerade Educator

Problem 26

The concentration of $\mathrm{Ag}^{+}$ in a solution saturated with $\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(s)$ is $2.2 \times 10^{-4} \mathrm{M} .$ Calculate $K_{\mathrm{sp}}$ for $\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}$.

Ly Tran

Numerade Educator

Problem 27

Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid-base properties.
a. $\mathrm{Ag}_{3} \mathrm{PO}_{4}, K_{\mathrm{sp}}=1.8 \times 10^{-18}$
b. $\mathrm{CaCO}_{3}, K_{\mathrm{sp}}=8.7 \times 10^{-9}$
c. $\mathrm{Hg}_{2} \mathrm{Cl}_{2}, K_{\mathrm{sp}}=1.1 \times 10^{-18}$ $\left(\mathrm{Hg}_{2}^{2+}\right.$is the cation in solution.)

David Collins

Numerade Educator

Problem 28

Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid-base properties.
a. $\mathrm{PbI}_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-8}$
b. $\mathrm{CdCO}_{3}, K_{\mathrm{sp}}=5.2 \times 10^{-12}$
c. $\operatorname{Sr}_{3}\left(\mathrm{PO}_{4}\right)_{2}, K_{\mathrm{sp}}=1 \times 10^{-31}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 29

Cream of tartar, a common ingredient in cooking, is the common name for potassium bitartrate (abbreviated KBT, molar mass $=188.2 \mathrm{g} / \mathrm{mol}$ ). Historically, KBT was a crystalline solid that formed on the casks of wine barrels during the fermentation process. Calculate the maximum mass of KBT that can dissolve in $250.0 \mathrm{mL}$ of solution to make a saturated solution. The $K_{\mathrm{sp}}$ value for $\mathrm{KBT}$ is $3.8 \times 10^{-4}$.

David Collins

Numerade Educator

Problem 30

Barium sulfate is a contrast agent for X-ray scans that are most often associated with the gastrointestinal tract. Calculate the mass of $\mathrm{BaSO}_{4}$that can dissolve in $100.0 \mathrm{mL}$ of solution. The $K_{\mathrm{sp}}$ value for $\mathrm{BaSO}_{4}$ is $1.5 \times 10^{-9}$.

Rashmi Sinha

Numerade Educator

Problem 31

Calculate the molar solubility of $\mathrm{Mg}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=8.9 \times 10^{-12}$.

Stephanie L

Numerade Educator

Problem 32

Calculate the molar solubility of $\mathrm{Cd}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=5.9 \times 10^{-11}$.

Rashmi Sinha

Numerade Educator

Problem 33

Calculate the molar solubility of $\mathrm{Al}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2 \times 10^{-32}$.

David Collins

Numerade Educator

Problem 34

Calculate the molar solubility of $\mathrm{Co}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2.5 \times 10^{-43}$.

Sisi Gao

Numerade Educator

Problem 35

For each of the following pairs of solids, determine which solid has the smallest molar solubility.
a. $\mathrm{CaF}_{2}(s), K_{\mathrm{sp}}=4.0 \times 10^{-11},$ or $\mathrm{BaF}_{2}(s), K_{\mathrm{sp}}=2.4 \times 10^{-5}$
b. $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s), K_{\mathrm{sp}}=1.3 \times 10^{-32},$ or $\mathrm{FePO}_{4}(s)$ $K_{\mathrm{sp}}=1.0 \times 10^{-22}$

Aadit Sharma

Numerade Educator

Problem 36

For each of the following pairs of solids, determine which solid has the smallest molar solubility.
a. $\mathrm{FeC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.1 \times 10^{-7},$ or $\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-7}$
b. $\mathrm{Ag}_{2} \mathrm{CO}_{3}, K_{\mathrm{sp}}=8.1 \times 10^{-12},$ or $\mathrm{Mn}(\mathrm{OH})_{2}$ $K_{\mathrm{sp}}=2 \times 10^{-13}$

Sisi Gao

Numerade Educator

Problem 37

Calculate the solubility (in moles per liter) of $\mathrm{Fe}(\mathrm{OH})_{3}$ $\left(K_{\mathrm{sp}}=4 \times 10^{-38}\right)$ in each of the following.
a. water
b. a solution buffered at $\mathrm{pH}=5.0$
c. a solution buffered at $\mathrm{pH}=11.0$

David Collins

Numerade Educator

Problem 38

Calculate the solubility of $\operatorname{Co}(\mathrm{OH})_{2}(s)\left(K_{\mathrm{sp}}=2.5 \times 10^{-16}\right)$ in a buffered solution with a pH of $11.00 .$

Sisi Gao

Numerade Educator

Problem 39

The $K_{\mathrm{sp}}$ for silver sulfate $\left(\mathrm{Ag}_{2} \mathrm{SO}_{4}\right)$ is $1.2 \times 10^{-5} .$ Calculate the solubility of silver sulfate in each of the following.
a. water
b. $0.10 M$ AgNO $_{3}$
c. $0.20 M \mathrm{K}_{2} \mathrm{SO}_{4}$

David Collins

Numerade Educator

Problem 40

The $K_{\mathrm{sp}}$ for lead iodide $\left(\mathrm{PbI}_{2}\right)$ is $1.4 \times 10^{-8} .$ Calculate the solubility of lead iodide in each of the following.
a. water
b. $0.10 M \operatorname{Pb}\left(\mathrm{NO}_{3}\right)_{2}$
c. $0.010 M$ NaI

Rashmi Sinha

Numerade Educator

Problem 41

Calculate the solubility of solid $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(K_{\mathrm{sp}}=1.3 \times 10^{-32}\right)$ in a $0.20-M \mathrm{Na}_{3} \mathrm{PO}_{4}$ solution.

David Collins

Numerade Educator

Problem 42

Calculate the solubility of solid $\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(K_{\mathrm{sp}}=1 \times 10^{-54}\right)$ in a $0.10-M \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ solution.

Sisi Gao

Numerade Educator

Problem 43

The solubility of $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}$ in a $0.20-M$ KIO $_{3}$ solution is $4.4 \times 10^{-8} \mathrm{mol} / \mathrm{L} .$ Calculate $K_{\mathrm{sp}}$ for $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}$.

David Collins

Numerade Educator

Problem 44

The solubility of $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)$ in a $0.10-M \mathrm{KIO}_{3}$ solution is $2.6 \times 10^{-11} \mathrm{mol} / \mathrm{L} .$ Calculate $K_{\mathrm{sp}}$ for $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)$.

Sisi Gao

Numerade Educator

Problem 45

Which of the substances in Exercises 27 and 28 show increased solubility as the $\mathrm{pH}$ of the solution becomes more acidic? Write equations for the reactions that occur to increase the solubility.

David Collins

Numerade Educator

Problem 46

For which salt in each of the following groups will the solubility depend on pH?
a. $\mathrm{AgF}, \mathrm{AgCl}, \mathrm{AgBr}$
b. $\mathrm{Pb}(\mathrm{OH})_{2}, \mathrm{PbCl}_{2}$
c. $\operatorname{Sr}\left(\mathrm{NO}_{3}\right)_{2}, \operatorname{Sr}\left(\mathrm{NO}_{2}\right)_{2}$
d. $\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{Ni}(\mathrm{CN})_{2}$

Rashmi Sinha

Numerade Educator

Problem 47

What mass of ZnS $\left(K_{\mathrm{sp}}=2.5 \times 10^{-22}\right)$ will dissolve in $300.0 \mathrm{mL}$ of $0.050 \mathrm{M} \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} ?$ Ignore the basic properties of $\mathrm{S}^{2-}$.

David Collins

Numerade Educator

Problem 48

The concentration of $\mathrm{Mg}^{2+}$ in seawater is $0.052 \mathrm{M}$. At what $\mathrm{pH}$ will $99 \%$ of the $\mathrm{Mg}^{2+}$ be precipitated as the hydroxide salt? $\left[K_{\mathrm{sp}} \text { for } \mathrm{Mg}(\mathrm{OH})_{2}=8.9 \times 10^{-12} .\right]$

Sisi Gao

Numerade Educator

Problem 49

Will a precipitate form when $100.0 \mathrm{mL}$ of $4.0 \times 10^{-4} \mathrm{M}$ $\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ is added to $100.0 \mathrm{mL}$ of $2.0 \times 10^{-4}$ $M$ $\mathrm{NaOH} ?$

David Collins

Numerade Educator

Problem 50

A solution contains $1.0 \times 10^{-5} M \mathrm{Ag}^{+}$ and $2.0 \times 10^{-6} M \mathrm{CN}^{-}$ Will AgCN( $s$ ) precipitate? $\left(K_{\mathrm{sp}} \text { for } \mathrm{AgCN}(s) \text { is } 2.2 \times 10^{-12} .\right)$

Rashmi Sinha

Numerade Educator

Problem 51

$100.0 \mathrm{mL}$ of $1.0 \times 10^{-2}$ $M$ $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ and $100.0 \mathrm{mL}$ of $1.0 \times 10^{-3} \mathrm{M}$ NaF. Will $\mathrm{PbF}_{2}(s)$ $\left(K_{\mathrm{sp}}=4 \times 10^{-8}\right)$ precipitate?

David Collins

Numerade Educator

Problem 52

A solution contains $2.0 \times 10^{-3} M \mathrm{Ce}^{3+}$ and $1.0 \times 10^{-2} M$ IO $_{3}^{3-}$ Will $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}(s)$ $\left[K_{\mathrm{sp}} \text { for } \mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3} \text { is } 3.2 \times 10^{-10} .\right]$

Rashmi Sinha

Numerade Educator

Problem 53

Calculate the final concentrations of $\mathrm{K}^{+}(a q), \mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q)$,$\mathrm{Ba}^{2+}(a q),$ and $\mathrm{Br}^{-}(a q)$ in a solution prepared by adding $0.100 \mathrm{L}$ of $0.200 M \mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}$ to $0.150 \mathrm{L}$ of $0.250 M \mathrm{BaBr}_{2}$. (For $\left.\mathrm{BaC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.3 \times 10^{-8} .\right)$

David Collins

Numerade Educator

Problem 54

A solution is prepared by mixing $75.0 \mathrm{mL}$ of $0.020$ $M$ $\mathrm{BaCl}_{2}$ and $125 \mathrm{mL}$ of $0.040$ $M$ $\mathrm{K}_{2} \mathrm{SO}_{4}$. What are the concentrations of barium and sulfate ions in this solution? Assume only $\mathrm{SO}_{4}^{2-}$ ions $\left(\text { no } \mathrm{HSO}_{4}^{-}\right)$ are present.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 55

A 50.0 -mL sample of $0.00200$ $M$ $\mathrm{AgNO}_{3}$ is added to $50.0 \mathrm{mL}$ of 0.0100 $M \mathrm{NaIO}_{3} .$ What is the equilibrium concentration of $\mathrm{Ag}^{+}$ in solution? $\left(K_{\mathrm{sp}} \text { for } \mathrm{AgIO}_{3} \text { is } 3.0 \times 10^{-8} .\right)$

Gina Sporleder

Numerade Educator

Problem 56

A solution is prepared by mixing $50.0 \mathrm{mL}$ of $0.10$ $M$ $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ with $50.0 \mathrm{mL}$ of $1.0 \mathrm{M}$ KCl. Calculate the concentrations of $\mathrm{Pb}^{2+}$ and $\mathrm{Cl}^{-}$ at equilibrium. $\left[K_{\mathrm{sp}} \text { for } \mathrm{PbCl}_{2}(s) \text { is } 1.6 \times 10^{-5} .\right]$

Rashmi Sinha

Numerade Educator

Problem 57

A solution contains $1.0 \times 10^{-5} M \mathrm{Na}_{3} \mathrm{PO}_{4} .$ What is the minimum concentration of $\mathrm{AgNO}_{3}$ that would cause precipitation of solid $\mathrm{Ag}_{3} \mathrm{PO}_{4}\left(K_{\mathrm{sp}}=1.8 \times 10^{-18}\right) ?$

David Collins

Numerade Educator

Problem 58

The $K_{\mathrm{sp}}$ of $\mathrm{Al}(\mathrm{OH})_{3}$ is $2 \times 10^{-32} .$ At what $\mathrm{pH}$ will a $0.2-M$ $\mathrm{Al}^{3+}$ solution begin to show precipitation of $\mathrm{Al}(\mathrm{OH})_{3} ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 59

A solution is $1 \times 10^{-4} M$ in $\mathrm{NaF}, \mathrm{Na}_{2} \mathrm{S},$ and $\mathrm{Na}_{3} \mathrm{PO}_{4} .$ What would be the order of precipitation as a source of $\mathrm{Pb}^{2+}$ is added gradually to the solution? The relevant $K_{\mathrm{sp}}$ values are $K_{\mathrm{sp}}\left(\mathrm{PbF}_{2}\right)$ $=4 \times 10^{-8}, K_{\mathrm{sp}}(\mathrm{PbS})=7 \times 10^{-29},$ and $K_{\mathrm{sp}}\left[\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right]=$
$1 \times 10^{-54}$.

David Collins

Numerade Educator

Problem 60

A solution contains $0.25$ $M$ $\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}$ and $0.25 M \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ Can the metal ions be separated by slowly adding $\mathrm{Na}_{2} \mathrm{CO}_{3} ?$ Assume that for successful separation $99 \%$ of the metal ion must be precipitated before the other metal ion begins to precipitate, and assume no volume change on addition of $\mathrm{Na}_{2} \mathrm{CO}_{3}$.

David Collins

Numerade Educator

Problem 61

Write equations for the stepwise formation of each of the following complex ions.
a. $\mathrm{Ni}(\mathrm{CN})_{4}^{2-}$
b. $\mathrm{V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}^{3-}$

David Collins

Numerade Educator

Problem 62

Write equations for the stepwise formation of each of the following complex ions.
a. $\mathrm{CoF}_{6}^{3-}$
b. $\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$

Rashmi Sinha

Numerade Educator

Problem 63

In the presence of $\mathrm{CN}^{-}, \mathrm{Fe}^{3+}$ forms the complex ion $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}$ The equilibrium concentrations of $\mathrm{Fe}^{3+}$ and $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}$ are $8.5 \times 10^{-40} M$ and $1.5 \times 10^{-3} M,$ respectively, in a $0.11-M$ KCN solution. Calculate the value for the overall formation constant of $\mathrm{Fe}(\mathrm{CN})_{6}^{3-}$
$$\mathrm{Fe}^{3+}(a q)+6 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Fe}(\mathrm{CN})_{6}^{3-}(a q) \quad K_{\mathrm{overall}}=?$$

David Collins

Numerade Educator

Problem 64

In the presence of $\mathrm{NH}_{3}, \mathrm{Cu}^{2+}$ forms the complex ion $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+} .$ If the equilibrium concentrations of $\mathrm{Cu}^{2+}$ and $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$ are $1.8 \times 10^{-17} M$ and $1.0 \times 10^{-3} M,$ respectively, in a $1.5-M \mathrm{NH}_{3}$ solution, calculate the value for the overall formation constant of $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$.
$$\mathrm{Cu}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q) \quad K_{\mathrm{overall}}=?$$

Sisi Gao

Numerade Educator

Problem 65

When aqueous KI is added gradually to mercury(II) nitrate, an orange precipitate forms. Continued addition of KI causes the precipitate to dissolve. Write balanced equations to explain these observations. (Hint: $\mathrm{Hg}^{2+}$ reacts with $\mathrm{I}^{-}$ to form $\mathrm{Hg} \mathrm{I}_{4}^{2-} .$ )

David Collins

Numerade Educator

Problem 66

As sodium chloride solution is added to a solution of silver nitrate, a white precipitate forms. Ammonia is added to the mixture and the precipitate dissolves. When potassium bromide solution is then added, a pale yellow precipitate appears. When a solution of sodium thiosulfate is added, the yellow precipitate dissolves. Finally, potassium iodide is added to the solution and a yellow precipitate forms. Write equations for all the changes mentioned above. What conclusions can you draw concerning the sizes of the $K_{\mathrm{sp}}$ values for $\mathrm{AgCl}, \mathrm{AgBr},$ and $\mathrm{AgI} ?$

Sisi Gao

Numerade Educator

Problem 67

The overall formation constant for $\mathrm{HgI}_{4}^{2-}$ is $1.0 \times 10^{30}$ That is,
$$
1.0 \times 10^{30}=\frac{\left[\mathrm{HgI}_{4}^{2-}\right]}{\left[\mathrm{Hg}^{2+}\right]\left[\mathrm{I}^{-}\right]^{4}}
$$
What is the concentration of $\mathrm{Hg}^{2+}$ in $500.0 \mathrm{mL}$ of a solution that was originally $0.010$ $M$ $\mathrm{Hg}^{2+}$ and $0.78$ $M$ $\mathrm{I}^{-} ?$ The reaction is
$$\mathrm{Hg}^{2+}(a q)+4 \mathrm{I}^{-}(a q) \rightleftharpoons \mathrm{HgI}_{4}^{2-}(a q)$$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 68

A solution is prepared by adding 0.10 mole of $\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}$ to $0.50 \mathrm{L}$ of $3.0 M \mathrm{NH}_{3} .$ Calculate $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]$ and $\left[\mathrm{Ni}^{2+}\right]$ in
this solution. $K_{\text {overall }}$ for $\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}$ is $5.5 \times 10^{8} .$ That is,
$$5.5 \times 10^{8}=\frac{\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]}{\left[\mathrm{Ni}^{2+}\right]\left[\mathrm{NH}_{3}\right]^{6}}$$
for the overall reaction
$$
\mathrm{Ni}^{2+}(a q)+6 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}(a q)
$$

Sisi Gao

Numerade Educator

Problem 69

A solution is formed by mixing $50.0 \mathrm{mL}$ of $10.0 \mathrm{M}$ NaX with $50.0 \mathrm{mL}$ of $2.0 \times 10^{-3} \mathrm{M} \mathrm{CuNO}_{3} .$ Assume that $\mathrm{Cu}^{+}$ forms complex ions with $X^{-}$ as follows:
$$\mathrm{Cu}^{+}(a q)+\mathrm{X}^{-}(a q) \rightleftharpoons \mathrm{CuX}(a q) \quad K_{1}=1.0 \times 10^{2}$$
$$\mathrm{CuX}(a q)+\mathrm{X}^{-}(a q) \rightleftharpoons \mathrm{CuX}_{2}^{-}(a q) \quad K_{2}=1.0 \times 10^{4}$$
$$\mathrm{CuX}_{2}^{-}(a q)+\mathrm{X}^{-}(a q) \rightleftharpoons \mathrm{CuX}_{3}^{2-}(a q) \quad K_{3}=1.0 \times 10^{3}$$
with an overall reaction
$$\mathrm{Cu}^{+}(a q)+3 \mathrm{X}^{-}(a q) \rightleftharpoons \mathrm{CuX}_{3}^{2-}(a q) \quad K=1.0 \times 10^{9}$$
Calculate the following concentrations at equilibrium.
a. $\mathrm{CuX}_{3}^{2-}$
b. $\mathrm{CuX}_{2}^{-}$
c. $\mathrm{Cu}^{+}$

David Collins

Numerade Educator

Problem 70

A solution is prepared by mixing $100.0 \mathrm{mL}$ of $1.0 \times 10^{-4} \mathrm{M}$ $\mathrm{Be}\left(\mathrm{NO}_{3}\right)_{2}$ and $100.0 \mathrm{mL}$ of $8.0 M \mathrm{NaF}$.
$$\mathrm{Be}^{2+}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}^{+}(a q) \quad K_{1}=7.9 \times 10^{4}$$
$$\mathrm{BeF}^{+}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{2}(a q) \quad K_{2}=5.8 \times 10^{3}$$
$$\operatorname{BeF}_{2}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{3}^{-}(a q) \quad K_{3}=6.1 \times 10^{2}$$
$$\mathrm{BeF}_{3}^{-}(a q)+\mathrm{F}^{-}(a q) \rightleftharpoons \mathrm{BeF}_{4}^{2-}(a q) \quad K_{4}=2.7 \times 10^{1}$$
Calculate the equilibrium concentrations of $\mathrm{F}^{-}, \mathrm{Be}^{2+}, \mathrm{BeF}^{+}$ $\mathrm{BeF}_{2}, \mathrm{BeF}_{3}^{-},$ and $\mathrm{BeF}_{4}^{2-}$ in this solution.

Sisi Gao

Numerade Educator

Problem 71

a. Calculate the molar solubility of AgI in pure water. $K_{\mathrm{sp}}$ for AgI is $1.5 \times 10^{-16}$
b. Calculate the molar solubility of AgI in 3.0 $M \mathrm{NH}_{3}$. The overall formation constant for $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}$ is $1.7 \times 10^{7}$.
c. Compare the calculated solubilities from parts a and b. Explain any differences.

David Collins

Numerade Educator

Problem 72

Solutions of sodium thiosulfate are used to dissolve unexposed $\operatorname{AgBr}\left(K_{\mathrm{sp}}=5.0 \times 10^{-13}\right)$ in the developing process for blackand-white film. What mass of AgBr can dissolve in $1.00 \mathrm{L}$ of $0.500 M \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} ? \mathrm{Ag}^{+}$ reacts with $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}$ to form a complex ion:
$$\begin{aligned}
\mathrm{Ag}^{+}(a q)+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}^{3-}(a q) & \\
K &=2.9 \times 10^{13}
\end{aligned}$$

David Collins

Numerade Educator

Problem 73

$K_{\mathrm{f}}$ for the complex ion $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}$ is $1.7 \times 10^{7} . K_{\mathrm{sp}}$ for $\mathrm{AgCl}$ is $1.6 \times 10^{-10} .$ Calculate the molar solubility of $\mathrm{AgCl}$ in $1.0 M \mathrm{NH}_{3}$.

David Collins

Numerade Educator

Problem 74

The copper(I) ion forms a chloride salt that has $K_{\mathrm{sp}}=1.2 \times$ $10^{-6} .$ Copper(I) also forms a complex ion with $\mathrm{Cl}^{-}:$
$$\mathrm{Cu}^{+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{CuCl}_{2}^{-}(a q) \quad K=8.7 \times 10^{4}$$
a. Calculate the solubility of copper(I) chloride in pure water. (Ignore $\mathrm{CuCl}_{2}^{-}$ formation for part a.)
b. Calculate the solubility of copper(I) chloride in $0.10 M$ NaCl.

Sisi Gao

Numerade Educator

Problem 75

A series of chemicals were added to some $\mathrm{AgNO}_{3}(a q)$ NaCl(aq). was added first to the silver nitrate solution with the end result shown below in test tube $1, \mathrm{NH}_{3}(a q)$ was then added with the end result shown in test tube $2,$ and $\mathrm{HNO}_{3}(a q)$ was added last with the end result shown in test tube $3 .$
Explain the results shown in each test tube. Include a balanced equation for the reaction(s) taking place.

David Collins

Numerade Educator

Problem 76

The solubility of copper(II) hydroxide in water can be increased by adding either the base $\mathrm{NH}_{3}$ or the acid HNO $_{3}$. Explain. Would added $\mathrm{NH}_{3}$ or $\mathrm{HNO}_{3}$ have the same effect on the solubility of silver acetate or silver chloride? Explain.

Sisi Gao

Numerade Educator

Problem 77

A solution contains 0.018 molel each of $\mathrm{I}^{-}, \mathrm{Br}^{-},$ and $\mathrm{Cl}^{-}$. When the solution is mixed with $200 . \mathrm{mL}$ of $0.24$ $M$ $\mathrm{AgNO}_{3}$, what mass of $\mathrm{AgCl}(s)$ precipitates out, and what is $\left[\mathrm{Ag}^{+}\right] ?$ Assume no volume change.
$$\begin{aligned}
\operatorname{AgI}: K_{\mathrm{sp}} &=1.5 \times 10^{-16} \\
\operatorname{AgBr}: K_{\mathrm{sp}} &=5.0 \times 10^{-13} \\
\mathrm{AgCl}: K_{\mathrm{sp}} &=1.6 \times 10^{-10}
\end{aligned}$$

David Collins

Numerade Educator

Problem 78

You have two salts, AgX and AgY, with very similar $K_{\mathrm{sp}}$ values. You know that $K_{\mathrm{a}}$ for $\mathrm{HX}$ is much greater than $K_{\mathrm{a}}$ for HY. Which salt is more soluble in acidic solution? Explain.

Rashmi Sinha

Numerade Educator

Problem 79

Tooth enamel is composed of the mineral hydroxyapatite. The $K_{\mathrm{sp}}$ of hydroxyapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH},$ is $6.8 \times 10^{-37} .$ Calculate
the solubility of hydroxyapatite in pure water in moles per liter. How is the solubility of hydroxyapatite affected by adding acid? When hydroxyapatite is treated with fluoride, the mineral fluorapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F},$ forms. The $K_{\mathrm{sp}}$ of this substance is $1 \times 10^{-60} .$ Calculate the solubility of fluorapatite in water. How do these calculations provide a rationale for the fluoridation of drinking water?

David Collins

Numerade Educator

Problem 80

The U.S. Public Health Service recommends the fluoridation of water as a means for preventing tooth decay. The recommended concentration is $1 \mathrm{mg} \mathrm{F}^{-}$ per liter. The presence of calcium ions in hard water can precipitate the added fluoride. What is the maximum molarity of calcium ions in hard water if the fluoride concentration is at the USPHS recommended level? $\left(K_{\mathrm{sp}} \text { for } \mathrm{CaF}_{2}=4.0 \times 10^{-11}\right)$

Sisi Gao

Numerade Educator

Problem 81

What mass of $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}$ must be added to $1.0 \mathrm{L}$ of a $1.0-M \mathrm{HF}$ solution to begin precipitation of $\mathrm{CaF}_{2}(s) ?$ For $\mathrm{CaF}_{2}, K_{\mathrm{sp}}=$ $4.0 \times 10^{-11}$ and $K_{\mathrm{a}}$ for $\mathrm{HF}=7.2 \times 10^{-4} .$ Assume no volume change on addition of $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(s)$.

David Collins

Numerade Educator

Problem 82

Calculate the mass of manganese hydroxide present in $1300 \mathrm{mL}$ of a saturated manganese hydroxide solution. For $\mathrm{Mn}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=$ $2.0 \times 10^{-13}$.

Rashmi Sinha

Numerade Educator

Problem 83

On a hot day, a 200.0 -mL sample of a saturated solution of $\mathrm{PbI}_{2}$ was allowed to evaporate until dry. If $240 \mathrm{mg}$ of solid $\mathrm{PbI}_{2}$ was collected after evaporation was complete, calculate the $K_{\mathrm{sp}}$ value for $\mathrm{PbI}_{2}$ on this hot day.

David Collins

Numerade Educator

Problem 84

The active ingredient of Pepto-Bismol is the compound bismuth subsalicylate, which undergoes the following dissociation when added to water:
$$\begin{aligned}
\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{7} \mathrm{H}_{4} \mathrm{O}_{3}^{2-}(a q) \\
+\mathrm{Bi}^{3+}(a q)+\mathrm{OH}^{-}(a q) & K=?
\end{aligned}$$
If the maximum amount of bismuth subsalicylate that reacts by this reaction is $3.2 \times 10^{-19} \mathrm{mol} / \mathrm{L},$ calculate the equilibrium constant for the preceding reaction.

Sisi Gao

Numerade Educator

Problem 85

$$K=\frac{\left[\mathrm{Mn}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}^{2-}\right]}{\left[\mathrm{Mn}^{2+}\right]\left[\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right]^{2}}$$

David Collins

Numerade Educator

Problem 86

The equilibrium constant for the following reaction is $1.0 \times 10^{23}:$
$$\mathrm{Cr}^{3+}(a q)+\mathrm{H}_{2} \mathrm{EDTA}^{2-}(a q) \rightleftharpoons \mathrm{CrEDTA}^{-}(a q)+2 \mathrm{H}^{+}(a q)$$
EDTA is used as a complexing agent in chemical analysis. Solutions of EDTA, usually containing the disodium salt $\mathrm{Na}_{2} \mathrm{H}_{2} \mathrm{EDTA},$ are used to treat heavy metal poisoning. Calculate $\left[\mathrm{Cr}^{3+}\right]$ at equilibrium in a solution originally $0.0010 \mathrm{M}$ in $\mathrm{Cr}^{3+}$ and $0.050 M$ in $\mathrm{H}_{2} \mathrm{EDTA}^{2-}$ and buffered at $\mathrm{pH}=6.00$.

Sisi Gao

Numerade Educator

Problem 87

Calculate the concentration of $\mathrm{Pb}^{2+}$ in each of the following.
a. a saturated solution of $\mathrm{Pb}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=1.2 \times 10^{-15}$
b. a saturated solution of $\mathrm{Pb}(\mathrm{OH})_{2}$ buffered at $\mathrm{pH}=13.00$
c. Ethylenediaminetetraacetate (EDTA $^{4-}$ ) is used as a complexing agent in chemical analysis and has the following structure:
Solutions of EDTA $^{4-}$ are used to treat heavy metal poisoning by removing the heavy metal in the form of a soluble complex ion. The reaction of EDTA $^{4-}$ with $\mathrm{Pb}^{2+}$ is
$$\begin{aligned}
\mathrm{Pb}^{2+}(a q)+\mathrm{EDTA}^{4-}(a q) \rightleftharpoons \mathrm{PbEDTA}^{2-}(a q) & \\
K &=1.1 \times 10^{18}
\end{aligned}$$
Consider a solution with 0.010 mole of $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ added to $1.0 \mathrm{L}$ of an aqueous solution buffered at $\mathrm{pH}=13.00$ and containing 0.050 $M$ $\mathrm{Na}_{4} \mathrm{EDTA}$. Does $\mathrm{Pb}(\mathrm{OH})_{2}$ precipitate from this solution?

David Collins

Numerade Educator

Problem 88

Will a precipitate of $\mathrm{Cd}(\mathrm{OH})_{2}$ form if $1.0 \mathrm{mL}$ of $1.0$ $M$ $\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}$ is added to $1.0 \mathrm{L}$ of $5.0$ $M$ $\mathrm{NH}_{3} ?$
$$\begin{array}{r}
\mathrm{Cd}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q) \\
K=1.0 \times 10^{7} \\
\mathrm{Cd}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Cd}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) \\
K_{\mathrm{sp}}=5.9 \times 10^{-15}
\end{array}$$

Sisi Gao

Numerade Educator

Problem 89

a. Using the $K_{\mathrm{sp}}$ value for $\mathrm{Cu}(\mathrm{OH})_{2}\left(1.6 \times 10^{-19}\right)$ and the overall formation constant for $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\left(1.0 \times 10^{13}\right)$ calculate the value for the equilibrium constant for the following reaction:
$$\mathrm{Cu}(\mathrm{OH})_{2}(s)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)$$
b. Use the value of the equilibrium constant you calculated in part a to calculate the solubility (in mol/L) of $\mathrm{Cu}(\mathrm{OH})_{2}$ in $5.0 M \mathrm{NH}_{3} .$ In $5.0 \mathrm{M} \mathrm{NH}_{3}$ the concentration of $\mathrm{OH}^{-}$ is $0.0095 M$.

David Collins

Numerade Educator

Problem 90

Describe how you could separate the ions in each of the following groups by selective precipitation.
a. $\mathrm{Ag}^{+}, \mathrm{Mg}^{2+}, \mathrm{Cu}^{2+}$
b. $\mathrm{Pb}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Fe}^{2+}$
c. $\mathrm{Pb}^{2+}, \mathrm{Bi}^{3+}$

Sisi Gao

Numerade Educator

Problem 91

The solubility rules outlined in Chapter 6 say that $\mathrm{Ba}(\mathrm{OH})_{2}$ $\operatorname{Sr}(\mathrm{OH})_{2},$ and $\mathrm{Ca}(\mathrm{OH})_{2}$ are marginally soluble hydroxides. Calculate the $\mathrm{pH}$ of a saturated solution of each of these marginally soluble hydroxides.

David Collins

Numerade Educator

Problem 92

In the chapter discussion of precipitate formation, we ran the precipitation reaction to completion and then let some of the precipitate redissolve to get back to equilibrium. To see why, redo Example $15-6,$ where

Sisi Gao

Numerade Educator

Problem 93

Assuming that the solubility of $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)$ is $1.6 \times 10^{-7}$ $\operatorname{mol} / \mathrm{L}$ at $25^{\circ} \mathrm{C},$ calculate the $K_{\mathrm{sp}}$ for this salt. Ignore any potential reactions of the ions with water.

David Collins

Numerade Educator

Problem 94

Order the following solids (a-d) from least soluble to most soluble. Ignore any potential reactions of the ions with water.
a. $\mathrm{AgCl} \quad K_{\mathrm{sp}}=1.6 \times 10^{-10}$
b. $\mathrm{Ag}_{2} \mathrm{S} \quad K_{\mathrm{sp}}=1.6 \times 10^{-49}$
c. $\mathrm{CaF}_{2} \quad K_{\mathrm{sp}}=4.0 \times 10^{-11}$
d. CuS $\quad K_{\mathrm{sp}}=8.5 \times 10^{-45}$

Rashmi Sinha

Numerade Educator

Problem 95

The $K_{\mathrm{sp}}$ for $\mathrm{PbI}_{2}(s)$ is $1.4 \times 10^{-8} .$ Calculate the solubility of $\mathrm{PbI}_{2}(s)$ in $0.048$ $M$ $\mathrm{NaI}$.

David Collins

Numerade Educator

Problem 96

The solubility of $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)$ in a $7.2 \times 10^{-2}-M \mathrm{KIO}_{3}$ solution is $6.0 \times 10^{-9} \mathrm{mol} / \mathrm{L} .$ Calculate the $K_{\mathrm{sp}}$ value for $\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)$.

Rashmi Sinha

Numerade Educator

Problem 97

A 50.0 -mL sample of $0.0413$ $M$ $\mathrm{AgNO}_{3}(a q)$ is added to $50.0 \mathrm{mL}$ of 0.100 $M \mathrm{NaIO}_{3}(a q) .$ Calculate the $\left[\mathrm{Ag}^{+}\right]$ at equilibrium in the resulting solution. $\left[K_{\mathrm{sp}} \text { for } \mathrm{AgIO}_{3}(s)=3.17 \times 10^{-8} .\right]$

Anand Jangid

Numerade Educator

Problem 98

The $\mathrm{Hg}^{2+}$ ion forms complex ions with $\mathrm{I}^{-}$ as follows:
$$\begin{aligned}
\mathrm{Hg}^{2+}(a q)+\mathrm{I}^{-}(a q) & \rightleftharpoons \mathrm{HgI}^{+}(a q) & & K_{1}=1.0 \times 10^{8} \\
\mathrm{HgI}^{+}(a q)+\mathrm{I}^{-}(a q) & \rightleftharpoons \mathrm{HgI}_{2}(a q) & & K_{2}=1.0 \times 10^{5} \\
\mathrm{HgI}_{2}(a q)+\mathrm{I}^{-}(a q) & \rightleftharpoons \mathrm{HgI}_{3}^{-}(a q) & & K_{3}=1.0 \times 10^{9} \\
\mathrm{HgI}_{3}^{-}(a q)+\mathrm{I}^{-}(a q) & \rightleftharpoons \mathrm{HgI}_{4}^{2-}(a q) & & K_{4}=1.0 \times 10^{8}
\end{aligned}$$
A solution is prepared by dissolving 0.088 mole of $\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}$ and 5.00 moles of NaI in enough water to make 1.0 L of solution.
a. Calculate the equilibrium concentration of $\left[\mathrm{HgI}_{4}^{2-}\right] .$
b. Calculate the equilibrium concentration of $\left[\mathrm{I}^{-}\right] .$
c. Calculate the equilibrium concentration of $\left[\mathrm{Hg}^{2+}\right]$.

Sisi Gao

Numerade Educator

Problem 99

The copper(I) ion forms a complex ion with CN $^{-}$ according to the following equation:
$$\mathrm{Cu}^{+}(a q)+3 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Cu}(\mathrm{CN})_{3}^{2-}(a q) \quad K=1.0 \times 10^{11}$$
a. Calculate the solubility of $\operatorname{CuBr}(s)\left(K_{\mathrm{sp}}=1.0 \times 10^{-5}\right)$ in 1.0 L of 1.0 $M$ NaCN.
b. Calculate the concentration of $\mathrm{Br}^{-}$ at equilibrium.
c. Calculate the concentration of $\mathrm{CN}^{-}$ at equilibrium.

David Collins

Numerade Educator

Problem 100

Consider a solution made by mixing $500.0 \mathrm{mL}$ of $4.0$ $M$ $\mathrm{NH}_{3}$ and $500.0 \mathrm{mL}$ of $0.40$ $M$ $\mathrm{AgNO}_{3} . \mathrm{Ag}^{+}$ reacts with $\mathrm{NH}_{3}$ to form $\mathrm{AgNH}_{3}^{+}$ and $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}:$
$$\begin{aligned}
\mathrm{Ag}^{+}(a q)+\mathrm{NH}_{3}(a q) & \rightleftharpoons \mathrm{AgNH}_{3}^{+}(a q) & K_{1} &=2.1 \times 10^{3} \\
\mathrm{AgNH}_{3}^{+}(a q)+\mathrm{NH}_{3}(a q) & \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q) & K_{2} &=8.2 \times 10^{3}
\end{aligned}$$
Determine the concentration of all species in solution.

Sisi Gao

Numerade Educator

Problem 101

a. Calculate the molar solubility of AgBr in pure water. $K_{\mathrm{sp}}$ for AgBr is $5.0 \times 10^{-13}$.
b. Calculate the molar solubility of $\mathrm{AgBr}$ in $3.0$ $M$ $\mathrm{NH}_{3} .$ The overall formation constant for $\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}$ is $1.7 \times 10^{7}$ that is,
$$\mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \longrightarrow \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q) \quad K=1.7 \times 10^{7}$$
c. Compare the calculated solubilities from parts a and b. Explain any differences.
d. What mass of AgBr will dissolve in $250.0 \mathrm{mL}$ of $3.0 M \mathrm{NH}_{3} ?$
e. What effect does adding $\mathrm{HNO}_{3}$ have on the solubilities calculated in parts a and b?

Aadit Sharma

Numerade Educator

Problem 102

Calculate the equilibrium concentrations of $\mathrm{NH}_{3}, \mathrm{Cu}^{2+}$ $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)^{2+}, \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{2}^{2+}, \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{3}^{2+},$ and $\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}$ in a solution prepared by mixing $500.0 \mathrm{mL}$ of $3.00 M \mathrm{NH}_{3}$ with $500.0 \mathrm{mL}$ of $2.00 \times 10^{-3}$ $M$ $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} .$ The stepwise equilibria are

Sisi Gao

Numerade Educator

Problem 103

Calculate the solubility of $\mathrm{AgCN}(s)\left(K_{\mathrm{sp}}=2.2 \times 10^{-12}\right)$ in a solution containing $1.0 M \mathrm{H}^{+} .\left(K_{\mathrm{a}} \text { for } \mathrm{HCN} \text { is } 6.2 \times 10^{-10} .\right)$

David Collins

Numerade Educator

Problem 104

Calcium oxalate $\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)$ is relatively insoluble in water $\left(K_{\mathrm{sp}}=2 \times 10^{-9}\right) .$ However, calcium oxalate is more soluble in acidic solution. How much more soluble is calcium oxalate in $0.10 \mathrm{M} \mathrm{H}^{+}$ than in pure water? In pure water, ignore the basic properties of $\mathrm{C}_{2} \mathrm{O}_{4}^{2-}$.

Aadit Sharma

Numerade Educator

Problem 105

What is the maximum possible concentration of $\mathrm{Ni}^{2+}$ ion in water at $25^{\circ} \mathrm{C}$ that is saturated with $0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{S}$ and maintained at $\mathrm{pH} 3.0$ with HCl?What is the maximum possible concentration of $\mathrm{Ni}^{2+}$ ion in water at $25^{\circ} \mathrm{C}$ that is saturated with $0.10$ $M$ $\mathrm{H}_{2} \mathrm{S}$ and maintained at $\mathrm{pH} 3.0$ with $\mathrm{HCl}$?

David Collins

Numerade Educator

Problem 106

A mixture contains $1.0 \times 10^{-3} M$ Cu $^{2+}$ and $1.0 \times 10^{-3} M$ $\mathrm{Mn}^{2+}$ and is saturated with $0.10 M \mathrm{H}_{2} \mathrm{S} .$ Determine a $\mathrm{pH}$ where CuS precipitates but MnS does not precipitate. $K_{\mathrm{sp}}$ for $\mathrm{CuS}=8.5 \times 10^{-45}$ and $K_{\mathrm{sp}}$ for $\mathrm{MnS}=2.3 \times 10^{-13}$.

Aadit Sharma

Numerade Educator

Problem 107

Sodium tripolyphosphate $\left(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\right)$ is used in many synthetic detergents. Its major effect is to soften the water by complexing $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid's surface tension. The $K$ value for the formation of $\mathrm{MgP}_{3} \mathrm{O}_{10}^{3-}$ is $4.0 \times 10^{8} .$ The reaction is $\mathrm{Mg}^{2+}(a q)+\mathrm{P}_{3} \mathrm{O}_{10}^{5-}(a q) \rightleftharpoons \mathrm{MgP}_{3} \mathrm{O}_{10}^{3-}(a q)$ Calculate the concentration of $\mathrm{Mg}^{2+}$ in a solution that was originally $50 .$ ppm $\mathrm{Mg}^{2+}(50 . \mathrm{mg} / \mathrm{L} \text { of solution) after } 40 . \mathrm{g}$ $\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}$ is added to $1.0 \mathrm{L}$ of the solution.

Aadit Sharma

Numerade Educator

Problem 108

You add an excess of solid $\mathrm{MX}$ in $250 \mathrm{g}$ water. You measure the freezing point and find it to be $-0.028^{\circ} \mathrm{C}$. What is the $K_{\mathrm{sp}}$ of the solid? Assume the density of the solution is $1.0 \mathrm{g} / \mathrm{cm}^{3}$.

Aadit Sharma

Numerade Educator

Problem 109

a. Calculate the molar solubility of $\operatorname{Sr} \mathrm{F}_{2}$ in water, ignoring the basic properties of $\left.\mathrm{F}^{-} . \text {(For } \operatorname{Sr} \mathrm{F}_{2}, K_{\mathrm{sp}}=7.9 \times 10^{-10} .\right)$.
b. Would the measured molar solubility of $\operatorname{Sr} \mathrm{F}_{2}$ be greater than or less than the value calculated in part a? Explain.
c. Calculate the molar solubility of $\operatorname{Sr} \mathrm{F}_{2}$ in a solution buffered at $\mathrm{pH}=2.00 .\left(K_{\mathrm{a}} \text { for } \mathrm{HF} \text { is } 7.2 \times 10^{-4} .\right)$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 110

A solution saturated with a salt of the type $\mathrm{M}_{3} \mathrm{X}_{2}$ has an osmotic pressure of $2.64 \times 10^{-2}$ atm at $25^{\circ} \mathrm{C}$. Calculate the $K_{\mathrm{sp}}$ value for the salt, assuming ideal behavior.

Aadit Sharma

Numerade Educator

Problem 111

Consider $1.0 \mathrm{L}$ of an aqueous solution that contains $0.10$ $M$ sulfuric acid to which 0.30 mole of barium nitrate is added. Assuming no change in volume of the solution, determine the $\mathrm{pH},$ the concentration of barium ions in the final solution, and the mass of solid formed.

Aadit Sharma

Numerade Educator

Problem 112

The $K_{\mathrm{sp}}$ for $Q,$ a slightly soluble ionic compound composed of $\mathrm{M}_{2}^{2+}$ and $\mathrm{X}^{-}$ ions, is $4.5 \times 10^{-29} .$ The electron configuration of $\mathbf{M}^{+}$ is $[\mathrm{Xe}] 6 s^{1} 4 f^{14} 5 d^{10} .$ The $\mathrm{X}^{-}$ anion has 54 electrons. What is the molar solubility of $Q$ in a solution of $\mathrm{NaX}$ prepared by dissolving 1.98 g $\mathrm{NaX}$ in $150 .$ mL solution?

Aadit Sharma

Numerade Educator

Problem 113

Aluminum ions react with the hydroxide ion to form the precipitate $\mathrm{Al}(\mathrm{OH})_{3}(s),$ but can also react to form the soluble complex ion $\mathrm{Al}(\mathrm{OH})_{4}^{-} .$ In terms of solubility, $\mathrm{Al}(\mathrm{OH})_{3}(s)$ will be more soluble in very acidic solutions as well as more soluble in very basic solutions.
a. Write equations for the reactions that occur to increase the solubility of $\mathrm{Al}(\mathrm{OH})_{3}(s)$ in very acidic solutions and in very basic solutions.
b. Let's study the $\mathrm{pH}$ dependence of the solubility of Al(OH) $_{3}(s)$ in more detail. Show that the solubility of $\mathrm{Al}(\mathrm{OH})_{3},$ as a function of $\left[\mathrm{H}^{+}\right],$ obeys the equation
$$
S=\left[\mathbf{H}^{+}\right]^{3} K_{\mathrm{sp}} / K_{\mathrm{w}}^{3}+K K_{\mathrm{w}} /\left[\mathrm{H}^{+}\right]
$$
where $S=$ solubility $=\left[\mathrm{Al}^{3+}\right]+\left[\mathrm{Al}(\mathrm{OH})_{4}^{-}\right]$ and $K$ is the equilibrium constant for
$$
\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)
$$
c. The value of $K$ is 40.0 and $K_{\mathrm{sp}}$ for $\mathrm{Al}(\mathrm{OH})_{3}$ is $2 \times 10^{-32}$ Plot the solubility of $\mathrm{Al}(\mathrm{OH})_{3}$ in the pH range $4-12$.

Aadit Sharma

Numerade Educator