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22.14.15: Chapter 15

Chemistry - Atoms First · LibreTexts

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    1. (a)

    \[
    \begin{array}{ccc}
    \operatorname{AgI}(s) \rightleftharpoons & \operatorname{Ag}^{+}(a q)+ & \mathrm{I}^{-}(a q) \\
    & x & \underline{x}
    \end{array}
    \notag \]


    (b)

    \[
    \mathrm{CaCO}_3(s) \rightleftharpoons \begin{array}{ccc} 
    & \mathrm{Ca}^{2+}(a q)+ & \mathrm{CO}_3^{2-}(a q) \\
    & \underline{x} & x
    \end{array}
    \notag \]

    (c)

    \[
    \begin{array}{ll}
    \mathrm{Mg}(\mathrm{OH})_2(s) \rightleftharpoons & \mathrm{Mg}^{2+}(a q) \\
    & x
    \end{array}+2 \mathrm{OH}^{-}(a q) ~ 2 x .
    \notag \]

    (d)

    \[
    \mathrm{Mg}_3\left(\mathrm{PO}_4\right)_2(s) \rightleftharpoons 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{PO}_4^{3-}(a q)
    \notag \]

    (e)

    \[
    \begin{array}{cccc}
    \mathrm{Ca}_5\left(\mathrm{PO}_4\right)_3 \mathrm{OH}(s) \rightleftharpoons & 5 \mathrm{Ca}^{2+}(a q)+ & 3 \mathrm{PO}_4^{3-}(a q)+ & \mathrm{OH}^{-}(a q) \\
    \underline{5 x} & \underline{3 x} & x
    \end{array}
    \notag \]
    3. There is no change. A solid has an activity of 1 whether there is a little or a lot.

    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.

    7. \(\mathrm{CaF}_2, \mathrm{MnCO}_3\), and ZnS

    9. (a) \(\mathrm{LaF}_3(s) \rightleftharpoons \mathrm{La}^{3+}(a q)+3 \mathrm{~F}^{-}(a q)\)

    \[
    \begin{aligned}
    & K_{\mathrm{sp}}=\left[\mathrm{La}^{3+}\right]\left[\mathrm{F}^{-}\right]^3 ; \\
    & K_{\mathrm{sp}}=\left[\mathrm{Ca}^{2+}\right]\left[\mathrm{CO}_3{ }^{2-}\right] ; \\
    & K_{\mathrm{sp}}=\left[\mathrm{Ag}^{+}\right]^2\left[\mathrm{SO}_4{ }^{2-}\right] ; \\
    & K_{\mathrm{sp}}=\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{OH}^{-}\right]^2
    \end{aligned}
    \notag \]

    11. (a) \(1.77 \times 10^{-7}\); (b) \(1.6 \times 10^{-6}\); (c) \(2.2 \times 10^{-9}\); (d) \(7.91 \times 10^{-22}\)

    13. (a) \(2 \times 10^{-2} M\); (b) \(1.5 \times 10^{-3} M\); (c) \(2.27 \times 10^{-9} M\); (d) \(2.2 \times 10^{-10} M\)

    15. (a) \(6.4 \times 10^{-9} M=\left[\mathrm{Ag}^{+}\right],\left[\mathrm{Cl}^{-}\right]=0.025 M\). Check: \(\dfrac{6.4 \times 10^{-9} M}{0.025 M} \times 100 \%=2.6 \times 10^{-5} \%\),an insignificant change;


    (b) \(2.2 \times 10^{-5} M=\left[\mathrm{Ca}^{2+}\right],\left[\mathrm{F}^{-}\right]=0.0013 M\). Check: \(\dfrac{2.26 \times 10^{-5} M}{0.00133 M} \times 100 \%=1.70 \%\). This value is less than 5\% and can be ignored.
    (c) \(0.2238 M=\left[\mathrm{SO}_4{ }^{2-}\right]\); \(\left[\mathrm{Ag}^{+}\right]=7.4 \times 10^{-3} M\). Check: \(\dfrac{3.7 \times 10^{-3}}{0.2238} \times 100 \%=1.64 \times 10^{-2}\); the condition is satisfied.
    (d) \(\left[\mathrm{OH}^{-}\right]=2.8 \times 10^{-3} M ; 5.7 \times 10^{-12} M=\left[\mathrm{Zn}^{2+}\right]\). Check: \(\dfrac{5.7 \times 10^{-12}}{2.8 \times 10^{-3}} \times 100 \%=2.0 \times 10^{-7} \% ; x\) is less than \(5 \%\) of \(\left[\mathrm{OH}^{-}\right]\)and is, therefore, negligible.

    17. (a) The change in initial concentration of common ion may not be neglected (must solve quadratic equation)

    \[
    \begin{aligned}
    & {\left[\mathrm{Ti}^{+}\right]=0.031 \mathrm{M}} \\
    & {\left[\mathrm{Cl}^{-}\right]=0.0056 \mathrm{M}(\mathrm{~b}) \mathrm{Th}} \\
    & {\left[\mathrm{Ba}^{2+}\right]=2.4 \times 10^{-4} \mathrm{M}} \\
    & {\left[\mathrm{~F}^{-}\right]=0.313 \mathrm{M} ;}
    \end{aligned}
    \notag \]


    (c) The change in initial concentration of common ion may be neglected.

    \[
    \begin{aligned}
    & {\left[\mathrm{Mg}^{2+}\right]=0.0244 \mathrm{M}} \\
    & {\left[\mathrm{C}_2 \mathrm{O}_4{ }^{2-}\right]=2.9 \times 10^{-5} M}
    \end{aligned}
    \notag \]

    (d) The change in initial concentration of common ion may be neglected.

    \[
    \begin{aligned}
    & {\left[\mathrm{Ca}^{2+}\right]=5.18 \times 10^{-4} \mathrm{M}} \\
    & \left.\left[\mathrm{C}_2\right)_4{ }^{2-}\right]=0.051 \mathrm{M}
    \end{aligned}
    \notag \]

    19. The changes in concentration are greater than 5\% and thus exceed the maximum value for disregarding the change.

    21. \(\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}\) is the most soluble Ca salt in mol/L, and it is also the most soluble Ca salt in g/L.

    23. \(7.8 \times 10^{-3} M=\left[\mathrm{SO}_4{ }^{2-}\right]=\left[\mathrm{Ca}^{2+}\right]\); Since this concentration is higher than \(2.60 \times 10^{-3} M\), "gyp" water does not meet the standards.

    25. Mass \(\left(\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}\right)=0.72 \mathrm{~g}\)

    27. (a) \(\left[\mathrm{Ag}^{+}\right]=\left[\mathrm{l}^{-}\right]=1.3 \times 10^{-5} M\); (b) \(\left[\mathrm{Ag}^{+}\right]=2.88 \times 10^{-2} M\), \(\left[\mathrm{SO}_4{ }^{2-}\right]=1.44 \times 10^{-2} M\); (c) \(\left[\mathrm{Mn}^{2+}\right]=3.7 \times 10^{-5} M\), \(\left[\mathrm{OH}^{-}\right]=7.4 \times 10^{-5} M\); (d) \(\left[\mathrm{Sr}^{2+}\right]=4.3 \times 10^{-2} M,\left[\mathrm{OH}^{-}\right]=8.6 \times 10^{-2} M\); (e) \(\left[\mathrm{Mg}^{2+}\right]=1.3 \times 10^{-4} M\), \(\left[\mathrm{OH}^{-}\right]=2.6\) \(\times 10^{-4} M\).

    29. (a) \(1.45 \times 10^{-4}\); (b) \(8.2 \times 10^{-55}\); (c) \(1.35 \times 10^{-4}\); (d) \(1.18 \times 10^{-5}\); (e) \(1.08 \times 10^{-10}\)

    31. (a) \(\mathrm{CaCO}_3\) does precipitate. (b) The compound does not precipitate. (c) The compound does not precipitate. (d) The compound precipitates.

    33. \(1.42 \times 10^{-9} M\)

    35. \(9.2 \times 10^{-13} M\)

    37. \(\left[\mathrm{Ag}^{+}\right]=1.8 \times 10^{-3} \mathrm{M}\)

    39. \(6.3 \times 10^{-4}\)

    41. (a) 2.25 L ; (b) \(7.2 \times 10^{-7} \mathrm{~g}\)

    43. 100\% of it is dissolved

    45. (a) \(\mathrm{Hg}_2{ }^{2+}\) and \(\mathrm{Cu}^{2+}\) : Add \(\mathrm{SO}_4{ }^{2-}\). (b) \(\mathrm{SO}_4{ }^{2-}\) and \(\mathrm{Cl}^{-}\): Add \(\mathrm{Ba}^{2+}\). (c) \(\mathrm{Hg}^{2+}\) and \(\mathrm{Co}^{2+}\) : Add \(\mathrm{S}^{2-}\). (d) \(\mathrm{Zn}^{2+}\) and \(\mathrm{Sr}^{2+}\) : Add \(\mathrm{OH}^{-}\)until \(\left[\mathrm{OH}^{-}\right]=0.050 \mathrm{M}\). (e) \(\mathrm{Ba}^{2+}\) and \(\mathrm{Mg}^{2+}\) : Add \(\mathrm{SO}_4{ }^{2-}\). (f) \(\mathrm{CO}_3{ }^{2-}\) and \(\mathrm{OH}^{-}:\)Add \(\mathrm{Ba}^{2+}\).

    47. Agl will precipitate first.

    49. \(1.5 \times 10^{-12} M\)

    51. 3.99 kg

    53. (a) \(3.1 \times 10^{-11}\); (b) \(\left[\mathrm{Cu}^{2+}\right]=2.6 \times 10^{-3}\); \(\left[\mathrm{IO}_3{ }^{-}\right]=5.3 \times 10^{-3}\)

    55. \(9.3 \times 10^{-6} \mathrm{~g} \mathrm{~Pb}(\mathrm{OH})_2\)

    57. \(\mathrm{Mg}(\mathrm{OH})_2(s) \rightleftharpoons \mathrm{Mg}^{2+}+2 \mathrm{OH}^{-}\) \(K_{\mathrm{sp}}=\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]^2\) \(1.23 \times 10^{-3} \mathrm{~g} \mathrm{Mg}(\mathrm{OH})_2\)

    59. \(\mathrm{MnCO}_3\) will form first since it has the smallest \(K_{\mathrm{sp}}\) value among these homologous compounds and is therefore the least soluble. \(\mathrm{MgCO}_3 \bullet 3 \mathrm{H}_2 \mathrm{O}\) will be the last to precipitate since it has the largest K_sp value and is the most soluble. \(K_{\mathrm{sp}}\) value.

    62. when the amount of solid is so small that a saturated solution is not produced

    64. \(8.2 \times 10^{-5} M\)

    66. \(5 \times 10^{23}\)

    68.

    \[\left[\mathrm{Cd}^{2+}\right]=5.0 \times 10^{-5} M ;\left[\mathrm{CN}^{-}\right]=2.0 \times 10^{-4} M\notag \]

    70. \(\left[\mathrm{Co}^{3+}\right]=3.0 \times 10^{-6} M ;\left[\mathrm{NH}_3\right]=1.8 \times 10^{-5} M\)

    72. 1.3 g

    74. 0.79 g

    76. (a)

    This figure shows a chemical reaction modeled with structural formulas. On the left side is a structure with a central C atom. O atoms, each with two unshared electron pairs, are double bonded to the left and right sides of the C atom. Following a plus sign is another structure in brackets which has an O atom with three unshared electron dot pairs single bonded to an H atom on the right. Outside the brackets is superscript negative sign. Following a right pointing arrow is a structure in brackets that has a central C atom to which 3 O atoms are bonded. Above and slightly to the right, one of the O atoms is connected with a double bond. This O atom has two unshared electron pairs. The second O atom is single bonded below and slightly to the right. This O atom has three unshared electron pairs. The third O atom is bonded to the left of the C atom. This O atom has two unshared electron pairs and an H atom single bonded to its left. Outside the brackets to the right is a superscript negative symbol.

     

     

     

     

     

    (b)

    This figure shows a chemical reaction modeled with structural formulas. On the left side is a structure that has a central B atom to which 3 O atoms are bonded. The O atoms above and below slightly right of the B atom each have an H atom single bonded to the right. The third O atom is single bonded to the left side of the B atom. This O atom has an H atom single bonded to its left side. All O atoms in this structure have two unshared electron pairs. Following a plus sign is another structure which has an O atom single bonded to an H atom on its right. The O atom has three unshared electron pairs. The structure appears in brackets with a superscript negative sign. Following a right pointing arrow is a structure in brackets has a central B atom to which 4 O atoms are bonded. The O atoms above, below, and right of the B atom each hav an H atom single bonded to the right. The third O atom is single bonded to the left side of the B atom. This O atom has an H atom single bonded to its left side. All O atoms in this structure have two unshared electron pairs. Outside the brackets to the right is a superscript negative symbol.

    (c)

    This figure illustrates a chemical reaction using structural formulas. On the left, two I atoms, each with 3 unshared electron pairs, are joined with a single bond. Following a plus sign is another structure which has an I atom with four pairs of electron dots and a superscript negative sign. Following a right pointing arrow is a structure in brackets that has three I atoms connected in a line with single bonds. The two end I atoms have three unshared electron dot pairs and the I atom at the center has two unshared electron pairs. Outside the brackets is a superscript negative sign.

    (d)

    This figure illustrates a chemical reaction using structural formulas. On the left, an A l atom is positioned at the center of a structure and three Cl atoms are single bonded above, left, and below. Each C l atom has three pairs of electron dots. Following a plus sign is another structure which has an F atom is surrounded by four electron dot pairs and a superscript negative symbol. Following a right pointing arrow is a structure in brackets that has a central A l atom to which 4 C l atoms are connected with single bonds above, below, to the left, and to the right. Each C l atom in this structure has three pairs of electron dots. Outside the brackets is a superscript negative symbol.

    (e)

    This figure illustrates a chemical reaction using structural formulas. On the left is a structure which has an S atom at the center. O atoms are single bonded above and below. These O atoms have three electron dot pairs each. To the right of the S atom is a double bonded O atom which has two pairs of electron dots. Following a plus sign is an O atom which is surrounded by four electron dot pairs and has a superscript 2 negative. Following a right pointing arrow is a structure in brackets that has a central S atom to which 4 O atoms are connected with single bonds above, below, to the left, and to the right. Each of the O atoms has three pairs of electron dots. Outside the brackets is a superscript 2 negative.

    78. (a)

    This figure represents a chemical reaction in two rows. The top row shows the reaction using chemical formulas. The second row uses structural formulas to represent the reaction. The first row contains the equation H C l ( g ) plus P H subscript 3 ( g ) right pointing arrow left bracket P H subscript 4 right bracket superscript plus plus left bracket C l with 4 pairs of electron dots right bracket superscript negative sign. The second row begins on the left with H left bracket C l with four unshared electron pairs right bracket plus a structure in brackets with a central P atom with H atoms single bonded at the left, above, and to the right. A single unshared electron pair is on the central P atom. Outside the brackets to the right is a superscript plus sign. Following a right pointing arrow is a structure in brackets with a central P atom with H atoms single bonded at the left, above, below, and to the right. Outside the brackets is a superscript plus sign. This structure is followed by a plus and a C l atom in brackets with four unshared electron pairs and a superscript negative sign.

    (b)\(\mathrm{H}_3 \mathrm{O}^{+}+\mathrm{CH}_3{ }^{-} \longrightarrow \mathrm{CH}_4+\mathrm{H}_2 \mathrm{O}\)

    This figure represents a chemical reaction using structural formulas. A structure is shown in brackets on the left which is composed of a central O atom with one unshared electron pair and three single bonded H atoms to the left, right, and above the atom. Outside the brackets to the right is a superscript plus sign. Following a plus sign, is another structure in brackets composed of a central C atom with one unshared electron pair and three single bonded H atoms to the left, right, and above the atom. Outside the brackets to the right is a superscript negative sign. Following a right pointing arrow is a structure with a central C atom with H atoms single bonded above, below, left and right. Following a plus sign is a structure with a central O atom with two unshared electron pairs and two H atoms connected with single bonds.

    (c) \(\mathrm{CaO}+\mathrm{SO}_3 \longrightarrow \mathrm{CaSO} 4\)

    This figure represents a chemical reaction using structural formulas. On the left, C a superscript 2 plus is just left of bracket O with four unshared electron pairs right bracket superscript 2 negative plus a structure with a central S atom to which two O atoms are single bonded at the left and right, and a single O atom is double bonded above. The two single bonded O atoms each have three unshared electron pairs and the double bonded O atom has two unshared electron pairs. Following a right pointing arrow is C a superscript 2 plus just left of a structure in brackets with a central S atom which has 4 O atoms single bonded at the left, above, below, and to the right. Each of the O atoms has three unshared electron pairs. Outside the brackets to the right is a superscript two negative.

    (d) \(\mathrm{NH}_4^{+}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{O}^{-} \longrightarrow \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}+\mathrm{NH}_3\)

    This figure represents a chemical reaction using structural formulas. A structure is shown in brackets on the left which is composed of a central N atom with four single bonded H atoms to the left, right, above, and below the atom. Outside the brackets to the right is a superscript plus sign. Following a plus sign, is another structure in brackets composed of a C atom with three single bonded H atoms above, below, and to the left. A second C atom is single bonded to the right. This C atom has H atoms single bonded above and below. To the right of the second C atom, an O atom is single bonded. This O atom has three unshared electron pairs. Outside the brackets to the right is a subperscript negative. Following a right pointing arrow is a structure composed of a C atom with three single bonded H atoms above, below, and to the left. A second C atom is single bonded to the right. This C atom has H atoms single bonded above and below. To the right of the second C atom, an O atom is single bonded. This O atom has two unshared electron pairs and an H atom single bonded to its right.

    80. 0.0281 g

    82. HNO3⁢(𝑙)+HF⁡(𝑙)⟶H2⁢NO3⁢++F−; HF⁡(𝑙)+BF3⁢(𝑔)⟶H++BF4

    84. (a) H3⁢BO3+H2⁢O⟶H4⁢BO4⁢−+H+; (b) The electronic and molecular shapes are the same—both tetrahedral. (c) The tetrahedral structure is consistent with sp3 hybridization.

    86. 0.014 M

    88. 7.2 × 10–15 M

    90. 4.4 × 10−22 M

    93. [OH−] = 4.5 × 10−6; [Al3+] = 2 × 10–16 (molar solubility)

    95. Ksp=[Ba2+]⁢[SO4⁢2−]=[Ba2+]⁢(0.049)=1.08×10–10⁢[Ba2+]=2.2×10–9; (molar solubility)

    97. [OH–] = 7.6 × 10−3 M; [Pb2+] = 2.1 × 10–11 (molar solubility)

    99. 7.66

    101.  (a) Ksp = [Mg2+][F–]2 = (1.21 × 10–3)(2 × 1.21 × 10–3)2 = 7.09 × 10–9
    (b) 7.09 × 10–7 M
    (c) Determine the concentration of Mg2+ and F– that will be present in the final volume. Compare the value of the ion product [Mg2+][F–]2 with Ksp. If this value is larger than Ksp, precipitation will occur.
    0.1000 L × 3.00 × 10–3 M Mg(NO3)2 = 0.3000 L × M Mg(NO3)2
    M Mg(NO3)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 Ksp, so no precipitation will occur.
    (d) MgF2 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 Châtelier’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.

    103. BaF2, Ca3(PO4)2, ZnS; each is a salt of a weak acid, and the [H3⁢O+] from perchloric acid reduces the equilibrium concentration of the anion, thereby increasing the concentration of the cations

    105. Effect on amount of solid CaHPO4, [Ca2+], [OH–]: (a) increase, increase, decrease; (b) decrease, increase, decrease; (c) no effect, no effect, no effect; (d) decrease, increase, decrease; (e) increase, no effect, no effect

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