Calculate ΔS° for ⓐ dissolving one mole of calcium hydroxide in water. ⓑ the combustion of one gram of methane to form carbon dioxide and liquid water.

Question

Calculate ΔS° for

ⓐ dissolving one mole of calcium hydroxide in water.

ⓑ the combustion of one gram of methane to form carbon dioxide and liquid water.

ⓐ

STRATEGY

1. Write a balanced equation for dissolving [latex]Ca(OH)_{2}[/latex].
2. Find ΔS° by substituting S° values found in Table 16.1 into Equation 16.1.

Table 16.1 Standard Entropies at 25°C (J/mol·K) of Elements and Compounds at 1 atm, Aqueous Ions at 1 M

Elements

Ag(s) 42.6 [latex]Cl_{2}(g)[/latex] 223.0 [latex]I_{2}(s)[/latex] 116.1 [latex]O_{2}(g)[/latex] 205.0
Al(s) 28.3 Cr(s) 23.8 K(s) 64.2 Pb(s) 64.8
Ba(s) 62.8 Cu(s) 33.2 Mg(s) 32.7 [latex]P_{4}(s)[/latex] 164.4
[latex]Br_{2}(l)[/latex] 152.2 [latex]F_{2}(g)[/latex] 202.7 Mn(s) 32.0 S(s) 31.8
C(s) 5.7 Fe(s) 27.3 [latex]N_{2}(g)[/latex] 191.5 Si(s) 18.8
Ca(s) 41.4 [latex]H_{2}(g)[/latex] 130.6 Na(s) 51.2 Sn(s) 51.6
Cd(s) 51.8 Hg(l) 76.0 Ni(s) 29.9 Zn(s) 41.6

Compounds

AgBr(s) 107.1 [latex]CaCl_{2}(s)[/latex] 104.6 [latex]H_{2}O(g)[/latex] 188.7 [latex]NH_{4}NO_{3}(s)[/latex] 151.1
AgCl(s) 96.2 [latex]CaCO_{3}(s)[/latex] 92.9 [latex]H_{2}O(l)[/latex] 69.9 NO(g) 210.7
AgI(s) 115.5 CaO(s) 39.8 [latex]H_{2}O_{2}(l)[/latex] 109.6 [latex]NO_{2}(g)[/latex] 240.0
[latex]AgNO_{3}(s)[/latex] 140.9 [latex]Ca(OH)_{2}(s)[/latex] 83.4 [latex]H_{2}S(g)[/latex] 205.7 [latex]N_{2}O_{4}(g)[/latex] 304.2
[latex]Ag_{2}O(s)[/latex] 121.3 [latex]CaSO_{4}(s)[/latex] 106.7 [latex]H_{2}SO_{4}(l)[/latex] 156.9 NaCl(s) 72.1
[latex]Al_{2}O_{3}(s)[/latex] 50.9 [latex]CdCl_{2}(s)[/latex] 115.3 HgO(s) 70.3 NaF(s) 51.5
[latex]BaCl_{2}(s)[/latex] 123.7 CdO(s) 54.8 KBr(s) 95.9 NaOH(s) 64.5
[latex]BaCO_{3}(s)[/latex] 112.1 [latex]Cr_{2}O_{3}(s)[/latex] 81.2 KCl(s) 82.6 NiO(s) 38.0
BaO(s) 70.4 CuO(s) 42.6 [latex]KClO_{3}(s)[/latex] 143.1 [latex]PbBr_{2}(s)[/latex] 136.0
[latex]BaSO_{4}(s)[/latex] 132.2 [latex]Cu_{2}O(s)[/latex] 93.1 [latex]KClO_{4}(s)[/latex] 151.0 [latex]PbCl_{2}(s)[/latex] 136.0
[latex]CCl_{4}(l)[/latex] 216.4 CuS(s) 66.5 [latex]KNO_{3}(s)[/latex] 133.0 PbO(s) 66.5
[latex]CHCl_{3}(l)[/latex] 201.7 [latex]Cu_{2}S(s)[/latex] 120.9 [latex]MgCl_{2}(s)[/latex] 89.6 [latex]PbO_{2}(s)[/latex] 68.6
[latex]CH_{4}(g)[/latex] 186.2 [latex]CuSO_{4}(s)[/latex] 107.6 [latex]MgCO_{3}(s)[/latex] 65.7 [latex]PCl_{3}(g)[/latex] 311.7
[latex]C_{2}H_{2}(g)[/latex] 200.8 [latex]Fe(OH)_{3}(s)[/latex] 106.7 MgO(s) 26.9 [latex]PCl_{5}(g)[/latex] 364.5
[latex]C_{2}H_{4}(g)[/latex] 219.5 [latex]Fe_{2}O_{3}(s)[/latex] 87.4 [latex]Mg(OH)_{2}(s)[/latex] 63.2 [latex]SiO_{2}(s)[/latex] 41.8
[latex]C_{2}H_{6}(g)[/latex] 229.5 [latex]Fe_{3}O_{4}(s)[/latex] 146.4 [latex]MgSO_{4}(s)[/latex] 91.6 [latex]SnO_{2}(s)[/latex] 52.3
[latex]C_{3}H_{8}(g)[/latex] 269.9 HBr(g) 198.6 [latex]MnO(s)[/latex] 59.7 [latex]SO_{2}(g)[/latex] 248.1
[latex]CH_{3}OH(l)[/latex] 126.8 HCl(g) 186.8 [latex]MnO_{2}(s)[/latex] 53.0 [latex]SO_{3}(g)[/latex] 256.7
[latex]C_{2}H_{5}OH(l)[/latex] 160.7 HF(g) 173.7 [latex]NH_{3}(g)[/latex] 192.3 [latex]ZnI_{2}(s)[/latex] 161.1
CO(g) 197.6 HI(g) 206.5 [latex]N_{2}H_{4}(l)[/latex] 121.2 ZnO(s) 43.6
[latex]CO_{2}(g)[/latex] 213.6 [latex]HNO_{3}(l)[/latex] 155.6 [latex]NH_{4}Cl(s)[/latex] 94.6 ZnS(s) 57.7

Cations Anions

[latex]Ag^{+}(aq)[/latex] 72.7 [latex]Hg^{2+}(aq)[/latex] -32.2 [latex]Br^{-}(aq)[/latex] 82.4 [latex]HPO_{4}^{2-}(aq)[/latex] -33.5
[latex]Al^{3+}(aq)[/latex] -321.7 [latex]K^{+}(aq)[/latex] 102.5 [latex]CO_{3}^{2-}(aq)[/latex] -56.9 [latex]HSO_{4}^{-}(aq)[/latex] 131.8
[latex]Ba^{2+}(aq)[/latex] 9.6 [latex]Mg^{2+}(aq)[/latex] -138.1 [latex]Cl^{-}(aq)[/latex] 56.9 [latex]I^{-}(aq)[/latex] 111.3
[latex]Ca^{2+}(aq)[/latex] -53.1 [latex]Mn^{2+}(aq)[/latex] -73.6 [latex]ClO_{3}^{-}(aq)[/latex] 162.3 [latex]MnO_{4}^{-}(aq)[/latex] 191.2
[latex]Cd^{2+}(aq)[/latex] -73.2 [latex]Na^{+}(aq)[/latex] 59.0 [latex]ClO_{4}^{-}(aq)[/latex] 182.0 [latex]NO_{2}^{-}(aq)[/latex] 123.0
[latex]Cu^{+}(aq)[/latex] 40.6 [latex]NH_{4}^{+}(aq)[/latex] 113.4 [latex]CrO_{4}^{2-}(aq)[/latex] 50.2 [latex]NO_{3} ^{-}(aq)[/latex] 146.4
[latex]Cu^{2+}(aq)[/latex] -99.6 [latex]Ni^{2+}(aq)[/latex] -128.9 [latex]Cr_{2}O_{7}^{2-}(aq)[/latex] 261.9 [latex]OH^{-}(aq)[/latex] -10.8
[latex]Fe^{2+}(aq)[/latex] -137.7 [latex]Pb^{2+}(aq)[/latex] 10.5 [latex]F^{-}(aq)[/latex] -13.8 [latex]PO_{4}^{3-}(aq)[/latex] -222
[latex]Fe^{3+}(aq)[/latex] -315.9 [latex]Sn^{2+}(aq)[/latex] -17.4 [latex]HCO_{3}^{-}(aq)[/latex] 91.2 [latex]S^{2-}(aq)[/latex] -14.6
[latex]H^{+}(aq)[/latex] 0.0 [latex]Zn^{2+}(aq)[/latex] -112.1 [latex]H_{2}PO_{4}^{-}(aq)[/latex] 90.4 [latex]SO_{4}^{2-}(aq)[/latex] 20.1

ΔS° = Σ[latex]S°_{products}[/latex] - Σ[latex]S°_{reactants}[/latex] (16.1)

ⓑ

STRATEGY

1. Write a balanced equation for the reaction.
2. Find ΔS° by substituting S° values from Table 16.1 into Equation 16.1.
Note that the value you obtained is for the difference in entropy for one mole.
3. Use ΔS° for one mole as a conversion factor to obtain ΔS° for one gram of [latex]CH_{4}[/latex].

Accepted Answer

ⓐ

[latex]Ca(OH)_{2}(s) → Ca^{2+}(aq) + 2 OH^{-}(aq)[/latex]

1. Equation

ΔS° = S°[latex]Ca^{2+}(aq) + 2S° OH^{-}(aq) - S° Ca(OH)_{2}(s)[/latex]

= 1 mol[latex]\left(\frac{-53.1 J}{mol · K}\right) + 2 mol \left(\frac{-10.8 J}{mol · K}\right) - 1 mol\left(\frac{+83.4 J}{mol · K}\right)[/latex] = -158.1 J/K

2. ΔS°

ⓑ

[latex]CH_{4} + 2 O_{2}(g) → CO_{2}(g) + 2H_{2}O(l)[/latex]

1. Equation

ΔS° = S° [latex]CO_{2}(g) + 2S° H_{2}O(l) - [S° CH_{4}(g) + 2S° O_{2}(g)][/latex]

= 1 mol[latex]\left(\frac{+213.6 J}{mol · K}\right) + 2 mol \left(\frac{+69.9 J}{mol · K}\right) - \left[1 mol\left(\frac{+186.2 J}{mol · K} \right) + 2 mol \left(\frac{+205.0 J}{mol · K}\right)\right] [/latex]

= - 242.8 J/K for the combustion of one mole of [latex]CH_{4}[/latex].

2. ΔS° for one mole

[latex]\frac{-242.8 J/K}{1 mol CH_{4}} × \frac{1 mol CH_{4}}{16.04 g}[/latex] = -15.14 J/K

2. ΔS° for one gram

END POINT

Notice that when there is a decrease in the number of moles of gas (part b), ΔS° is negative.

Question 16.2: Calculate ΔS° for ⓐ dissolving one mole of calcium hydroxide...

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