For the reaction 3Ag(s) + NO3-(aq) + 4H+(aq) → 3Ag+(aq) + NO(g) + 2H2Ouse Table 17.1 to calculate, at 25°C,ⓐ ΔG° ⓑ K

Question

For the reaction

3Ag(s) + [latex]NO_{3}^{-}(aq) + 4H^{+}(aq) → 3Ag^{+}(aq) + NO(g) + 2H_{2}O[/latex]

use Table 17.1 to calculate, at 25°C,

Table 17.1 Standard Potentials in Water Solution at 25°C

Lithium is the strongest reducing agent. O = strongest oxidizing agent; R = strongest reducing agent. Fluorine is the strongest oxidizing agent. Lithium and fluorine are very dangerous materials to work with.	AcidicSolution,[latex][H^{+}][/latex] = 1 M
	[latex]E°_{red}[/latex](V)
	-3.040 -2.936 -2.906 -2.869 -2.714 -2.357 -1.680 -1.182 -0.762 -0.744 -0.409 -0.408 -0.402 -0.356 -0.336 -0.282 -0.236 -0.152 -0.141 -0.127 0.000 0.073 0.144 0.154 0.155 0.161 0.339 0.518 0.534 0.769 0.796 0.799 0.908 0.964 1.001 1.077 1.229 1.229 1.330 1.360 1.458 1.498 1.512 1.687 1.763 1.953 2.889		→Li(s) → K(s) → Ba(s) → Ca(s) →Na(s) → Mg(s) → Al(s) → Mn(s) → Zn(s) → Cr(s) → Fe(s) → [latex]Cr^{2+}(aq)[/latex] → Cd(s) → Pb(s) + [latex]SO_{4}^{2-}(aq)[/latex] → Tl(s) → Co(s) →Ni(s) → Ag(s) + [latex]I^{-}(aq)[/latex] → Sn(s) → Pb(s) →[latex]H_{2}(g)[/latex] → Ag(s) + [latex]Br^{-}(aq)[/latex] →[latex]H_{2}S(aq)[/latex] → [latex]Sn^{2+}(aq)[/latex] → [latex]SO_{2}(g) + 2H_{2}O[/latex] → [latex]Cu^{+}(aq)[/latex] → Cu(s) → Cu(s) → [latex]2I^{-}(aq)[/latex] → [latex]Fe^{2+}(aq)[/latex] → 2Hg(l) → Ag(s) →[latex]Hg_{2}^{2+}(aq)[/latex] →NO(g) + [latex]2H_{2}O[/latex] → [latex]Au(s) + 4Cl^{-}(aq)[/latex] → [latex]2Br^{-}(aq)[/latex] → [latex]2H_{2}O[/latex] → [latex]Mn^{2+}(aq) + 2H_{2}O[/latex] → [latex]2Cr^{3+}(aq) + 7H_{2}O[/latex] → [latex]2Cl^{-}(aq)[/latex] →[latex]\frac{1}{2} Cl_{2}(g) + 3H_{2}O[/latex] → Au(s) → [latex]Mn^{2+}(aq) + 4H_{2}O[/latex] → [latex]PbSO_{4}(s) + 2H_{2}O[/latex] → [latex]2H_{2}O[/latex] → [latex]Co^{2+}(aq)[/latex] → 2[latex]F^{-}(aq)[/latex]	[latex]Li^{+}(aq) + e^{-}[/latex] [latex]K^{+}(aq) + e^{-}[/latex] [latex]Ba^{2+}(aq) + 2e^{-}[/latex] [latex]Ca^{2+}(aq) + 2e^{-}[/latex] [latex]Na^{+}(aq) + e^{-}[/latex] [latex]Mg^{2+}(aq) + 2e^{-}[/latex] [latex]Al^{3+}(aq) + 3e^{-}[/latex] [latex]Mn^{2+}(aq) + 2e^{-}[/latex] [latex]Zn^{2+}(aq) + 2e^{-}[/latex] [latex]Cr^{3+}(aq) + 3e^{-}[/latex] [latex]Fe^{2+}(aq) + 2e^{-}[/latex] [latex]Cr^{3+}(aq) + e^{-}[/latex] [latex]Cd^{2+}(aq) + 2e^{-}[/latex] [latex]PbSO_{4}(s) + 2e^{-}[/latex] [latex]Tl^{+}(aq) + e^{-}[/latex] [latex]Co^{2+}(aq) + 2e^{-}[/latex] [latex]Ni^{2+}(aq) + 2e^{-}[/latex] [latex]AgI(s) + e^{-}[/latex] [latex]Sn^{2+}(aq) + 2e^{-}[/latex] [latex]Pb^{2+}(aq) + 2e^{-}[/latex] [latex]2H^{+}(aq) + 2e^{-}[/latex] [latex]AgBr(s) + e^{-}[/latex] [latex]S(s) + 2H^{+}(aq) + 2e^{-}[/latex] [latex]Sn^{4+}(aq) + 2e^{-}[/latex] [latex]SO_{4}^{2-}(aq) + 4H^{+}(aq) + 2e^{-}[/latex] [latex]Cu^{2+}(aq) + e^{-}[/latex] [latex]Cu^{2+}(aq) + 2e^{-}[/latex] [latex]Cu^{+}(aq) + e^{-}[/latex] [latex]I_{2}(s) + 2e^{-}[/latex] [latex]Fe^{3+}(aq) + e^{-}[/latex] [latex]Hg_{2}^{2+}(aq) + 2e^{-}[/latex] [latex]Ag^{+}(aq) + e^{-}[/latex] [latex]2Hg^{2+}(aq) + 2e^{-}[/latex] [latex]NO_{3}^{-}(aq) + 4H^{+}(aq) + 3e^{-}[/latex] [latex]AuCl_{4}^{-}(aq) + 3e^{-}[/latex] [latex]Br_{2}(l) + 2e^{-}[/latex] [latex]O_{2}(g) + 4H^{+}(aq) + 4e^{-}[/latex] [latex]MnO_{2}(s) + 4H^{+}(aq) + 2e^{-}[/latex] [latex]Cr_{2}O_{7}^{2-}(aq) + 14H^{+}(aq) + 6e^{-}[/latex] [latex]Cl_{2}(g) + 2e^{-}[/latex] [latex]ClO_{3}^{-}(aq) + 6H^{+}(aq) + 5e^{-}[/latex] [latex]Au^{3+}(aq) + 3e^{-}[/latex] [latex]MnO_{4}^{-}(aq) + 8H^{+}(aq) + 5e^{-}[/latex] [latex]PbO_{2}(s) + SO_{4}^{2-}(aq) + 4H^{+}(aq) + 2e^{-}[/latex] [latex]H_{2}O_{2}(aq) + 2H^{+}(aq) + 2e^{-}[/latex] [latex]Co^{3+}(aq) + e^{-}[/latex] [latex]F_{2}(g) + 2e^{-}[/latex]
	Basic Solution, [latex][OH^{-}][/latex] = 1 M
	[latex]E°_{red}[/latex](V)
	-0.891 -0.828 -0.547 -0.445 -0.140 0.004 0.398 0.401 0.614 0.890	→ Fe(s) + 2 [latex]OH^{-}[/latex](aq) →[latex]H_{2}(g)[/latex] + 2 [latex]OH^{-}[/latex](aq) → [latex]Fe(OH)_{2}(s)[/latex] + [latex]OH^{-}[/latex](aq) → [latex]S^{2-}(aq)[/latex] →NO(g) + 4 [latex]OH^{-}[/latex](aq) →[latex]NO_{2}^{-}[/latex](aq) + 2 [latex]OH^{-}[/latex](aq) → [latex]ClO_{3}^{-}[/latex](aq) + 2 [latex]OH^{-}[/latex](aq) → 4 [latex]OH^{-}[/latex](aq) → [latex]Cl^{-}(aq)[/latex] + 6 [latex]OH^{-}[/latex](aq) → [latex]Cl^{-}(aq)[/latex] + 2 [latex]OH^{-}[/latex](aq)		[latex]Fe(OH)_{2}(s) + 2e^{-}[/latex] [latex]2H_{2}O + 2e^{-}[/latex] [latex]Fe(OH)_{3}(s) + e^{-}[/latex] [latex]S(s) + 2e^{-}[/latex] [latex]NO_{3}^{-}(aq) + 2H_{2}O + 3e^{-}[/latex] [latex]NO_{3}^{-}(aq) + H_{2}O + 2e^{-}[/latex] [latex]ClO_{4}^{-}(aq) + H_{2}O + 2e^{-}[/latex] [latex]O_{2}(g) + 2H_{2}O + 4e^{-}[/latex] [latex]ClO_{3}^{-}(aq) + 3H_{2}O + 6e^{-}[/latex] [latex]ClO^{-}(aq) + H_{2}O + 2e^{-}[/latex]

ⓐ ΔG° ⓑ K

ⓐ

ANALYSIS
reaction: (3Ag(s) + [latex]NO_{3}^{-}(aq) + 4H^{+}(aq) → 3Ag^{+}(aq) + NO(g) + 2H_{2}O[/latex]) temperature (25°C)	Information given:
Table 17.1 (standard reduction potentials) Faraday constant (F)	Information implied
ΔG°	Asked for

STRATEGY

1. Assign oxidation numbers.
2. Split the redox reaction into oxidation and reduction half-reactions and find E°.
3. Determine the number of electrons cancelled out when balancing the equation to find n.
4. Substitute into Equation 17.2. Note that ΔG° will be in joules since the Faraday constant is in joules.

ΔG° = -nFE° (17.2)

ⓑ

ANALYSIS
From part (a): E° (0.165 V); n (3 mol)	Information given:
K	Asked for:

STRATEGY

Substitute into Equation 17.3.

E° = [latex]\frac{(0.0257 V)}{n}[/latex]ln K (at 25°C) (17.3)

Accepted Answer

ⓐ

N: +5 → +2 reduction Ag: 0 → +1 oxidation	1. oxidation numbers
[latex]NO_{3}^{-}(aq) + 4H^{+}(aq) + 3e^{-} → NO(g) + 2H_{2}O[/latex] [latex]E°_{red}[/latex] = 0.964 V Ag(s) + [latex]e^{-} → Ag^{+}(aq)[/latex] [latex]E°_{ox}[/latex] = -0.799 V E° = 0.964 V + (-0.799 V) = 0.165 V	2. half-reactions
Multiply the oxidation half-reaction by 3 to cancel out the three electrons in the reduction half-reaction. Three electrons cancel out: n = 3	3. n
ΔG° = -nFE = (-3 mol)(9.648 × [latex]10^{4}\frac{J}{mol · V}[/latex])(0.165 V) = -4.78 × [latex]10^{4}[/latex] J = -47.8 kJ	4. ΔG°

ⓑ

E° = [latex]\frac{0.0257 V}{n}[/latex]ln K; 0.165 V = [latex]\frac{0.0257 V}{3}[/latex]ln K; ln K = 19.3
K = [latex]e^{19.3}[/latex] = 2.4 × [latex]10^{8}[/latex]

K

Lithium is the strongest reducing agent. O = strongest oxidizing agent; R = strongest reducing agent. Fluorine is the strongest oxidizing agent. Lithium and fluorine are very dangerous materials to work with.	AcidicSolution, $[H^{+}]$ = 1 M
	$E°_{red}$ (V)
	-3.040 -2.936 -2.906 -2.869 -2.714 -2.357 -1.680 -1.182 -0.762 -0.744 -0.409 -0.408 -0.402 -0.356 -0.336 -0.282 -0.236 -0.152 -0.141 -0.127 0.000 0.073 0.144 0.154 0.155 0.161 0.339 0.518 0.534 0.769 0.796 0.799 0.908 0.964 1.001 1.077 1.229 1.229 1.330 1.360 1.458 1.498 1.512 1.687 1.763 1.953 2.889		→Li(s) → K(s) → Ba(s) → Ca(s) →Na(s) → Mg(s) → Al(s) → Mn(s) → Zn(s) → Cr(s) → Fe(s) → $Cr^{2+}(aq)$ → Cd(s) → Pb(s) + $SO_{4}^{2-}(aq)$ → Tl(s) → Co(s) →Ni(s) → Ag(s) + $I^{-}(aq)$ → Sn(s) → Pb(s) → $H_{2}(g)$ → Ag(s) + $Br^{-}(aq)$ → $H_{2}S(aq)$ → $Sn^{2+}(aq)$ → $SO_{2}(g) + 2H_{2}O$ → $Cu^{+}(aq)$ → Cu(s) → Cu(s) → $2I^{-}(aq)$ → $Fe^{2+}(aq)$ → 2Hg(l) → Ag(s) → $Hg_{2}^{2+}(aq)$ →NO(g) + $2H_{2}O$ → $Au(s) + 4Cl^{-}(aq)$ → $2Br^{-}(aq)$ → $2H_{2}O$ → $Mn^{2+}(aq) + 2H_{2}O$ → $2Cr^{3+}(aq) + 7H_{2}O$ → $2Cl^{-}(aq)$ → $\frac{1}{2} Cl_{2}(g) + 3H_{2}O$ → Au(s) → $Mn^{2+}(aq) + 4H_{2}O$ → $PbSO_{4}(s) + 2H_{2}O$ → $2H_{2}O$ → $Co^{2+}(aq)$ → 2 $F^{-}(aq)$	$Li^{+}(aq) + e^{-}$ $K^{+}(aq) + e^{-}$ $Ba^{2+}(aq) + 2e^{-}$ $Ca^{2+}(aq) + 2e^{-}$ $Na^{+}(aq) + e^{-}$ $Mg^{2+}(aq) + 2e^{-}$ $Al^{3+}(aq) + 3e^{-}$ $Mn^{2+}(aq) + 2e^{-}$ $Zn^{2+}(aq) + 2e^{-}$ $Cr^{3+}(aq) + 3e^{-}$ $Fe^{2+}(aq) + 2e^{-}$ $Cr^{3+}(aq) + e^{-}$ $Cd^{2+}(aq) + 2e^{-}$ $PbSO_{4}(s) + 2e^{-}$ $Tl^{+}(aq) + e^{-}$ $Co^{2+}(aq) + 2e^{-}$ $Ni^{2+}(aq) + 2e^{-}$ $AgI(s) + e^{-}$ $Sn^{2+}(aq) + 2e^{-}$ $Pb^{2+}(aq) + 2e^{-}$ $2H^{+}(aq) + 2e^{-}$ $AgBr(s) + e^{-}$ $S(s) + 2H^{+}(aq) + 2e^{-}$ $Sn^{4+}(aq) + 2e^{-}$ $SO_{4}^{2-}(aq) + 4H^{+}(aq) + 2e^{-}$ $Cu^{2+}(aq) + e^{-}$ $Cu^{2+}(aq) + 2e^{-}$ $Cu^{+}(aq) + e^{-}$ $I_{2}(s) + 2e^{-}$ $Fe^{3+}(aq) + e^{-}$ $Hg_{2}^{2+}(aq) + 2e^{-}$ $Ag^{+}(aq) + e^{-}$ $2Hg^{2+}(aq) + 2e^{-}$ $NO_{3}^{-}(aq) + 4H^{+}(aq) + 3e^{-}$ $AuCl_{4}^{-}(aq) + 3e^{-}$ $Br_{2}(l) + 2e^{-}$ $O_{2}(g) + 4H^{+}(aq) + 4e^{-}$ $MnO_{2}(s) + 4H^{+}(aq) + 2e^{-}$ $Cr_{2}O_{7}^{2-}(aq) + 14H^{+}(aq) + 6e^{-}$ $Cl_{2}(g) + 2e^{-}$ $ClO_{3}^{-}(aq) + 6H^{+}(aq) + 5e^{-}$ $Au^{3+}(aq) + 3e^{-}$ $MnO_{4}^{-}(aq) + 8H^{+}(aq) + 5e^{-}$ $PbO_{2}(s) + SO_{4}^{2-}(aq) + 4H^{+}(aq) + 2e^{-}$ $H_{2}O_{2}(aq) + 2H^{+}(aq) + 2e^{-}$ $Co^{3+}(aq) + e^{-}$ $F_{2}(g) + 2e^{-}$
	Basic Solution, $[OH^{-}]$ = 1 M
	$E°_{red}$ (V)
	-0.891 -0.828 -0.547 -0.445 -0.140 0.004 0.398 0.401 0.614 0.890	→ Fe(s) + 2 $OH^{-}$ (aq) → $H_{2}(g)$ + 2 $OH^{-}$ (aq) → $Fe(OH)_{2}(s)$ + $OH^{-}$ (aq) → $S^{2-}(aq)$ →NO(g) + 4 $OH^{-}$ (aq) → $NO_{2}^{-}$ (aq) + 2 $OH^{-}$ (aq) → $ClO_{3}^{-}$ (aq) + 2 $OH^{-}$ (aq) → 4 $OH^{-}$ (aq) → $Cl^{-}(aq)$ + 6 $OH^{-}$ (aq) → $Cl^{-}(aq)$ + 2 $OH^{-}$ (aq)		$Fe(OH)_{2}(s) + 2e^{-}$ $2H_{2}O + 2e^{-}$ $Fe(OH)_{3}(s) + e^{-}$ $S(s) + 2e^{-}$ $NO_{3}^{-}(aq) + 2H_{2}O + 3e^{-}$ $NO_{3}^{-}(aq) + H_{2}O + 2e^{-}$ $ClO_{4}^{-}(aq) + H_{2}O + 2e^{-}$ $O_{2}(g) + 2H_{2}O + 4e^{-}$ $ClO_{3}^{-}(aq) + 3H_{2}O + 6e^{-}$ $ClO^{-}(aq) + H_{2}O + 2e^{-}$

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