Question 17.9: Consider a voltaic cell at 25°C in which the reaction is Zn(...

Consider a voltaic cell at 25°C in which the reaction is

$Zn(s) + 2H^+(aq) \longrightarrow Zn^{2+}(aq) + H_2(g)$

It is found that the voltage is +0.560 V when $[Zn^{2+}]$ = 0.85 M and $P_{H_{2}}$ = 0.988 atm. What is the pH in the $H_{2}$ -H half-cell?

ANALYSIS

Information given: reaction: $(Zn(s) + 2H^+(aq) \longrightarrow Zn^{2+}(aq) + H_2(g))$ E (0.560 V); T (25°C) $P_{H_{2}}$ (0.988 atm); $[Zn^{2+}]$ (0.85 M) temperature (25°C)
Information implied: Table 17.1 (standard reduction potentials)
Asked for: pH

STRATEGY

1. Assign oxidation numbers, write oxidation and reduction half-reactions, and cancel electrons to find n.
2. Find E°. $(E^{\circ}_{red} + E^{\circ}_{ox})$
3. Substitute into the Nernst equation (Equation 17.4) for T = 25°C and find Q.

$E = E^{\circ} – \frac{(0.0257\> V)}{n} \ln Q$ (17.4)
4. Write the Q expression and substitute given concentrations and pressures to find $[H^+]$ . Change $[H^+]$ to pH.

Table 17.1 Standard Potentials in Water Solution at 25°C
Acidic Solution, $[H^+]$ = 1 M
${E^{\circ}}_{red}$ (V)
	$Li^+(aq) + e^-$	$\longrightarrow Li(s)\blacktriangleleft ⓘ$	-3.04
	$K^+(aq) + e^-$	$\longrightarrow K(s)$	-2.936
	$Ba^{2+}(aq) + 2e^{-}$	$\longrightarrow Ba(s)$	-2.906
	$Ca^{2+}(aq) + 2e^-$	$\longrightarrow Ca(s)$	-2.869
	$Na^+(aq) + e^-$	$\longrightarrow Na(s)$	-2.714
	$Mg^{2+}(aq) + 2e^-$	$\longrightarrow Mg(s)$	-2.357
	$Al^{3+}(aq) + 3e^-$	$\longrightarrow Al(s)$	-1.68
	$Mn^{2+}(aq) + 2e^-$	$\longrightarrow Mn(s)$	-1.182
	$Zn^{2+}(aq) + 2e^-$	$\longrightarrow Zn(s)$	-0.762
	$Cr^{3+}(aq) + 3e^-$	$\longrightarrow Cr(s)$	-0.744
	$Fe^{2+}(aq) + 2e^-$	$\longrightarrow Fe(s)$	-0.409
	$Cr^{3+}(aq) + e^-$	$\longrightarrow Cr^{2+}(aq)$	-0.408
	$Cd^{2+}(aq) + 2e^-$	$\longrightarrow Cd(s)$	-0.402
	$PbSO_4(s) + 2e^-$	$\longrightarrow Pb(s) + {SO_4}^{2-}(aq)$	-0.356
	$Tl^+(aq) + e^-$	$\longrightarrow Tl(s)$	-0.336
	$Co^{2+}(aq) + 2e^-$	$\longrightarrow Co(s)$	-0.282
	$Ni^{2+}(aq) + 2e^-$	$\longrightarrow Ni(s)$	-0.236
	$AgI(s) + e^-$	$\longrightarrow Ag(s) + I^-(aq)$	-0.152
	$Sn^{2+}(aq) + 2e^-$	$\longrightarrow Sn(s)$	-0.141
	$Pb^{2+}(aq) + 2e^-$	$\longrightarrow Pb(s)$	-0.127
	$2H^+(aq) + 2e^-$	$\longrightarrow H_2(g)$	0
	$AgBr(s) + e^-$	$\longrightarrow Ag(s) + Br^-(aq)$	0.073
	$S(s) + 2H^+(aq) + 2e^-$	$\longrightarrow H_2S(aq)$	0.144
	$Sn^{4+}(aq) + 2e^-$	$\longrightarrow Sn^{2+}(aq)$	0.154
	${SO_4}^{2-}(aq) + 4H^+(aq) + 2e^-$	$\longrightarrow SO_2(g)+ 2H_2O$	0.155
	$Cu^{2+}(aq) + e^-$	$\longrightarrow Cu^+(aq)$	0.161
	$Cu^{2+}(aq) + 2e^-$	$\longrightarrow Cu(s)$	0.339
	$Cu^+(aq) + e^-$	$\longrightarrow Cu(s)$	0.518
	$I_2(s) + 2e^-$	$\longrightarrow 2I^-(aq)$	0.534
	$Fe^{3+}(aq) + e^-$	$\longrightarrow Fe^{2+}(aq)$	0.769
	${Hg_2}^{2+}(aq) + 2e^-$	$\longrightarrow 2Hg(l)$	0.796
	$Ag^+(aq) + e^-$	$\longrightarrow Ag(s)$	0.799
	$2Hg^{2+}(aq) + 2e^-$	$\longrightarrow {Hg_{2}}^{2+}(aq)$	0.908
	${NO_3}^-(aq) + 4H^+(aq) + 3e^-$	$\longrightarrow NO(g) + 2H_2O$	0.964
	${AuCl_4}^-(aq) + 3e^-$	$\longrightarrow Au(s) + 4Cl^-(aq)$	1.001
	$Br_2(l) + 2e^-$	$\longrightarrow 2Br^-(aq)$	1.077
	$O_2(g) + 4H^+(aq) + 4e^-$	$\longrightarrow 2H_2O$	1.229
	$MnO_2(s) + 4H^+(aq) + 2e^-$	$\longrightarrow Mn^{2+}(aq) + 2H_2O$	1.229
	${Cr_2O_7}^{2-}(aq) + 14H^+(aq) + 6e^-$	$\longrightarrow 2Cr^{3+}(aq) + 7H_2O$	1.33
	$Cl_2(g) + 2e^-$	$\longrightarrow 2Cl^-(aq)$	1.36
	${ClO_3}^{-}(aq) + 6H^+(aq) + 5e^-$	$\longrightarrow \frac{1}{2} Cl_2(g) + 3H_2O$	1.458
	$Au^{3+}(aq) + 3e^-$	$\longrightarrow Au(s)$	1.498
	${MnO_4}^{-}(aq) + 8H^+(aq) + 5e^-$	$\longrightarrow Mn^{2+}(aq) + 4H_2O$	1.512
	$PbO_2(s) + {SO_4}^{2-}(aq) + 4H^+(aq) + 2e^-$	$\longrightarrow PbSO_4(s) + 2H_2O$	1.687
	$H_2O_2(aq) + 2H^+(aq) + 2e^-$	$\longrightarrow 2H_2O$	1.763
	$Co^{3+}(aq) + e^-$	$\longrightarrow Co^{2+}(aq)$	1.953
	$F_2(g) + 2e^- \blacktriangleleft ⓘ$	$\longrightarrow 2F^-(aq)$	2.889
Basic Solution, $[OH^-]$ = 1 M
${E^{\circ}}_{red}$ (V)
$Fe(OH)_2(s) + 2e^-$		$\longrightarrow Fe(s) + 2OH^-(aq)$	-0.891
$2H_2O + 2e^-$		$\longrightarrow H_2(g) + 2OH^-(aq)$	-0.828
$Fe(OH)_3(s) + e^-$		$\longrightarrow Fe(OH)_2(s) + OH^-(aq)$	-0.547
$S(s) + 2e^-$		$\longrightarrow S^{2-}(aq)$	-0.445
${NO_3}^{-}(aq) + 2H_2O + 3e^-$		$\longrightarrow NO(g) + 4OH^-(aq)$	-0.14
${NO_3}^-(aq) + H_2O + 2e^-$		$\longrightarrow {NO_2}^-(aq) + 2OH^-(aq)$	0.004
	${ClO_4}^-(aq) + H_2O + 2e^-$	$\longrightarrow {ClO_3}^-(aq) + 2OH^-(aq)$	0.398
$O_2(g) + 2H_2O + 4e^-$		$\longrightarrow 4OH^-(aq)$	0.401
${ClO_3}^-(aq) + 3H_2O + 6e^-$		$\longrightarrow Cl^-(aq) + 6OH^-(aq)$	0.614
$ClO^-(aq) + H_2O + 2e^-$		$\longrightarrow Cl^-(aq) + 2OH^-(aq)$	0.89

ⓘ Lithium is the strongest reducing agent.

ⓘ Lithium and fluorine are very dangerous materials to work with.

ⓘ O= strongest oxidizing agent;

R = strongest reducing agent.

ⓘ Fluorine is the strongest oxidizing agent.

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