Question 19.4: Calculating Standard Potentials for Electrochemical Cells fr...
Calculating Standard Potentials for Electrochemical Cells from Standard Electrode Potentials of the Half-Reactions
Use tabulated standard electrode potentials to calculate the standard cell potential for the following reaction occurring in an electrochemical cell at 25 °C. (The equation is balanced.)
Al (s)+ NO _3{}^{-}(a q)+4 H ^{+}(a q) \longrightarrow Al ^{3+}(a q)+ NO (g)+2 H _2 O (l)
| Begin by separating the reaction into oxidation and reduction half-reactions. (In this case, you can readily see that Al(s) is oxidized. In cases where it is not so apparent, you may want to assign oxidation states to determine the correct half-reactions.) | Oxidation: Al (s) \longrightarrow Al ^{3+}+ 3 e^-
Reduction: NO _3{}^{-}(a q)+4 H ^{+}(a q)+3 e^- \longrightarrow NO (g)+2 H _2 O (l) |
| Look up the standard electrode potentials for each half-reaction in Table 19.1. Add the half-cell reactions together to obtain the overall redox equation. Calculate the standard cell potential by subtracting the electrode potential of the anode from the electrode potential of the cathode. | Oxidation
(Anode): Al (s) \longrightarrow Al ^{3+}+\cancel{3 e^-} E° = -1.66 V Reduction (Cathode): \underline{NO _3{}^{-}(a q)+4 H ^{+}(a q)+ \cancel{3 e^-} \longrightarrow NO (g)+2 H _2 O (l) E° = 0.96 V} \\ Al (s)+ NO _3{}^{-}(a q)+4 H ^{+}(a q) \longrightarrow Al ^{3+}(a q)+ NO (g)+2 H _2 O (l) E^\circ _{cell} = E^\circ_{cat} – E^\circ_{an} = 0.96 V – (–1.66 V) = 2.62 V |
Table 19.1
| Standard Electrode Potentials at 25 °C | ||||
| Reduction Half-Reaction |
E°(V) | |||
 |
F_2(g) + 2 e^- | \longrightarrow 2 F^-(aq) | 2.87 |  |
| H_2O_2(aq) + 2 H^+(aq) + 2 e^- | \longrightarrow 2 H_2O(l) | 1.78 | ||
| PbO_2(s) + 4 H^+(aq) + SO_4{}^{2-}(aq) + 2 e^- | \longrightarrow PbSO_4(s) + 2 H_2O(l) | 1.69 | ||
| MnO_4^-(aq) + 4 H^+(aq) + 3 e^- | \longrightarrow MnO_2(s) + 2 H_2O(l) | 1.68 | ||
| MnO_4{}^-(aq) + 8 H^+(aq) + 5 e^- | \longrightarrow Mn^{2 +}(aq) + 4 H_2O(l) | 1.51 | ||
| Au^{3 +}(aq) + 3 e^- | \longrightarrow Au(s) | 1.50 | ||
| PbO_2(s) + 4 H^+(aq) + 2 e^- | \longrightarrow Pb^{2 +}(aq) + 2 H_2O(l) | 1.46 | ||
| Cl_2(g) + 2 e^- | \longrightarrow 2 Cl^-(aq) | 1.36 | ||
| Cr_2O_7{}^{2 -}(aq) + 14 H^+(aq) + 6 e^- | \longrightarrow 2 Cr^{3 +}(aq) + 7 H_2O(l) | 1.33 | ||
| O_2(g) + 4 H^+(aq) + 4 e^- | \longrightarrow 2 H_2O(l) | 1.23 | ||
| MnO_2(s) + 4 H^+(aq) + 2 e^- | \longrightarrow Mn^{2 +}(aq) + 2 H_2O(l) | 1.21 | ||
| IO_3^-(aq) + 6 H^+(aq) + 5 e^- | \longrightarrow \frac{1}{2} I_2(aq) + 3 H_2O(l) | 1.20 | ||
| Br_2(l) + 2 e^- | \longrightarrow 2 Br^-(aq) | 1.09 | ||
| VO_2^{+}(aq) + 2 H^+(aq) + e^- | \longrightarrow VO^{2 +}(aq) + H_2O(l) | 1.00 | ||
| NO_3{}^{-}(aq) + 4 H^+(aq) + 3 e^- | \longrightarrow NO(g) + 2 H_2O(l) | 0.96 | ||
| ClO_2(g) + e^- | \longrightarrow ClO_2{}^-(aq) | 0.95 | ||
| Ag^+(aq) + e^- | \longrightarrow Ag(s) | 0.80 | ||
| Fe^{3 +}(aq) + e^- | \longrightarrow Fe^{2 +}(aq) | 0.77 | ||
| O_2(g) + 2 H^+(aq) + 2 e^- | \longrightarrow H_2O_2(aq) | 0.70 | ||
| MnO_4{}^-(aq) + e^- | \longrightarrow MnO_4{}^{2-}(aq) | 0.56 | ||
| I_2(s) + 2 e^- | \longrightarrow 2 I^-(aq) | 0.54 | ||
| Cu^+(aq) + e^- | \longrightarrow Cu(s) | 0.52 | ||
| O_2(g) + 2 H_2O(l) + 4 e^- | \longrightarrow 4 OH^-(aq) | 0.40 | ||
| Cu^{2+}(aq) + 2 e^- | \longrightarrow Cu(s) | 0.34 | ||
| SO_4{}^{2 -}(aq) + 4 H^+(aq) + 2 e^- | \longrightarrow H_2SO_3(aq) + H_2O(l) | 0.20 | ||
| Cu^{2+}(aq) + e^- | \longrightarrow Cu^+(aq) | 0.16 | ||
| Sn^{4+}(aq) + 2 e^- | \longrightarrow Sn^{2 +}(aq) | 0.15 | ||
| 2 H^+(aq) + 2 e^- | \longrightarrow H_2(g) | 0 | ||
| Fe^{3+}(aq) + 3 e^- | \longrightarrow Fe(s) | –0.036 | ||
| Pb^{2+}(aq) + 2 e^- | \longrightarrow Pb(s) | -0.13 | ||
| Sn^{2+}(aq) + 2 e^- | \longrightarrow Sn(s) | -0.14 | ||
| Ni^{2+}(aq) + 2 e^- | \longrightarrow Ni(s) | -0.23 | ||
| Cd^{2+}(aq) + 2 e^- | \longrightarrow Cd(s) | -0.40 | ||
| Fe^{2+}(aq) + 2 e^- | \longrightarrow Fe(s) | -0.45 | ||
| Cr^{3+}(aq) + e^- | \longrightarrow Cr^{2+}(aq) | -0.50 | ||
| Cr^{3+}(aq) + 3 e^- | \longrightarrow Cr(s) | -0.73 | ||
| Zn^{2+}(aq) + 2 e^- | \longrightarrow Zn(s) | -0.76 | ||
| 2 H_2O(l) + 2 e^- | \longrightarrow H_2(g) + 2 OH^-(aq) | -0.83 | ||
| Mn^{2+}(aq) + 2 e^- | \longrightarrow Mn(s) | -1.18 | ||
| Al^{3+}(aq) + 3 e^- | \longrightarrow Al(s) | -1.66 | ||
| Mg^{2+}(aq) + 2 e^- | \longrightarrow Mg(s) | -2.37 | ||
| Na^+(aq) + e^- | \longrightarrow Na(s) | -2.71 | ||
| Ca^{2+}(aq) + 2 e^- | \longrightarrow Ca(s) | -2.76 | ||
| Ba^{2+}(aq) + 2 e^- | \longrightarrow Ba(s) | -2.90 | ||
| K^+(aq) + e^- | \longrightarrow K(s) | -2.92 | ||
| Li^+(aq) + e^- | \longrightarrow Li(s) | -3.04 | ||
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