Question 25.9: Write out the cell equation for the cell Fe(s)|Fe^2+(aq, 0.1......
Write out the cell equation for the cell
Fe(s)|Fe^{2+}(aq, 0.100\ M)||Fe^{2+}(aq, 2.00\ M)|Fe(s)Calculate the voltage generated by this “concentration cell” at 25.0°C. Why do you think this cell is called a concentration cell?
The two half reactions and the corresponding values of E^{\circ}_{red} from Table 25.3 are
Fe^{2+}(aq, 2.00\ M) + 2\ e^− → Fe(s) \qquad E^{\circ}_{red} = –0.45\ V
Fe(s) → Fe^{2+}(aq, 0.100\ M) + 2\ e^− \qquad E^{\circ}_{ox}= –E^{\circ}_{red} = +0.45\ V
Because the oxidation half reaction is the opposite of the reduction half reaction for this cell, E^{\circ}_{ox} = –E^{\circ}_{red}, and so
E^{\circ}_{cell} = E^{\circ}_{red} + E^{\circ}_{ox} = (–0.45\ V) + (0.45\ V) = 0\ VThus, the cell generates no voltage at standard conditions. However, the concentrations of the various species given are not at standard conditions and so we must apply the Nernst equation (Equation 25.13),
E_{cell} =E^{\circ}_{cell} – \left(\frac{0.02570\ V}{ν_e} \right) ln\ Q \qquad (at\ 25.0^{\circ}C) (25.13)
E_{cell} =E^{\circ}_{cell} – \left(\frac{0.02570\ V}{ν_e} \right) ln\ Q\\=E^{\circ}_{cell} – \left(\frac{0.02570\ V}{2} \right) ln\frac{[Fe^{2+}(aq,\ 0.100\ M]/M}{[Fe^{2+}(aq,\ 2.00\ M]/M} \\=0\ V – (0.01285\ V)ln\left(\frac{0.100}{2.00} \right) = 0.03850\ VThus, the cell generates 38.50 mV of electricity at 25.0°C. This sort of cell is called a concentration cell because it uses the difference in concentrations between the two solutions to generate a voltage. This is the electrical equivalent of the osmotic pressure discussed in Section 16-5.
| TABLE 25.3 Standard reduction voltages at 25.0°C for aqueous solutions (see also Appendix G)* | |||
| Electrode half reaction | E^{\circ}_{red}/V | ||
|
\uparrow |
Acidic solutions |
increasing strength |
|
| F_{2}(g) + 2\ e^− → 2\ F^−(aq) | +2.866 | ||
| O_{3}(g) + 2\ H^+(aq) + 2\ e^− → O_{2}(g) + H_2O(l ) | +2.076 | ||
| Co^{3+}(aq) + e^− → Co^{2+}(aq) | +1.92 | ||
| Cl_{2}(g) + 2\ e^− → 2\ Cl^−(aq) | +1.358 | ||
| O_{2}(g) + 4\ H^+(aq) + 4\ e^− → 2\ H_2O(l ) | +1.229 | ||
| Pt^{2+}(aq) + 2\ e^– → Pt(s) | +1.18 | ||
| NO_{3}^{–}(aq) + 4\ H^+(aq) + 3\ e^– → NO(g) + 2\ H_2O(l ) | +0.957 | ||
| Ag^+(aq) + e^− → Ag(s) | +0.7996 | ||
| Cu^+(aq) + e^− → Cu(s) | +0.521 | ||
| Cu^{+2}(aq) +2\ e^− → Cu(s) | +0.342 | ||
| Hg_2Cl_2(s) + 2\ e^− → 2\ Hg(l ) + 2\ Cl^−(aq) | +0.268 | ||
| AgCl(s) + e^− → Ag(s) + Cl^−(aq) | +0.2223 | ||
| Cu^{2+}(aq) + e^− → Cu^+(aq) | +0.153 | ||
| 2\ H^+(aq) + 2\ e^− → H_2(g) | +0.0 | ||
| Pb^{2+}(aq) + 2\ e^− → Pb(s) | -0.126 | ||
| V^{3+}(aq) + e^− → V^{2+}(aq) | -0.255 | ||
| Fe^{2+}(aq) + 2\ e^– → Fe(s) | –0.447 | ||
| Zn^{2+}(aq) + 2\ e^− → Zn(s) | -0.762 | ||
| Mn^{2+}(aq) + 2\ e^– → Mn(s) | –1.185 | ||
| Al^{3+}(aq) + 3\ e^− → Al(s) | -1.662 | ||
| H_2(g) + 2\ e^− → 2\ H^−(aq) | -2.23 | ||
| Mg^{2+}(aq) + 2\ e^− → Mg(s) | -2.372 | ||
| Na^+(aq) + e^− → Na(s) | -2.71 | ||
| Ca^{2+}(aq) + 2\ e^– → Ca(s) | –2.868 | ||
| K^+(aq) + e^– → K(s) | –2.931 | ||
| Li^+(aq) + e^− → Li(s) | -3.0401 | ||
| Basic solutions | |||
| O_2(g) + 2\ H_2O(l ) + 4\ e^− → 4\ OH^−(aq) | +0.401 | ||
| Cu(OH)_2(s) + 2\ e^− → Cu(s) + 2\ OH^−(aq) | -0.222 | ||
| Fe(OH)_3(s) + e^– → Fe(OH)_2(s) + OH^–(aq) | –0.56 | ||
| 2\ H_2O(l ) + 2\ e^− → H_2(g) + 2\ OH^−(aq) | -0.8277 | ||
| 2\ SO_{3}^{2−}(aq) + 2\ H_2O(l) + 2\ e^− → S_{2}O_{4}^{2−}(aq) + 4\ OH^−(aq) | -1.12 | ||
| *Data from CRC Handbook of Chemistry and Physics, 87th ed., ed. David R. Lide, CRC Press, 2006–2007 | |||