Calculate the cell potential for the following reaction as written at 25.00 °C,

Question

Calculate the cell potential for the following reaction as written at 25.00 °C, given that [Mg2 ] = 0.771 M and [Sn2 ] = 0.0110 M. Standard reduction potentials can be found here.

Mg(s) + Sn2+(aq) = Mg2+(aq) + Sn(s)

–3.04

Reduction Half-Reaction Standard Potential Ered° (V) F2(g) + 2e– 2F–(aq) +2.87 O3(g) + 2H3O+(aq) + 2e–   O2(g) + 3H2O(l) +2.076 Co3+(aq) + e–   Co2+(aq) +1.92 H2O2(aq) + 2H3O+(aq) + 2e–   2H2O(l) +1.776 N2O(g) + 2H3O+(aq) + 2e–   N2(g) + 3H2O(l) +1.766 Ce4+(aq) + e– Ce3+(aq) +1.72 PbO2(s) + SO42–(aq) + 4H3O+(aq) + 2e– PbSO4(s) + 6H2O(l) +1.6913 MnO4–(aq) + 4H3O+(aq) + 3e–   MnO2(s) + 6H2O(l) +1.679 NiO2(s) + 4H3O+(aq) + 2e–   Ni2+(aq) + 6H2O(l) +1.678 HClO2(aq) + 2H3O+(aq) + 2e- HClO(aq) + 3H2O(l) +1.645 2HClO2(aq) + 6H3O+(aq) + 6e- Cl2(g) + 10H2O(l) +1.628 2HClO(aq) + 2H3O+(aq) + 2e– Cl2(g) +4H2O(l) +1.611 H5IO6(s) + H3O+(aq) + 2e–   IO3–(aq) + 4H2O(l) +1.601 RuO4-(aq) + 4H3O+(aq) + 2e- RuO2+(aq) + 6H2O(l) +1.6 2NO(g) + 2H3O+(aq) + 2e–   N2O(g) + 3H2O(l) +1.591 IO4-(aq) + 2H3O+(aq) + 2e– IO3-(aq) + 3H2O(l) +1.589 MnO4–(aq) + 8H3O+(aq) + 5e–   Mn2+(aq) + 12H2O(l) +1.507 RuO2+(aq) + 2H3O+(aq) + e- Ru(OH)22+(aq) + 2H2O(l) +1.5 Au3+(aq) + 3e– Au(s) +1.498 2ClO3-(aq) + 12H3O+(aq) + 10e- Cl2(g) + 18H2O(l) +1.47 PbO2(s) + 4H3O+(aq)+ 2e– Pb2+(aq) + 6H2O(l) +1.455 ClO3–(aq) + 6H3O+(aq) + 6e–   Cl–(aq) + 9H2O(l) +1.451 BrO3–(aq) + 6H3O+(aq) + 5e– 1/2Br2(l) + 9H2O(l) +1.482 HOI(aq) + H3O+(aq) + e– 1/2I2(s) + 2H2O(l) +1.430 RuO4(aq) + 6H3O+(aq) + 4e- Ru(OH)22+(aq) + 8H2O(l) +1.40 2ClO4–(aq) + 16H3O+(aq) + 14e– Cl2(g) + 24H2O(l) +1.39 ClO4–(aq) + 8H3O+(aq) + 8e– Cl–(aq) + 12H2O(l)   +1.389 Cl2(g) + 2e– 2Cl–(aq) +1.36 ClO4–(aq) + 6H3O+(aq) + 6e– ClO–(aq) + 9H2O(l) +1.36 HBrO(aq) + H3O+(aq) + 2e– Br– + 2H2O(l) +1.331 IO4-(aq) + 8H3O+(aq) + 7e– 1/2I2(s) + 12H2O(l) +1.318 ClO2(aq) + H3O+(aq) + e- HClO2(aq) + H2O(l) +1.277 Cr2O72–(aq) + 14H3O+(aq) + 6e– 2Cr3+(aq) + 21H2O(l) +1.232 O2(g) + 4H+(aq) + 4e– 2H2O(l) +1.23 MnO2(s) + 4H3O+(aq) + 2e– Mn2+(aq) + 6H2O(l) +1.224 ClO3-(aq) + 3H3O+(aq) + 2e- HClO2(aq) + 4H2O(l) +1.214 2IO3–(aq) + 12H3O+(aq) + 10e– I2(s) + 18H2O(l) +1.195 ClO4–(aq) + 2H3O+(aq) + 2e– ClO3–(aq) + 3H2O(l) +1.189 Pt2+(aq) + 2e–   Pt(s) +1.18 IO3-(aq) + 5H3O+(aq) + 4e– HOI(aq) + 7H2O(l) +1.154 ClO3-(aq) + 2H3O+(aq) + e- ClO2(aq) + 3H2O(l) +1.152 Br2(aq) + 2e–   2Br–(aq) +1.0873 Br2(l) + 2e– 2Br–(aq) +1.07 RuO4(aq) + 8H3O+(aq) + 8e- Ru(s) + 12H2O(l) +1.04 NO2(g) + 2H3O+(aq) + 2e–   NO(g) + 3H2O(l) +1.03 RuO4(aq) + e- RuO4-(aq) +1.00 NO3–(aq) + 4H3O+(aq) +3e–   NO(g) + 6H2O(l) +0.957 2Hg2+(aq) + 2e–   Hg22+(aq) +0.920 Ru(OH)22+(aq) + 2H3O+(aq) + e- Ru3+(aq) + 4H2O(l) 0.86 Hg2+(aq) + 2e–   Hg(l) +0.851 ClO–(aq) + H2O(l) + 2e– Cl–(aq) + 2OH–(aq) +0.81 Ag+(aq) + e– Ag(s) +0.80 Hg22+(aq) + 2e–   2Hg(l) +0.7973 Fe3+(aq) + e–   Fe2+(aq) +0.771 Ni(OH)2(s) + 2e–   Ni(s) + 2OH–(aq) +0.72 p-benzoquinone + H3O+(aq) + 2e–   hydroquinone + H2O(l) +0.6992 O2(g) + 2H3O+(aq) + 2e–   H2O2(l) + 2H2O(l) +0.695 Ru(OH)22+(aq) + 2H3O+(aq) + 4e- Ru(s) + 4H2O(l) +0.68 MnO4–(aq) + 2H2O(l) + 3e–   MnO2(s) + 4OH–(aq) +0.595 I2(s) + 2e– 2I–(aq) +0.54 I3–(aq) + 2e– 3I–(aq) +0.536 Cu+(aq) + e– Cu(s) +0.52 Ru2+(aq) + 2e- Ru(s) +0.455 O2(g) + 2H2O + 4e–   4OH–(aq) +0.401 Fe(CN)63–(aq) + e–   Fe(CN)64–(aq) +0.358 Cu2+(aq) + 2e– Cu(s) +0.34 Hg2Cl2(s) + 2e–   2Hg(l) + 2Cl–(aq) +0.26808 Ru3+(aq) + e- Ru2+(aq) +0.249 HAsO2(s) + 3H3O+(aq) + 3e– As(s) + 5H2O +0.248 AgCl(s) + e–   Ag(s) + Cl-(aq) +0.22233 Cu2+(aq) + e–   Cu+(aq) +0.153 Sn4+(aq) +2e–   Sn2+(aq) +0.151 S(s) + 2H3O+(aq) + 2e–   H2S(s) + 2H2O(l) +0.14 NO3–(aq) +2H2O(l) + 3e– NO(g) + 4OH–(aq) +0.109 N2(g) + 8H3O+(aq) + 6e–   2NH4+(aq) +8H2O(l) +0.092 S4O62–(aq) + 2e–   2S3O32–(aq) +0.08 AgBr(s) + e–   Ag(s) + Br–(aq) +0.07133 2H+(aq) + 2e– H2(g) 0.00 Fe3+(aq) + 3e– Fe(s) -0.04 [Co(NH3)6]3+(aq) + e–   [Co(NH3)6]2+(aq) -0.108 Pb2+(aq) + 2e– Pb(s) –0.13 Sn2+(aq) + 2e– Sn(s) –0.14 O2(g) + 2H2O(l) + 2e–   H2O2(l) + 2OH–(aq) –0.146 AgI(s) + e–   Ag(s) + I– (aq) –0.15224 CO2(g) + 2H3O+(aq) + 2e–   HCO2H(s) + 2H2O(l) –0.199 Cu(OH)2(s) + 2e–   Cu(s) + 2OH–(aq) –0.222 Ni2+(aq) + 2e– Ni(s) –0.26 Co2+(aq) + 2e– Co(s) –0.28 PbSO4(s) + 2e–   Pb(s) + SO42–(aq) –0.3588 SeO32–(aq) + 3H2O(l) + 4e–   Se + 6OH–(aq) –0.366 Cd2+(aq) + 2e–    Cd(s) –0.403 Cr3+(aq) + e–   Cr2+(aq) –0.407 Fe2+(aq) + 2e– Fe(s) –0.44 NO2–(g) + H2O(l) + 3e–   NO(g) + 2OH–(aq) –0.46 S(s) + 2e– S2–(aq) –0.48 2CO2(g) + 2H3O+(aq) + 2e–   H2C2O4(s) + H2O(l) –0.49 TiO2(s) + 4H3O+ + 2e–   Ti2+(aq) + 6H2O(l) –0.502 Au(CN)2–(aq) + e–   Au(s) + 2CN–(aq) –0.60 Cr3+(aq) + 3e– Cr(s) –0.74 Zn2+(aq) + 2e– Zn(s) –0.76 Cd(OH)2(s) + 2e–    Cd(s) + 2OH–(aq) –0.809 2H2O(l) + 2e– H2(g) + 2OH–(aq) –0.83 Ti3+(aq) + e–   Ti2+(aq) –0.85 H3BO3(s) + 3H3O+ + 3e–   B(s) + 6H2O(l) –0.8698 Cr2+(aq) + 2e– Cr(s) –0.91 SO42–(aq) + H2O(l) + 2e–   SO32–(aq) + 2OH–(aq) –0.93 CNO–(aq) + H2O(l) + 2e–   CN–(aq) + 2OH–(aq) –0.970 [Zn(NH3)4]2+(aq) + 2e–   Zn(s) + 4NH3(aq) –1.04 Mn2+(aq) + 2e–   Mn(s) –1.185 Cr(OH)3(s) + 3e– Cr(s) + 3OH–(aq) –1.48 Ti2+(aq) + 2e–   Ti(s) –1.630 Al3+(aq) + 3e– Al(s) –1.66 Al(OH)3(s) + 3e– Al(s)+3OH–(aq) –2.31 Mg2+(aq) + 2e– Mg(s) –2.38 Mg(OH)2(s) + 2e– Mg(s) + 2OH–(aq) –2.69 Na+(aq) + e– Na(s) –2.71 Ca2+(aq) + 2e– Ca(s) –2.87 Ba2+(aq) + 2e– Ba(s) –2.912 K+(aq) + e–   K(s) –2.931 Ba(OH)2(s) + 2e–   Ba(s) + 2OH–(aq) –2.99 Ca(OH)2(s) + 2e–   Ca(s) + 2OH–(aq) –3.02 Cs+(aq) + e– Cs(s) –3.026 Li+(aq) + e– Li(s)

–3.04

Explanation / Answer

Mg(s) + Sn2+(aq) = Mg2+(aq) + Sn(s)

Mg2+(aq) + 2e– Mg(s) –2.38

Sn2+(aq) + 2e– Sn(s) –0.14

E°cell = Ered - Eox = -0.14 - (-2.38) = 2.24 V

Nernst equation

Ecell = E°cell - 0.0592/n*log(Q)

Q = [Mg+2]/[Sn+2]

Ecell = E°cell - 0.0592/n*log([Mg+2]/[Sn+2])

Ecell = 2.24 - 0.0952/2 * log(0.771/0.0110) = 2.1521

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