For the following half-reaction, \(\mathscr{E}^{\circ}=-2.07 \mathrm{~V}\) :

\[\mathrm{AlF}_{6}{ }^{3-}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}+6 \mathrm{~F}^{-}\]

Using data from Table 11.1, calculate the equilibrium constant at \(25^{\circ} \mathrm{C}\) for the reaction

\[\mathrm{Al}^{3+}(a q)+6 \mathrm{~F}^{-}(a q) ightleftharpoons \mathrm{AlF}_{6}{ }^{3-}(a q)\]

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TABLE II.I Standard Reduction Potentials at 25C (298 K) for Many Common Half-reactions Half-reaction 8 (V) F +2e 2F Ag+ e Ag Co+ + e Co+ HO + 2H+ + 2e 2HO Ce4+ +e Ce+ PbO + 4H+ + SO +2e PbSO4 + 2HO MnO4 + 4H+ + 3e MnO + 2HO 104 + 2H+ + 2e 103 + HO MnO4 + 8H+ + Se Mn+ + 4HO Au+ + 3e Au PbO + 4H+ + 2e Pb+ + 2HO Cl +2e2CI CrO + 14H+ + 6e 2Cr+ + 7HO O + 4H+ + 4e 2HO MnO + 4H+ + 2e 103 + 6H + Se Br + 2e 2Br VO + 2H+ + VO+ AuCl4 + 3e Au + 4CI NO3 + 4H+ + 3e NO + 2HO CIO + e CIO 2Hg+ + 2e Hg+ - 4 Mn+ + 2HO 1+ 3HO Ag + e Ag 2+ Hg+ + 2e 2Hg Fe+ + e Fe+ O + 2H+ 2e HO MnO4 + e MnO4 1 +2e 21 Cute Cu + HO 2.87 1.99 1.82 1.78 1.70 1.69 1.68 1.60 1.51 1.50 1.46 1.36 1.33 1.23 1.21 1.20 1.09 1.00 0.99 0.96 0.954 0.91 0.80 0.80 0.77 0.68 0.56 0.54 0.52 Half-reaction O + 2HO + 4e Cu+ + 2e Cu HgCl +2e AgCl + e SO4 + 4H+ Cu+ +e 2H+2e7 4 1 Fe+ + 3e7 Pb+ + 2e7 Sn+ + 2e Ni+ + 2e H Fe Pb PbSO4 + 2e7 Cd+ + 2e 2HO +2e Mn+ + 2e Al+ + 3e 2Hg + 2CI+ Ag + CI + 2e HSO3 + HO Cu* - Sn Ni Pb + SO Cd - Fe Cr+ Cr Zn Fe+ + 2e Cr+ + e Cr+ + 3e Zn+ + 2e7 - - 40H- H + 2OH- Mn Al H + 2e 2H Mg2+ + 2e La+ + 3e7 Nae Ca+ + 2e Ba2+ + 2e K + e Li + e Mg La Na Ca Ba K Li 8 (V) 0.40 0.34 0.27 0.22 0.20 0.16 0.00 -0.036 -0.13 -0.14 -0.23 -0.35 -0.40 -0.44 -0.50 -0.73 -0.76 -0.83 -1.18 -1.66 -2.23 -2.37 -2.37 -2.71 -2.76 -2.90 -2.92 -3.05