Chapter 19, Problem 74RQ

Calculate $K_{\text{c}}$ for the system

${\text{Ni}}^{\text{2+}}+\text{Co}\rightleftharpoons {\text{Ni+Co}}^{\text{2+}}$

Use the data in Table 19.1 and assume $\text{T= 298 }K$.

TABLE 19.1 Standard Reduction Potentials at $25°C^a$

Half Reaction	${}^{E°\left(\text{volts}\right)}$
$\text{F2}\left(g\right)+2e^{-}\rightleftharpoons 2{\text{F}}^{\text{-}}\left(aq\right)$	+2.87
${\text{S}}_{\text{2}}{\text{O}}_{\text{8}}{}^{\text{2-}}\left(aq\right)+2e^{-}\rightleftharpoons 2{\text{SO}}_{\text{4}}{}^{\text{2-}}\left(aq\right)$	+2.01
${\text{PbO}}_{\text{2}}\left(s\right)+{\text{HSO}}_{\text{4}}{}^{\text{-}}+3{\text{H}}^{\text{+}}+2e^{-}\rightleftharpoons {\text{PbSO}}_{\text{4}}\left(s\right)+{\text{2H}}_{\text{2}}\text{O}$	+1.69
${\text{MnO}}_{\text{4}}{}^{\text{-}}\left(aq\right)+8{\text{H}}^{\text{+}}\left(aq\right)+5e^{-}\rightleftharpoons {\text{Mn}}^{\text{2+}}\left(aq\right)+4{\text{H}}_{\text{2}}\text{O}$	+1.51
$\text{PbO2}\left(s\right)+4{\text{H}}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons {\text{Pb}}^{\text{2+}}\left(aq\right)+2{\text{H}}_{\text{2}}\text{O}$	+1.46
${\text{BrO}}_{\text{3}}{}^{\text{-}}\left(aq\right)+6{\text{H}}^{\text{+}}\left(aq\right)+6e^{-}\rightleftharpoons {\text{Br}}^{\text{-}}\left(aq\right)+3{\text{H}}_{\text{2}}\text{O}$	+1.44
${\text{Au}}^{\text{3+}}\left(aq\right)+3e^{-}\rightleftharpoons \text{Au}\left(s\right)$	+1.42
${\text{Cl}}_{\text{2}}\left(g\right)+2e^{-}\rightleftharpoons 2{\text{Cl}}^{\text{-}}\left(aq\right)$	+1.36
${\text{O}}_{\text{2}}\left(g\right)+4{\text{H}}^{\text{+}}\left(aq\right)+4e^{-}\rightleftharpoons 2{\text{H}}_{\text{2}}\text{O}$	+1.23
${\text{Br}}_{\text{2}}\left(aq\right)+2e^{-}\rightleftharpoons 2{\text{Br}}^{\text{-}}\left(aq\right)$	+1.07
${\text{NO}}_{\text{3}}{}^{\text{-}}+4{\text{H}}^{\text{+}}\left(aq\right)+3e^{-}\rightleftharpoons \text{NO}\left(g\right)+2{\text{H}}_{\text{2}}\text{O}$	+0.96
${\text{Ag}}^{\text{+}}\left(aq\right)+e^{-}\rightleftharpoons \text{Ag}\left(s\right)$	+0.80
${\text{Fe}}^{\text{3}}{}^{\text{+}}\left(aq\right)+e^{-}\rightleftharpoons {\text{Fe}}^{\text{2+}}\left(aq\right)$	+0.77
${\text{I}}_{\text{2}}\left(s\right)+2e^{-}\rightleftharpoons 2{\text{I}}^{\text{-}}\left(aq\right)$	+0.54
${\text{NiO}}_{\text{2}}\left(s\right)+2{\text{H}}_{\text{2}}\text{O+}2e^{-}\rightleftharpoons \text{Ni}{\left(\text{OH}\right)}_2\left(s\right)+2{\text{OH}}^{\text{-}}\left(aq\right)$	+0.49
${\text{Cu}}^{\text{2+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Cu}\left(s\right)$	+0.34
${\text{SO}}_{\text{4}}{}^{\text{2-}}\left(aq\right)+4{\text{H}}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons {\text{H}}_{\text{2}}{\text{SO}}_{\text{3}}\left(aq\right)+{\text{H}}_{\text{2}}\text{O}$	0.17
$\text{AgBr}\left(s\right)+e^{-}\rightleftharpoons \text{Ag}\left(s\right)+{\text{Br}}^{\text{-}}\left(aq\right)$	+0.07
${\text{2H}}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons {\text{H}}_{\text{2}}\left(g\right)$	0
${\text{Sn2}}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Sn}\left(s\right)$	-0.14
${\text{Ni}}^{\text{2}}{}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Ni}\left(s\right)$	-0.25
${\text{Co}}^{\text{2}}{}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Co}\left(s\right)$	-0.28
${\text{Cd}}^{\text{2}}{}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Cd}\left(s\right)$	-0.40
${\text{Fe}}^{\text{2}}{}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Fe}\left(s\right)$	-0.44
${\text{Cr}}^{\text{3}}{}^{\text{+}}\left(aq\right)+3e^{-}\rightleftharpoons \text{Cr}\left(s\right)$	-0.74
${\text{Zn}}^2{}^{\text{+}}\left(aq\right)+2e^{-}\rightleftharpoons \text{Zn}\left(s\right)$	-0.76
${\text{2H}}_{\text{2}}\text{O+}2e^{-}\rightleftharpoons {\text{H}}_{\text{2}}\left(g\right){\text{+2OH}}^{\text{-}}\left(aq\right)$	-0.83
${\text{Al}}^{\text{3+}}\left(aq\right)\text{+3}{e}^{-}\rightleftharpoons \text{Al}\left(s\right)$	-1.66
${\text{Mg}}^{\text{2+}}\left(aq\right)\text{+2}{e}^{-}\rightleftharpoons \text{Mg}\left(s\right)$	-2.37
${\text{Na}}^{\text{+}}\left(aq\right)\text{+}{e}^{-}\rightleftharpoons \text{Na}\left(s\right)$	-2.71
${\text{Ca}}^{\text{2}}{}^{\text{+}}\left(aq\right)\text{+2}{e}^{-}\rightleftharpoons \text{Ca}\left(s\right)$	-2.87
${\text{K}}^{\text{+}}\left(aq\right)\text{+}{e}^{-}\rightleftharpoons \text{K}\left(s\right)$	-2.92
${\text{Li}}^{\text{+}}\left(aq\right)\text{+}{e}^{-}\rightleftharpoons \text{Li}\left(s\right)$	-3.05

^a See Appendix C, Table C.9 for a more complete listing.