Use the following half-reactions to write three spontaneous reactions, calculate${E^{\circ }}_{cell}$for each reaction, and rank the strengths of the oxidizing and reducing agents:

(1)role="math" localid="1663755364258" ${\mathbf{\text{Al}}}^{\mathbf{\text{3 +}}}{\mathbf{\text{(aq) + 3e}}}^{\mathbf{\text{-}}}\mathbf{\text{nAl(s)}}$${\mathit{E}}^{\mathbf{\circ }}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{66}\mathit{V}$(2) ${\mathbf{\text{N}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{4}}}{\mathbf{\text{(g) + 2e}}}^{\mathbf{\text{-}}}{\mathbf{\text{n2NO}}}_{\mathbf{\text{2}}}^{\mathbf{\text{-}}}\mathbf{\text{(aq)}}$${\mathit{E}}^{\mathbf{\circ }}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{867}\mathit{V}$

(3)${\mathbf{\text{SO}}}_{\mathbf{\text{4}}}^{\mathbf{\text{2 -}}}{\mathbf{\text{(aq) +H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(l) + 2e}}}^{\mathbf{\text{-}}}{\mathbf{\text{nSO}}}_{\mathbf{\text{3}}}^{\mathbf{\text{2 -}}}{\mathbf{\text{(aq) + 2OH}}}^{\mathbf{\text{-}}}\mathbf{\text{(aq)}}$${\mathit{E}}^{\mathbf{\circ }}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{93}\mathit{V}$acidic solutions react spontaneously to the process of reduction and oxidation also used into half reaction and the electrons and atoms on both sides.

(1)${\text{Al}}^{3+}\left(\text{aq}\right)+3{\text{e}}^{-}\to \text{Al}\left(\text{s}\right)E^{\circ }=-1.66V$

(2)$N_2{O}_4\left(g\right)+2e^{-}\to 2N{O_2}^{-}\$\left(aq\right)\$E^{\circ }=0.867V$

(3)${\text{SO}}_4^{2-}\left(\text{aq}\right)+{\text{H}}_2\text{O}\left(\text{l}\right)+2{\text{e}}^{-}\to {\text{SO}}_3^{2-}\left(\text{aq}\right)+2{\text{OH}}^{-}{\text{E}}^{\circ }\text{=0.93V}$

For a reaction to be spontaneous,${{E^{\circ }}_{cell}}^{>0}$(a) We have to write three spontaneous reactions from the given half-reactions:

For a reaction to be spontaneous,${{E^{\circ }}_{cell}}^{>0}$

(a) Combinelocalid="1663756589726" ${}^{3\times \left(2\right)}$and reversed of${}^{2\times \left(1\right)}$

$3{\text{N}}_2{\text{O}}_4\left(\text{g}\right)+6{\text{e}}^{-}+2\text{Al}\left(\text{s}\right)\to 6{\text{NO}}_2^{-}\left(\text{aq}\right)+2{\text{Al}}^{3+}\left(\text{aq}\right)+6{\text{e}}^{-}$width="393">3N2O4(g)+6e-2AI(s)→6NO2-(aq)+2AI3+(aq)+6e-

Cancel common terms to obtain the spontaneous reaction:

$3N_2{O}_4\left(g\right)+2AI\left(s\right)\to 6N{O_2}^{-}\left(aq\right)+2A{I}^{3+}\left(aq\right){E^{\circ }}_{cell}={E^{\circ }}_{red}-{E^{\circ }}_{oxi}=0.867-(-1.66)=2.527V$

Cancel common to obtain the spontaneous reaction:

${\text{SO}}_{\text{4}}^{\text{2 -}}{\text{(aq) + II}}_{\text{2}}{\text{O(l) + 2NO}}_{\text{2}}^{\text{-}}\text{(aq)}\to {\text{SO}}_{\text{3}}^{\text{2 -}}{\text{(aq) + 2OII}}^{\text{-}}{\text{+N}}_{\text{2}}{\text{O}}_{\text{4}}{\text{(g) E}}_{\text{cell}}^{\text{a}}{\text{= E}}_{\text{red}}^{\text{a}}{\text{- E}}_{\text{oxi}}^{\text{a}}\text{= 0.93 - 0.867 = 0.063V}$

Cancel common terms to obtain the spontaneous reaction:

$3S{O_4}^{2-}\left(aq\right)+3H_{2}O\left(I\right)+AI\left(s\right)\to 3S{O_3}^{2-}\left(aq\right)+6O{H}^{-}+2A{I}^{3+}\left(aq\right){E^{\circ }}_{cell}={E^{\circ }}_{red-}{E^{\circ }}_{oxi}=0.93-(-1.66)=2.59V$

Oxidising agents :${\text{SO}}_4^{2-}\left(\text{aq}\right)>{\text{N}}_2{\text{O}}_4\left(\text{g}\right)>{\text{Al}}^{3+}\left(\text{aq}\right)$

Reducing agents :$\text{Al}\left(\text{s}\right)>{\text{NO}}_2^{-}\left(\text{aq}\right)>{\text{SO}}_3^{2-}\left(\text{aq}\right)$

Therefore, the work done is

(a)$3N_2{O}_4\left(g\right)+2AI\left(s\right)\to 6N{O_2}^{-}\left(aq\right)+2A{I}^{3+}\left(aq\right);{E^{\circ }}_{cell}=2.527V$

(b)$S{O_4}^{2-}\left(aq\right)+H_{2}O\left(I\right)+2N{O_2}^{-}\left(aq\right)\to S{O_3}^{2-}\left(aq\right)+2O{H}^{-}+N_2{O}_4\left(g\right);{E^{\circ }}_{cell}=0.063V$

(c)$3S{O_4}^{2-}\left(aq\right)+3H_{2}O\left(I\right)+2AI\left(s\right)\to 3S{O_3}^{2-}\left(aq\right)+6O{H}^{-}+2A{I}^{3+}\left(aq\right);{E^{\circ }}_{cell}=2.59V$

Oxidising agents :${\text{SO}}_4^{2-}\left(\text{aq}\right)>{\text{N}}_2{\text{O}}_4\left(\text{g}\right)>{\text{Al}}^{3+}\left(\text{aq}\right)$

Reducing agents :$\text{Al}\left(\text{s}\right)>{\text{NO}}_2^{-}\left(\text{aq}\right)>{\text{SO}}_3^{2-}\left(aq\right)$