Question

In acidic solution${\mathbf{\text{O}}}_{\mathbf{\text{3}}}$,and${\mathbf{\text{Mn}}}^{\mathbf{\text{2+}}}$ion react spontaneously:

${\mathbf{\text{O}}}_{\mathbf{\text{3}}}{\mathbf{\text{(g)+Mn}}}^{\mathbf{\text{2+}}}{\mathbf{\text{(aq)+H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(l)O}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+MnO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(s)+2H}}}^{\mathbf{\text{+}}}{\mathbf{\text{(aq)\hspace{1em}E}}}_{\mathbf{\text{cell}}}^{\mathbf{\text{°}}}\mathbf{\text{=0.84V}}$

(a) Write the balanced half-reactions.

(b) Using Appendix D to find${\mathbf{\text{E}}}_{\mathbf{\text{casne}}}^{\mathbf{\text{°}}}{\mathbf{\text{,calculateE}}}_{\mathbf{\text{manganese}}}^{\mathbf{\text{°}}}\mathbf{\text{.}}$

Short answer

The required work is used to acidic solutions react spontaneously process of reduction and oxidation also used to get the standard reduction potential of manganese.

Step-by-step solution

Given acid solution reacts

(a) In acidic solution, ${\text{Mn}}^{\text{2+}}$is oxidized to, ${\text{Mn}}^{\text{4+}}$while${\text{O}}_{\text{3}}$ is reduced to ${\text{O}}_{\text{2}}$and${\text{H}}_{\text{2}}\text{O}$

${\text{Reduction:2H}}_{\text{(aq)}}^{\text{+}}{\text{+2e}}^{\text{-}}{\text{+O}}_{\text{3(g)}}\to {\text{O}}_{\text{2(g)}}{\text{+H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

${\text{Oxidation:2H}}_{\text{2}}{\text{O}}_{\text{(l)}}{\text{+Mnn}}_{\text{(aq)}}^{\text{2+}}\to {\text{MnOO}}_{\text{2(s)}}{\text{+2e}}^{\text{-}}{\text{+4H}}_{\text{(aq)}}^{\text{+}}$

Find standard reduction equations

(b) Given that ${\text{E}}_{\text{ozone}}^{\text{o}}\text{=-2.07V}$and${\text{E}}_{\text{cell}}^{\text{o}}\text{=0.84V}$, it is possible to get the standard reduction potential of Manganese by manipulating the equation used to get the

${\text{E}}_{\text{cell}}^{\text{o}}{\text{=E}}_{\text{reduced}}^{\text{o}}{\text{-E}}_{\text{oxidized}}^{\text{o}}$

Given the reactions above,

${\text{E}}_{\text{cell}}^{\text{o}}{\text{=E}}_{\text{ozone}}^{\text{o}}{\text{-E}}_{\text{manganese}}^{\text{o}}$

Substituting the known values for ${\text{E}}_{\text{cell}}^{\text{o}}$and${\text{E}}_{\text{ozone}}^{\text{o}}\text{,}$${\text{E}}_{\text{manganese}}^{\text{o}}$ can be isolated.

${\text{E}}_{\text{cell}}^{\text{o}}{\text{=E}}_{\text{ozone}}^{\text{o}}{\text{-E}}_{\text{manganese}}^{\text{o}}$${\text{E}}_{\text{manganese}}^{\text{o}}{\text{=E}}_{\text{ozone}}^{\text{o}}{\text{-E}}_{\text{cell}}^{\text{o}}$

${\text{E}}_{\text{manganese}}^{\text{o}}\text{=2.07-0.84}$

${\text{E}}_{\text{manganese}}^{\text{o}}\text{=1.23V.}$

Therefore, the work done is

${\text{(a)Reduction:2H}}_{\text{(aq)}}^{\text{+}}{\text{+2e}}^{\text{-}}{\text{+O}}_{\text{3(g)}}\to {\text{O}}_{\text{2(g)}}{\text{+H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

${\text{Oxidation:2H}}_{\text{2}}{\text{O}}_{\text{(l)}}{\text{+Mn}}_{\text{(aq)}}^{\text{2+}}\to {\text{MnMn}}_{\text{2(s)}}{\text{+2e}}^{\text{-}}{\text{+4H}}_{\text{(aq)}}^{\text{+}}\text{a}$

${\text{(b)E}}_{\text{manganese}}^{\text{o}}\text{=1.23V}$