Question

Calculatevalues for the following cells. Which reactions are spontaneous as written (under standard conditions)? Balance the equations. Standard reduction potentials are found in Table 11.1.

$\begin{array}{l}\mathbf{a}\mathbf{.}{{\mathbf{MnO}}_{\mathbf{4}}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{I}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\rightleftarrows }{\mathbf{I}}_{\mathbf{2}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{Mn}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\\ \mathbf{b}\mathbf{.}{{\mathbf{MnO}}_{\mathbf{4}}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{F}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\rightleftarrows }{\mathbf{F}}_{\mathbf{2}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{Mn}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\\ \mathbf{c}\mathbf{.}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftarrows }{\mathbf{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{H}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\\ \mathbf{d}\mathbf{.}{\mathbf{Au}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{Ag}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\rightleftarrows }{\mathbf{Ag}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{Au}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\end{array}$

Short answer

The values of ${{\mathrm{E}}^0}_{\mathrm{cell}}$ are,

a. 0.97V (Spontaneous)

b. -1.36V (Non-spontaneous)

c. -2.23V (Non-spontaneous)

d. 0.70V (Spontaneous)

Step-by-step solution

Definition of spontaneous reaction

Spontaneous reactions are those which is aspontaneous process under given conditions without any intervention. Such reactions are accompanied by certain distortion or change in
entropy.

Explanation of a.MnO4-(aq)+I-(aq)⇄I2(aq)+Mn2+(aq)

$\begin{array}{l}{\mathrm{E}}^0={{\mathrm{E}}^0}_{\mathrm{cathode}}-{{\mathrm{E}}^0}_{\mathrm{anode}}\\ {\mathrm{E}}^0=1.51-0.54\\ {\mathrm{E}}^0=0.97\mathrm{V}\end{array}$

Explanation of b.MnO4-(aq)+F-(aq)⇄F2(aq)+Mn2+(aq)

$\begin{array}{l}{\mathrm{E}}^0={{\mathrm{E}}^0}_{\mathrm{cathode}}-{{\mathrm{E}}^0}_{\mathrm{anode}}\\ {\mathrm{E}}^0=1.51-2.87\\ {\mathrm{E}}^0=-1.36\mathrm{V}\end{array}$

Explanation of c.H2(g)⇄H+(aq)+H-(aq)

$\begin{array}{l}{\mathrm{E}}^0={{\mathrm{E}}^0}_{\mathrm{cathode}}-{{\mathrm{E}}^0}_{\mathrm{anode}}\\ {\mathrm{E}}^0=-2.23-0.00\\ {\mathrm{E}}^0=-2.23\mathrm{V}\end{array}$

Explanation of d.Au3+(aq)+Ag(s)⇄Ag+(aq)+Au(s)E0

$\begin{array}{l}{\mathrm{E}}^0={{\mathrm{E}}^0}_{\mathrm{cathode}}-{{\mathrm{E}}^0}_{\mathrm{anode}}\\ {\mathrm{E}}^0=1.51-0.80\\ {\mathrm{E}}^0=0.70\mathrm{V}\end{array}$