Balance each skeleton reaction, calculateand state whether the reaction is spontaneous:

(a) ${\mathbf{\text{Ag(s) + Cu}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{(aq)Ag}}}^{\mathbf{\text{+}}}\mathbf{\text{(aq) + Cu(s)}}$

(b) ${\mathbf{\text{Cd(s) + Cr}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{7}}}^{\mathbf{\text{2 -}}}{\mathbf{\text{(aq)Cd}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{(aq) + Cr}}}^{\mathbf{\text{3 +}}}\mathbf{\text{(aq)}}$

c) ${\mathbf{\text{Ni}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{(aq) + Pb(s)Ni(s) + Pb}}}^{\mathbf{\text{2 +}}}\mathbf{\text{(aq)}}$

(a) To balance each reaction, divide into half reactions and balance the electrons and atoms on both sides.

${\text{Ag}}_{\text{(s)}}{\text{+ Cu}}_{\text{(aq)}}^{\text{2 +}}\to {\text{Ag}}_{\text{(aq)}}^{\text{+}}{\text{+ Cu}}_{\text{(s)}}{\text{2xOHR:2Ag}}_{\text{(s)}}\to {\text{2Ag}}_{\text{(aq)}}^{\text{+}}{\text{+ 2e}}^{\text{-}}{\text{RHR:Cu}}_{\text{(aq)}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}\to {\text{Cu}}_{\text{(s)}}{\text{Reaction :Cu}}_{\text{(aq)}}^{\text{2 +}}{\text{+ 2Ag}}_{\text{(s)}}\to {\text{Cu}}_{\text{(s)}}{\text{+ Ag}}_{\text{(aq)}}^{\text{+}}$

${\text{E}}_{\text{oxidation}}^{\text{o}}{\text{= E}}_{{\text{Ag}}^{\text{+}}}^{\text{o}}{\text{= 0.80VE}}_{\text{reduction}}^{\text{o}}{\text{= E}}_{{\text{Cu}}^{\text{2 +}}}^{\text{o}}{\text{= 0.15VE}}_{\text{cell}}^{\text{o}}{\text{= E}}_{\text{reduction}}^{\text{o}}{\text{- E}}_{\text{oxidation}}^{\text{o}}{\text{= E}}_{{\text{Cu}}^{\text{2 +}}}^{\text{o}}{\text{- E}}_{{\text{Ag}}^{\text{+}}}^{\text{o}}{\text{= 0.15 - 0.80 = - 0.65VE}}_{\text{cell}}^{\text{o}}\text{= - 0.65V}$non-spontaneous reaction

(b) to balance each reaction, divide into half reactions and balance the redox through the half-reaction method.

${\text{Cr}}_{\text{2}}{\text{O}}_{\text{7(aq)}}^{\text{2 -}}{\text{+ Cd}}_{\text{(s)}}\to {\text{Cd}}_{\text{(aq)}}^{\text{2 +}}{\text{+ Cr}}_{\text{(aq)}}^{\text{3 +}}$

Separate the half reactions.

$\text{OHR:Cd}\to {\text{Cd}}^{\text{2 +}}{\text{RHR:Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}\to {\text{+ Cr}}^{\text{3 +}}$

Balance electrons and non-O atoms.

$\text{OHR:Cd}\to {\text{Cd}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}{\text{RHR:Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}{\text{+ 6e}}^{\text{-}}\to {\text{+ 2Cr}}^{\text{3 +}}$

Balance reaction charges with$H^{+}$(acidic environment).

$\text{OHR:Cd}\to {\text{Cd}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}{\text{RHR:Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}{\text{+ 6e}}^{\text{-}}{\text{+ 14H}}^{\text{+}}\to {\text{+ 2Cr}}^{\text{3 +}}$

Balanceatoms by adding$H_{2}O$to the opposite side.

localid="1663850791778" $\text{OHR:Cd}\to {\text{Cd}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}{\text{RHR:Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}{\text{+ 6e}}^{\text{-}}{\text{+ 14H}}^{\text{+}}\to {\text{+ 2Cr}}^{\text{3 +}}{\text{+ 7H}}_{\text{2}}\text{O}$$\text{OHR:Cd}\to {\text{Cd}}^{\text{2 +}}{\text{+ 2e}}^{\text{-}}{\text{RHR:Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}{\text{+ 6e}}^{\text{-}}{\text{+ 14H}}^{\text{+}}\to {\text{+ 2Cr}}^{\text{3 +}}{\text{+ 7H}}_{\text{2}}\text{O}$

Finding multiply reactions by least common factor and combine half reactions, and cancel common ions/ compounds on both sides accordingly.

$3xOHR:3\text{Cd}\to 3{\text{Cd}}^{2+}+2e^{-}RHR:{\text{Cr}}_2{\text{O}}_7^{2-}+6e^{-}+14{\text{H}}^{+}\to +2{\text{Cr}}^{3+}+7{\text{H}}_2\text{O Reaction}:{\text{Cr}}_2{\text{O}}_{7\left(aq\right)}^{2-}+3{\text{Cd}}_{\left(s\right)}+14{\text{H}}_{\left(aq\right)}^{+}\to +2{\text{Cr}}_{\left(aq\right)}^{3+}+7{\text{H}}_2\text{O}\left(l\right)+3{\text{Cd}}_{\left(aq\right)}^{2+}$localid="1663850738508" ${\text{E}}_{\text{oxidation}}^{\text{o}}{\text{= E}}_{{\text{Cd}}^{\text{2 +}}}^{\text{o}}{\text{= - 0.40VE}}_{\text{reduction}}^{\text{o}}{\text{= E}}_{{\text{C}}_{{\text{r}}_{\text{2}}}{\text{O}}_{\text{7}}^{\text{2 -}}}^{\text{o}}{\text{= 1.33VE}}_{\text{cell}}^{\text{o}}{\text{= E}}_{\text{reduction}}^{\text{o}}{\text{-E}}^{\text{o}}{\text{oxidation = E}}_{{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}^{\text{2 -}}}^{\text{o}}{\text{- E}}_{{\text{Cd}}^{\text{2 +}}}^{\text{o}}{\text{= 1.33 - ( - 0.40) = 1.74VE}}_{\text{cell}}^{\text{o}}\text{= 1.74}$To balance each reaction, divide into half reactions and balance the electrons and atoms on both sides.

$N{i}_{\left(aq\right)}^{2+}+P{b}_{\left(s\right)}\to P{b}_{\left(aq\right)}^{2+}+N{i}_{\left(s\right)}$

$RHR:N{i}_{\left(aq\right)}^{2+}+2e^{-}\to N{i}_{\left(s\right)}OHR:P{b}_{\left(s\right)}\to P{b}_{\left(aq\right)}^{2+}+2e^{-}$

$\text{Reaction}:N{i}_{\left(aq\right)}^{2+}+P{b}_{\left(s\right)}\to P{b}_{\left(aq\right)}^{2+}+N{i}_{\left(s\right)}$

${\text{E}}_{\text{oxidation}}^{\text{o}}{\text{= E}}_{{\text{Pb}}^{\text{2 +}}}^{\text{o}}\text{= - 0.13}$

${\text{E}}_{\text{reduction}}^{\text{o}}{\text{= E}}_{{\text{Ni}}^{\text{2 +}}}^{\text{o}}{\text{= - 0.25E}}_{\text{cell}}^{\text{o}}{\text{= E}}_{\text{reduction}}^{\text{o}}{\text{-E}}^{\text{o}}\text{oxidation}$

${\text{= E}}_{{\text{Ni}}^{\text{2 +}}}^{\text{o}}{\text{- E}}_{{\text{Ni}}^{\text{2 +}}}^{\text{o}}$

$=-0.25-(-0.13)=-0.12V$

${\text{E}}_{\text{cell}}^{\text{o}}\text{= - 0.12,}$non-spontaneous reaction

Therefore ,the work done is

$\left(\text{a}\right){\text{Cu}}_{\left(aq\right)}^{2+}+2{\text{Ag}}_{\left(\text{s}\right)}\to \text{Cu}{u}_{\left(s\right)}+{\text{Ag}}_{\left(aq\right)}^{+};E_{cell}^o=-0.65\text{V},\text{non - spontaneous reaction}$

localid="1663850751129" $\left(b\right){\text{Cr}}_2{\text{O}}_{7\left(aq\right)}^{2-}+3{\text{Cd}}_{\left(s\right)}+14{\text{H}}_{\left(aq\right)}^{+}\to +2C{r}_{\left(aq\right)}^{3+}+7{\text{H}}_2\text{O}\left(l\right)+3C{d}_{\left(aq\right)}^{2+};E_{cell}^o=1.74\text{, spontaneous reaction}$$\text{(c)}N{i}_{\left(aq\right)}^{2+}+P{b}_{\left(s\right)}\to P{b}_{\left(aq\right)}^{2+}+N{i}_{\left(s\right)};E_{cell}^o=-0.12\text{, non - spontaneous reaction}$

${\text{H}}_2{\text{O}}_{2\left(aq\right)}+N{i}_{\left(aq\right)}^{2+}\to 2H_{\left(aq\right)}^{+}+N{i}_{\left(s\right)}+H_2{O}_{2\left(aq\right)};E_{cell}^o=-0.93,$non-spontaneous reaction