Question

The standard reduction potentials of \[C{{u}^{2+}}\parallel Cu\]and \[C{{u}^{2+}}\parallel C{{u}^{+}}\]are \[0.337V\]and\[0.153V\],respectively . The standard electrode potential of \[C{{u}^{2+}}\parallel C{{u}^{+}}\]half cell is:
A. \[0.184V\]
B. \[0.827V\]
C. \[0.521V\]
D. \[0.490V\]

Answer 1

Hint: The standard reduction potential can be subtracted by taking away the standard reduction potential for the response happening at the anode from the standard reduction potential for the response happening at the cathode.

Step by step answer:
Galvanic cells have positive cell potentials, and all the reduction reactions are reversible. The reaction at the anode will be the half-reaction with the smaller or more negative standard reduction potential.
Given:
Standard reduction potential of\[C{{u}^{2+}}\parallel Cu\] = \[0.337V\]
Standard reduction potential of \[C{{u}^{2+}}\parallel C{{u}^{+}}\] = \[0.153V\]
To find:
The standard electrode potential of half cell = ?
Formula to be used:
\[\vartriangle {{G}^{\circ }}=-nF{{E}^{\circ }}\]
Calculation:
\[C{{u}^{2+}}+2{{e}^{-}}\to Cu-1\]
  \[C{{u}^{2+}}+{{e}^{-}}\to C{{u}^{+}}-2\]
\[\vartriangle {{G}^{\circ }}of2=-\left( 1 \right)\left( F \right)\left( 0.153V \right)\]
When equation 1 and 2 are subtracted it gives
\[C{{u}^{+}}+{{e}^{-}}\to Cu\]
\[\vartriangle {{G}^{\circ }}\]for the obtained equation is
\[\vartriangle {{G}^{\circ }}=\vartriangle {{G}^{\circ }}of1=\vartriangle {{G}^{\circ }}of2\]
\[\vartriangle {{G}^{\circ }}=-\left( 4 \right)F\left\{ \left( 2*0.337-0.153 \right) \right\}\]
\[{{E}_{C{{u}^{+}}\parallel Cu}}=2*0.337-0.153=0.521V\]
Conclusion:
The standard electrode potential of Cu+|Cu half cell is \[0.521V\],

Additional Information: Element \[\left( {{F}_{2}} \right)\]at the topmost position of electrochemical series which has the highest reduction potential is the strongest oxidizing agent. Oxidizing power decreases from top to bottom in the series. The standard electrode potential of an electrode can be measured by the quantity pairing it with the SHE and measuring the cell potential of the resulting galvanic cell.

Note: The standard reduction potential is the reduction potential of a molecule under specific, standard conditions. Standard reduction potentials can be useful in determining the directionality of a reaction. The reduction potential of a given species can be considered to be the negative of the oxidation potential.