Question

Calculate the standard cell potentials of galvanic cell in which the following reactions take place:
$2{\text{Cr}}\left( {\text{s}} \right) + 3{\text{C}}{{\text{d}}^{2 + }}\left( {{\text{aq}}} \right) \to 2{\text{C}}{{\text{r}}^{3 + }}\left( {{\text{aq}}} \right) + 3{\text{Cd}}\left( {\text{s}} \right)$

Answer 1

To solve this question, knowledge on Electrochemical cells is required. An electrochemical cell which is composed of two half-cells, One at which oxidation occurs is known as the anode and the other at which reduction occurs, known as the cathode. The cell potential of the reaction can be given by:
Formula used:
${{\text{E}}^0}_{{\text{cell}}}{\text{ = }}{{\text{E}}^0}_{{\text{cathode}}} - {{\text{E}}^0}_{{\text{anode}}}$
${\text{E}}_{{\text{cell}}}^{\text{0}}{\text{ = cell potential or the EMF of the cell}}$
${\text{E}}_{{\text{cathode}}}^{\text{0}}{\text{ = standard potential at the cathode}}$
${\text{E}}_{{\text{anode}}}^{\text{0}}{\text{ = standard potential at the anode}}$

Complete step by step answer:
Using the above equation we have:
${\text{E}}_{{\text{cell}}}^{\text{0}} = - 0.40 - \left( { - 0.74} \right) = 0.34{\text{V}}$
${\text{E}}_{{\text{cathode}}}^{\text{0}}{\text{ = standard reduction potential of the C}}{{\text{d}}^{2 + }}/{\text{Cd}}$
${\text{E}}_{{\text{anode}}}^{\text{0}}{\text{ = standard reduction potential of C}}{{\text{r}}^{{\text{3 + }}}}{\text{/Cr}}$
The Gibbs free energy of the cell can also be calculated from the cell potential or the EMF by the formula:
${{\Delta }}{{\text{G}}^0}{\text{ = }} - {{nF\Delta E}}_{{\text{cell}}}^0$.
Hence the Gibbs free energy for the above reaction is,
${{\Delta }}{{\text{G}}^0} = - \left[ {6 \times 96500 \times 0.34} \right] = 196860{\text{J/mol = }}196.86{\text{kJ/mol}}$

Note:
An electrochemical cell and an electrolytic cell are not similar. In an electrochemical cell, chemical energy is converted to electrical energy while in an electrolytic cell electrical energy is converted to chemical energy.
The cathode of an electrochemical cell is the site where reduction occurs and is represented by a positive charge, while the anode is the place where oxidation occurs and is represented by a negative charge.
An electrochemical cell and an electrolytic cell are not similar. In an electrochemical cell, chemical energy is converted to electrical energy while in an electrolytic cell electrical energy is converted to chemical energy.
The cathode of an electrochemical cell is the site where reduction occurs and is represented by a positive charge, while the anode is the place where oxidation occurs and is represented by a negative charge.