Question

In the button cells widely used in watches and other devices the following reaction takes place:
\[Zn\left( s \right) + A{g_2}O\left( s \right) + {H_2}O\left( l \right) \to Z{n^{2 + }}\left( {aq} \right) + 2Ag\left( s \right) + 2O{H^ - }\left( {aq} \right)\]
Determine \[{\Delta _r}{G^\theta }\] and \[{E^\theta }\] for the reaction.

Answer 1

Hint: In an electrolytic cell, there are two electrodes. These two electrodes are cathode and anode. At the cathode, reduction occurs and at the anode oxidation occurs.

Complete step by step answer:
For the reaction,
\[Zn\left( s \right) + A{g_2}O\left( s \right) + {H_2}O\left( l \right) \to Z{n^{2 + }}\left( {aq} \right) + 2Ag\left( s \right) + 2O{H^ - }\left( {aq} \right)\]
We will now calculate \[{\Delta _r}{G^\theta }\] and \[{E^\theta }\] values.
We know that,
\[E_{cell}^\theta = E_{cathode}^0 - E_{anode}^0\]
Here, \[E_{cell}^\theta \] = cell potential
\[E_{cathode}^0\] = electrode potential of cathode
\[E_{anode}^0\] = electrode potential of anode
In the above reaction, the cathode is silver and anode is zinc.
So, we can write the same for zinc and silver in the following way.
\[
  {\text{E}}_{{\text{cell}}}^{{\theta }} = {\text{E}}_{{\text{cathode}}}^{\text{0}} - {\text{E}}_{{\text{anode}}}^{\text{0}} \\
   = {\text{E}}_{{\text{Ag}}}^{\text{0}} - {\text{E}}_{{\text{Zn}}}^{\text{0}} \\
   = 0.344 - \left( { - 0.76} \right) \\
   = 1.104\,{\text{V}} \\
 \]
We know that,
\[{{\Delta }}{{\text{G}}^{\text{0}}}{\text{ = }} - {\text{nFE}}_{{\text{cell}}}^{\text{0}}\],
So we can find the value of \[{{\Delta }}{{\text{G}}^{\text{0}}}\] for the above reaction using the following expression.
\[
  {{\Delta }}{{\text{G}}^{\text{0}}}{\text{ = }} - {\text{nFE}}_{{\text{cell}}}^{\text{0}} \\
   = - 2 \times 96500 \times 1.104 \\
   = - 213072\,{\text{J}} \\
  {\text{ = - 213}}\,\,{\text{kJ}}\, \\
 \]

Additional information:
An electrochemical cell produces electrical energy. Two most commonly used electrolytic cells are the electrolytic cell and the galvanic cell. This cell can convert the chemical energy into the electrical energy. An electrochemical cell consists of two half cells. In the electrochemical cell the two electrodes, the cathode and the anode, are connected through a salt bridge. The reduction takes place at the cathode and the oxidation takes place at the anode. A voltmeter is also connected joining the cathode and the anode. A cathode is represented by a positive sign as the electrons go into the cathode and an anode is represented by a negative sign as the electrons come off the anode in the cell.

Note: There are two common electrochemical cells. These are galvanic cells and electrolytic cells. In the galvanic cell, chemical energy is converted to electrical energy and in the electrolytic cell, electrical energy is converted into chemical energy.