Standard Cell Potential and Electrochemistry Study Notes

Electrochemistry: Standard Cell Potential

Standard Cell Potential ($E_{cell}^\circ$)

The standard cell potential is a measure of the driving force of the reduction potential ($E^\circ$) in a galvanic (voltaic) cell between two half-cells under standard conditions (1 M, 1 atm, 25°C).

• Standard reduction potentials are tabulated for half-reactions, typically referenced to the standard hydrogen electrode (SHE), which is assigned a potential of 0.00 V.

• The cell potential is calculated as the difference between the reduction potentials of the cathode and anode.

• Electrons flow from the anode (oxidation) to the cathode (reduction).

Standard Cell Potential Formula

The standard cell potential of an electrochemical cell is calculated using the following formula:

$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$

Example Calculation

Example: What is $E_{cell}^\circ$ for a voltaic cell based on the following reduction reactions in which the copper electrode is the cathode and the zinc electrode is the anode?

• $Cu^{2+} (aq) + 2e^- \rightarrow Cu (s)$    $E^\circ = +0.337$ V

• $Zn^{2+} (aq) + 2e^- \rightarrow Zn (s)$    $E^\circ = -0.763$ V

Solution:

$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ = 0.337\,V - (-0.763\,V) = 1.10\,V$

Spontaneity of a Chemical Reaction

The sign of $E_{cell}$ determines whether a reaction is spontaneous:

• If $E_{cell} > 0$, the reaction is spontaneous.

• If $E_{cell} < 0$, the reaction is nonspontaneous.

Example: Determining Spontaneity

Given the following half-reactions:

• $Cr^{3+} + 3e^- \rightarrow Cr (s)$    $E^\circ = -0.74$ V

• $Ag^+ + e^- \rightarrow Ag (s)$    $E^\circ = +0.80$ V

Find the standard cell potential and determine if the reaction is spontaneous.

$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ = 0.80\,V - (-0.74\,V) = 1.54\,V$

Since $E_{cell}^\circ > 0$, the reaction is spontaneous.

Practice Problems

Practice calculating the standard cell potential for various electrochemical cells using the provided standard reduction potentials.

Practice Example 1

• $Fe^{3+} + e^- \rightarrow Fe^{2+}$    $E^\circ = +0.77$ V

• $I_2 (s) + 2e^- \rightarrow 2I^-$    $E^\circ = +0.535$ V

$E_{cell}^\circ = 0.535\,V - 0.77\,V = -0.235\,V$

The negative value indicates the reaction as written is not spontaneous.

Practice Example 2

• $Cl_2 (g) + 2e^- \rightarrow 2Cl^-$    $E^\circ = +1.36$ V

• $Fe^{3+} + e^- \rightarrow Fe^{2+}$    $E^\circ = +0.77$ V

$E_{cell}^\circ = 1.36\,V - 0.77\,V = 0.59\,V$

The positive value indicates the reaction is spontaneous as written.

Practice Example 3

• $Ag^+ + e^- \rightarrow Ag (s)$    $E^\circ = +0.80$ V

• $Au^+ + e^- \rightarrow Au (s)$    $E^\circ = +1.69$ V

$E_{cell}^\circ = 0.80\,V - 1.69\,V = -0.89\,V$

The negative value indicates the reaction as written is not spontaneous.

Summary Table: Standard Reduction Potentials (Selected)

Half-Reaction	Standard Reduction Potential ($E^\circ$, V)
$Cu^{2+} + 2e^- \rightarrow Cu (s)$	+0.337
$Zn^{2+} + 2e^- \rightarrow Zn (s)$	-0.763
$Ag^+ + e^- \rightarrow Ag (s)$	+0.80
$Fe^{3+} + e^- \rightarrow Fe^{2+}$	+0.77
$Cl_2 (g) + 2e^- \rightarrow 2Cl^-$	+1.36
$I_2 (s) + 2e^- \rightarrow 2I^-$	+0.535
$Cr^{3+} + 3e^- \rightarrow Cr (s)$	-0.74
$Au^+ + e^- \rightarrow Au (s)$	+1.69

Key Points to Remember

• Always write half-reactions as reductions when using standard reduction potentials.

• The cathode is where reduction occurs; the anode is where oxidation occurs.

• Electrons flow from anode to cathode in the external circuit.

• A positive $E_{cell}^\circ$ indicates a spontaneous reaction under standard conditions.

Additional info: The above notes include inferred context and expanded explanations for clarity and completeness, as the original material was in outline and practice problem format.