The Electrochemical Series and Galvanic Cells

Introduction to the Electrochemical Series

The electrochemical series is a list of half-equations, arranged in order of their standard electrode potentials ($E^\ominus$). It provides a convenient way to predict the spontaneity of redox reactions and to design galvanic cells.

The electrochemical series ranks the relative strength of oxidants and reductants under standard conditions.

Structure of the Electrochemical Series

The series typically lists:

• Half-equations (reduction half-reactions).
• Standard electrode potentials ($E^\ominus$ in volts) measured relative to the standard hydrogen electrode (SHE).
• Oxidants on the left and reductants on the right.

Note: The more positive the $E^\ominus$ value, the stronger the oxidizing agent on the left-hand side of the half-equation.

Using the Electrochemical Series to Design Galvanic Cells

Predicting Spontaneity

A redox reaction is spontaneous if the oxidant is higher in the electrochemical series than the reductant. In other words, a species on the left of a half-equation will spontaneously oxidize a species on the right of any half-equation below it in the table.

Constructing Galvanic Cells

1. Identify the strongest oxidant and reductant: Use the electrochemical series to identify the strongest oxidizing agent (highest $E^\ominus$ value) and the strongest reducing agent (lowest $E^\ominus$ value).
2. Write the half-equations: Write the reduction half-equation for the oxidant and the oxidation half-equation for the reductant (reverse the reduction half-equation).
3. Construct the cell: Design a galvanic cell with two half-cells, one containing the oxidant and its reduced form, and the other containing the reductant and its oxidized form. Connect the half-cells with a salt bridge.

4. Calculate the cell potential: Calculate the standard cell potential ($E^\ominus_{cell}$) using the formula:

   $$E^\ominus_{cell} = E^\ominus_{reduction} - E^\ominus_{oxidation}$$

   Where:
   * $E^\ominus_{reduction}$ is the standard reduction potential of the reduction half-cell (cathode).
   * $E^\ominus_{oxidation}$ is the standard reduction potential of the oxidation half-cell (anode).

Example

Consider a galvanic cell using $Zn^{2+}/Zn$ and $Cu^{2+}/Cu$ half-cells. From the electrochemical series:

• $Cu^{2+}(aq) + 2e^- \rightleftharpoons Cu(s) \quad E^\ominus = +0.34 V$
• $Zn^{2+}(aq) + 2e^- \rightleftharpoons Zn(s) \quad E^\ominus = -0.76 V$

$Cu^{2+}$ is a stronger oxidant than $Zn^{2+}$, so it will be reduced at the cathode. $Zn$ will be oxidized at the anode.

• Reduction (Cathode): $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
• Oxidation (Anode): $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$

$E^\ominus_{cell} = +0.34 - (-0.76) = +1.10 V$

Limitations of the Electrochemical Series

1. Standard Conditions: The electrochemical series is based on standard conditions (298 K, 1 atm pressure, 1 M concentration). Deviations from these conditions can affect electrode potentials and cell voltages.

2. Reaction Rate: The electrochemical series indicates spontaneity but provides no information about the rate of the reaction. Some spontaneous reactions may be very slow.

3. Overpotential: In some cases, the actual potential required for a reaction to occur (especially at an electrode) is higher than the theoretical potential predicted by the electrochemical series. This is known as overpotential.

4. Non-Standard Concentrations: The Nernst equation must be used to calculate cell potentials under non-standard conditions.

   $$E_{cell} = E^\ominus_{cell} - \frac{RT}{nF}lnQ$$

   Where:
   * $E_{cell}$ is the cell potential under non-standard conditions.
   * $R$ is the ideal gas constant (8.314 J/mol·K).
   * $T$ is the temperature in Kelvin.
   * $n$ is the number of moles of electrons transferred in the balanced redox reaction.
   * $F$ is Faraday’s constant (96485 C/mol).
   * $Q$ is the reaction quotient.

5. Aqueous Solutions: The electrochemical series is most directly applicable to aqueous solutions. Different solvents can affect the relative strengths of oxidants and reductants.

6. Electrode Material: The electrochemical series assumes inert electrodes. If the electrodes themselves participate in the redox reaction, the series may not accurately predict the cell potential.

Predicting Products of Redox Reactions

The electrochemical series can be used to predict the products of redox reactions by identifying the strongest oxidant and reductant present.

Example

Consider a solution containing $Fe^{3+}$ and $I^-$. From the electrochemical series:

• $Fe^{3+}(aq) + e^- \rightleftharpoons Fe^{2+}(aq) \quad E^\ominus = +0.77 V$
• $I_2(s) + 2e^- \rightleftharpoons 2I^-(aq) \quad E^\ominus = +0.54 V$

$Fe^{3+}$ is a stronger oxidant than $I_2$, and $I^-$ is a stronger reductant than $Fe^{2+}$. Therefore, the spontaneous reaction is:

$2Fe^{3+}(aq) + 2I^-(aq) \rightarrow 2Fe^{2+}(aq) + I_2(s)$

Deducing Overall Equations from Redox Half-Equations

1. Identify the half-equations: Determine the oxidation and reduction half-equations.
2. Balance the electron transfer: Multiply each half-equation by a factor so that the number of electrons lost in oxidation equals the number of electrons gained in reduction.
3. Add the half-equations: Add the balanced half-equations together, canceling out the electrons.
4. Simplify the equation: Simplify the overall equation by canceling out any species that appear on both sides.