Electrochemistry: Reduction Potentials, Galvanic Cells, and Applications

Electrochemistry: Reduction Potentials and Galvanic Cells

Introduction to Galvanic Cells

Galvanic cells (also known as voltaic cells) are devices that generate electrical energy from spontaneous redox (reduction-oxidation) reactions. In these cells, oxidation and reduction reactions are separated into two half-cells, allowing electrons to flow through an external circuit, producing an electric current.

• Oxidation occurs at the anode (loss of electrons).

• Reduction occurs at the cathode (gain of electrons).

• The flow of electrons from anode to cathode generates electricity.

Reduction Potentials

The reduction potential (Ered) of a half-cell measures its tendency to gain electrons and be reduced. The higher (more positive) the reduction potential, the greater the tendency for reduction to occur.

• Standard Reduction Potential (Eθred): Measured under standard conditions (1 M concentration, 1 × 105 Pa pressure, 25°C).

• Cell Potential (Ecell): The maximum potential difference between the two half-cells in a galvanic cell.

• Spontaneity: A positive Ecell indicates a spontaneous reaction.

Key Equations

• Standard cell potential: $E^{\theta}_{\text{cell}} = E^{\theta}_{\text{cathode}} - E^{\theta}_{\text{anode}}$

Determining Electron Flow and Cell Reactions

When two half-cells are connected:

• The half-cell with the higher reduction potential acts as the cathode (reduction occurs).

• The half-cell with the lower reduction potential acts as the anode (oxidation occurs).

• Electrons flow from anode to cathode.

Example: In a silver-copper cell, Ag+ is reduced and Cu is oxidized, indicating that Eθred (Ag+/Ag) > Eθred (Cu2+/Cu).

The Standard Hydrogen Electrode (SHE)

The standard hydrogen electrode (SHE) is the reference electrode with an assigned potential of 0 V. It consists of a platinum electrode in contact with 1 M H3O+ and H2 gas at 1 atm.

• Any half-cell's Eθred is measured relative to the SHE.

• If the measured voltage is positive, the unknown half-cell is the cathode; if negative, it is the anode.

Electron Flow with SHE

• Positive voltage: Electrons flow from SHE (anode) to unknown half-cell (cathode).

• Negative voltage: Electrons flow from unknown half-cell (anode) to SHE (cathode).

Interpreting Reduction Potential Tables

Standard reduction potential tables list half-reactions as reductions. Key points:

• More positive Eθred: Stronger oxidizing agent (better at gaining electrons).

• More negative Eθred: Stronger reducing agent (better at losing electrons).

• Hydrogen is the reference point (Eθred = 0 V).

Calculating Standard Cell Potentials

To calculate the standard cell potential (Eθcell):

1. Identify the cathode (higher Eθred) and anode (lower Eθred).

2. Use the formula: $E^{\theta}_{\text{cell}} = E^{\theta}_{\text{cathode}} - E^{\theta}_{\text{anode}}$

Example: For a Zn-Cu cell:

• $E^{\theta}_{\text{red}} (\text{Cu}^{2+}/\text{Cu}) = 0.34\ \text{V}$

• $E^{\theta}_{\text{red}} (\text{Zn}^{2+}/\text{Zn}) = -0.76\ \text{V}$

• Cu2+/Cu is the cathode; Zn2+/Zn is the anode.

• $E^{\theta}_{\text{cell}} = 0.34\ \text{V} - (-0.76\ \text{V}) = 1.10\ \text{V}$

Writing Spontaneous Redox Reactions

Electrode potentials are written as reductions, but to write the overall cell reaction, one half-reaction must be reversed (as oxidation). The sign of Eθred is not changed when reversing the reaction for calculation purposes.

• Reactants: Stronger oxidizing agent (more positive Eθred) and stronger reducing agent (more negative Eθred).

• If Eθcell is positive, the reaction is spontaneous.

• If Eθcell is negative, the reaction is non-spontaneous (requires external energy, as in charging a battery).

Example: For Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), Eθcell = +1.10 V (spontaneous).

Oxidizing and Non-Oxidizing Acids

Acids can participate in redox reactions. Their ability to oxidize metals depends on the oxidizing strength of their anions compared to H+.

• Non-oxidizing acids: Anion is a weaker oxidizing agent than H+ (e.g., HCl, dilute H2SO4, H3PO4, most carboxylic acids).

• Oxidizing acids: Anion is a stronger oxidizing agent than H+ (e.g., HNO3, hot concentrated H2SO4, HClO4).

Table: Examples of Oxidizing and Non-Oxidizing Acids

Type	Acid	Reduction Reaction
Non-oxidizing	HCl (aq)	Cl– is a weaker oxidizing agent than H+
Non-oxidizing	H2SO4 (cold, dilute)	SO42– is a weaker oxidizing agent than H+
Non-oxidizing	H3PO4 (aq)	PO43– is a weaker oxidizing agent than H+
Non-oxidizing	Most carboxylic acids	e.g., CH3COOH, HCOOH
Oxidizing	HNO3 (conc)	$\text{NO}_3^- (aq) + 2\text{H}^+ (aq) + e^- \rightarrow \text{NO}_2 (g) + \text{H}_2\text{O} (l)$
Oxidizing	HNO3 (dilute)	$\text{NO}_3^- (aq) + 4\text{H}^+ (aq) + 3e^- \rightarrow \text{NO} (g) + 2\text{H}_2\text{O} (l)$
Oxidizing	HNO3 (very dilute, strong reducing agent)	$\text{NO}_3^- (aq) + 10\text{H}^+ (aq) + 8e^- \rightarrow \text{NH}_4^+ (aq) + 3\text{H}_2\text{O} (l)$
Oxidizing	H2SO4 (hot, conc)	$\text{SO}_4^{2-} (aq) + 4\text{H}^+ (aq) + 2e^- \rightarrow \text{SO}_2 (g) + 2\text{H}_2\text{O} (l)$
Oxidizing	H2SO4 (hot, conc, strong reducing agent)	$\text{SO}_4^{2-} (aq) + 10\text{H}^+ (aq) + 8e^- \rightarrow \text{H}_2\text{S}_2 (g) + 4\text{H}_2\text{O} (l)$
Oxidizing	HClO4 (aq)	$\text{ClO}_4^- (aq) + 8\text{H}^+ (aq) + 8e^- \rightarrow \text{Cl}^- (aq) + 4\text{H}_2\text{O} (l)$

Applications: The Potato Battery

Redox reactions can be harnessed in simple batteries, such as the potato battery. In this setup, two different metals are inserted into a potato, which acts as an electrolyte, allowing electron transfer between the metals.

• The voltage produced depends on the reduction potentials of the metals used.

• Potatoes (and other fruits/vegetables) serve as a medium for ion flow, not as the source of energy.

Example Calculations:

• Measured voltages: 0.400 V and 0.600 V (actual), compared to theoretical values (e.g., 1.10 V, 1.61 V).

• Difference between theoretical and actual values indicates inefficiencies in the system.

Additional info: The potato battery demonstrates practical aspects of electrochemistry, including the importance of electrode choice, electrolyte properties, and real-world inefficiencies.