Electrochemistry: Redox Reactions, Electrochemical Cells, and Cell Potentials

Electrochemistry

Learning Objectives

• Identify redox reactions and the species being oxidized and reduced using oxidation numbers.

• Describe the components of an electrochemical cell.

• Determine if a redox reaction is spontaneous under standard conditions using cell potentials and their relationships to Gibbs free energy and equilibrium.

• Calculate the cell potential under nonstandard conditions and understand the effect of concentration on the cell potential and their relationships to Gibbs free energy and equilibrium.

15.1 Redox Reactions

Introduction to Redox Reactions

Electrochemistry focuses on chemical reactions involving the transfer of electrons, known as redox reactions. These reactions are fundamental to the generation of electrical energy from chemical processes.

• Redox Reaction Example: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

• Electrons are transferred from Zn(s) to Cu2+(aq).

Types of Redox Reactions

• Molecular Reaction: $\text{Zn}(s) + \text{CuSO}_4(aq) \rightarrow \text{Cu}(s) + \text{ZnSO}_4(aq)$

• Net Ionic Reaction: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

Characteristics of Redox Reactions

• Oxidation-reduction (redox) reactions are characterized by a transfer of electrons from one reactant to another.

• Many common redox reactions involve the reaction of something with oxygen.

• Examples:

  • Formation of rust: $4\text{Fe}(s) + 3\text{O}_2(g) \rightarrow 2\text{Fe}_2\text{O}_3(s)$

  • Combustion: $2\text{C}_4\text{H}_{10}(l) + 25\text{O}_2(g) \rightarrow 16\text{CO}_2(g) + 18\text{H}_2\text{O}(g)$

Half-Reactions in Redox Processes

Redox reactions can be split into two half-reactions to better understand electron flow:

• Oxidation half-reaction:

  • Involves the loss of electrons.

  • Electrons appear as a product.

  • Oxidation results in an increase in oxidation number.

• Reduction half-reaction:

  • Involves the gain of electrons.

  • Electrons appear as a reactant.

  • Reduction results in a decrease in oxidation number.

Mnemonic: Oxidation Is Loss of electrons (OIL) Reduction Is Gain of electrons (RIG)

Example: Redox Reaction Breakdown

• Redox Reaction: $\text{Cu}^{2+}(aq) + \text{Zn}(s) \rightarrow \text{Cu}(s) + \text{Zn}^{2+}(aq)$

• Reduction: $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$

• Oxidation: $\text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^-$

• Cu2+ is reduced to Cu (oxidizing agent); Zn is oxidized to Zn2+ (reducing agent).

Tracking Electron Flow: Oxidation Numbers

One easy way to track the flow of electrons in a redox reaction is to use oxidation numbers.

Rules for Assigning Oxidation Numbers

Rule	Element/Group	Oxidation Number
Free element	Any	0
Monatomic ion	F-	-1
Hydrogen in compounds	H	+1
Group 7A (halogens)	Group 7A	-1
Group 1A metals	Group 1A	+1
Group 2A metals	Group 2A	+2

Additional info: The sum of oxidation numbers in a neutral molecule is zero; in a polyatomic ion, it equals the ion's charge.

Example 15.1: Assigning Oxidation Numbers

• Rule #1: The oxidation number for an atom in a free element is zero. Example: $\text{oxidation number of H (in H}_2) = 0$

• Rule #3: The sum of all oxidation numbers in a polyatomic ion equals the ion's charge. Example: $\text{S (ox state)} + 3 \times \text{O (ox state)} = -2$ If O is -2, then S is +4.

• Rule #4: Group 1A metals have oxidation number +1. Example: $2 \times \text{K (ox state)} + 2 \times \text{O (ox state)} = 0$ If K is +1, then O is -1.

15.2 Electrochemical Cells

Generating Electricity from Redox Reactions

Electrochemical cells convert chemical energy from redox reactions into electrical energy.

• Electrochemical cell: Consists of two half-cells, each containing an electrode and an electrolyte, connected by a wire and a salt bridge.

• Example Reaction: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

Components of an Electrochemical Cell

• Anode: Electrode at which oxidation occurs (loss of electrons).

• Cathode: Electrode at which reduction occurs (gain of electrons).

• Salt Bridge: Porous membrane that allows ions to flow, maintaining electrical neutrality by allowing passage of background electrolyte.

Voltaic (Galvanic) Cells

• Voltaic cell: Chemical energy is transformed into electrical work from a spontaneous chemical reaction.

• Electrolytic cell: Electrical energy is used to drive a nonspontaneous chemical reaction.

11.3 Spontaneous Redox Reactions

Determining Spontaneity

To determine if a redox reaction is spontaneous, we use cell potentials and the activity series of metals.

Single-Displacement Reactions and the Activity Series

• Single-displacement reaction: An elemental metal replaces a metal cation in solution.

• Use the metal activity series to predict if a reaction will occur. A metal higher in the series will displace a metal ion lower in the series.

Activity Series	Oxidation Reaction
Li(s)	Li+ + e-
K(s)	K+ + e-
Ca(s)	Ca2+ + 2e-
Na(s)	Na+ + e-
Mg(s)	Mg2+ + 2e-
Al(s)	Al3+ + 3e-
Zn(s)	Zn2+ + 2e-
Fe(s)	Fe2+ + 2e-
Cu(s)	Cu2+ + 2e-
Ag(s)	Ag+ + e-
Au(s)	Au3+ + 3e-

Standard Reduction Potentials

• Standard reduction potential (E0): The voltage of a half-cell paired with a reference electrode under standard conditions (1 M, 1 atm).

• All standard reduction potentials are reported as reduction half-reactions.

• The greater the E0, the greater the probability the half-reaction will occur as a reduction, resulting in a spontaneous redox reaction (when paired with an oxidation half-reaction).

Example Table: Standard Reduction Potentials

Half-Reaction	E0 (V)
F2(g) + 2e- → 2F-(aq)	+2.87
Cu2+(aq) + 2e- → Cu(s)	+0.34
Zn2+(aq) + 2e- → Zn(s)	-0.76
Ag+(aq) + e- → Ag(s)	+0.80
Co2+(aq) + 2e- → Co(s)	-0.28

Calculating Standard Cell Potential

The standard cell potential (Ecell0) is calculated by combining the reduction and oxidation half-reactions:

• Reduction: $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$, $E^0 = +0.34\text{ V}$

• Oxidation: $\text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^-$, $E^0 = -0.76\text{ V}$ (flip sign for oxidation)

• Cell Potential: $E_{cell}^0 = E_{red}^0 - E_{ox}^0 = 0.34 - (-0.76) = 1.10\text{ V}$

Example 15.3: Silver and Cobalt Cell

• Redox Reaction: $2\text{Ag}^+(aq) + \text{Co}(s) \rightarrow 2\text{Ag}(s) + \text{Co}^{2+}(aq)$

• Given:

  • $\text{Co}^{2+}(aq) + 2e^- \rightarrow \text{Co}(s)$, $E^0 = -0.28\text{ V}$

  • $\text{Ag}^+(aq) + e^- \rightarrow \text{Ag}(s)$, $E^0 = +0.80\text{ V}$

• Cell Potential: $E_{cell}^0 = E_{red}^0 - E_{ox}^0 = 0.80 - (-0.28) = 1.08\text{ V}$

Standard Hydrogen Electrode (SHE)

• Consists of a platinum electrode in contact with 1.00 M H+ and H2 gas at 1 atm.

• Serves as the reference electrode for measuring standard reduction potentials.

Relationship Between Cell Potential and Gibbs Free Energy

• Spontaneity is determined by Gibbs Free Energy (ΔG).

• The cell potential (Ecell) is related to ΔG as follows:

$\Delta G = -nFE_{cell}$

• n = moles of electrons transferred

• F = Faraday's constant ($96,485\ \text{C/mol e}^-$)

Nonstandard Conditions: The Nernst Equation

• Under nonstandard conditions, cell potential is calculated using the Nernst Equation:

$E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q$

• R = gas constant ($8.314\ \text{J/mol K}$)

• T = temperature (K)

• Q = reaction quotient

Example 15.4: Nonstandard Cell Potential

• Redox Reaction: $2\text{Ag}^+(aq) + \text{Ni}(s) \rightarrow 2\text{Ag}(s) + \text{Ni}^{2+}(aq)$

• Given:

  • $\text{Ag}^+(aq) + e^- \rightarrow \text{Ag}(s)$, $E^0 = +0.80\text{ V}$

  • $\text{Ni}^{2+}(aq) + 2e^- \rightarrow \text{Ni}(s)$, $E^0 = -0.20\text{ V}$

• Cell Potential: $E_{cell}^0 = 0.80 - (-0.20) = 1.00\text{ V}$

• Use the Nernst equation to calculate Ecell under nonstandard conditions.

Applications: Batteries

Types of Batteries

• Lead-acid batteries: Used in cars; consist of multiple cells connected in series.

• Lithium-ion batteries: Used in portable electronics and electric vehicles; involve intercalation of lithium ions between graphene sheets at the anode.

Structure of Lithium-Ion Battery

• Anode: Typically composed of graphene sheets in contact with copper.

• Cathode: Composed of a metal oxide material in contact with aluminum.

• Both compartments are immersed in an organic electrolyte.

• During discharge, lithium ions move from the anode to the cathode, generating electrical current.

Additional info: The operation of batteries is based on the principles of electrochemical cells and redox reactions, with electron flow generating usable electrical energy.