Electrochemistry and Redox Reactions: Principles, Calculations, and Applications

Electrochemistry: Fundamental Concepts

Faraday Constant and Charge

Electrochemistry studies the relationship between electricity and chemical reactions. The Faraday constant (F) represents the magnitude of electric charge per mole of electrons.

• Faraday constant (F): $F = 9.6485 \times 10^4 \text{ C mol}^{-1}$

• Work done by a cell: $w = -F \times \text{potential difference}$

• The negative sign indicates the cell does work by generating current (electron flow).

Cell Potential and Maximum Work

The cell potential (also called electromotive force (emf), $E_{cell}$) is the maximum potential difference between electrodes in a voltaic cell. It determines the cell's ability to do electrical work.

• Maximum work ($\Delta G$): $W_{max} = -nFE_{cell}$

• $n$ = number of moles of electrons transferred

Relationships Among Thermodynamic Variables

Electrochemical data, calorimetric data, and composition data are interrelated through thermodynamic equations. These relationships connect cell potential, equilibrium constants, and Gibbs free energy.

• $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$ (from calorimetry)

• $\Delta G^\circ = -nFE_{cell}$ (from electrochemistry)

• $\Delta G^\circ = -RT \ln K$ (from equilibrium)

• $E_{cell} = \frac{RT}{nF} \ln K$

Types of Reactions in Electrochemical Cells

Overview of Reaction Types

Electrochemical cells can involve several types of chemical reactions, each with distinct characteristics:

• Combination reaction

• Decomposition reaction

• Displacement reaction

• Combustion reaction

Combination Reaction

A combination reaction involves two or more substances combining to form a new compound. Typically, one species is oxidized and another is reduced.

• General form: $A + B \rightarrow AB$

• Example: $2\text{Na}(s) + \text{Cl}_2(g) \rightarrow 2\text{NaCl}(s)$

• During this reaction, sodium is oxidized and chlorine is reduced.

Decomposition Reaction

A decomposition reaction occurs when a single compound breaks down into two or more products, with some species being oxidized and others reduced.

• General form: $AB \rightarrow A + B$

• Example: $2\text{HgO}(s) \rightarrow 2\text{Hg}(l) + \text{O}_2(g)$

Displacement Reaction

In a displacement reaction, an element reacts with a compound, displacing another element. One species is oxidized, and one is reduced.

• General form: $A + BC \rightarrow AC + B$

• Example: $\text{Zn}(s) + 2\text{HCl}(aq) \rightarrow \text{H}_2(g) + \text{ZnCl}_2(aq)$

• This reaction is a form of corrosion.

Combustion Reaction

A combustion reaction involves a substance reacting rapidly with oxygen, releasing heat and producing a flame. It is also a form of corrosion for metals.

• General form: $A + O_2 \rightarrow AO_x$

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

Batteries and Electrochemical Cells

Structure of a Battery

Batteries are practical applications of electrochemical cells. They consist of:

• Positive terminal and negative terminal

• Graphite rod (cathode)

• Zinc can (anode)

• Paste of MnO2, ZnCl2, NH4Cl, and C

• Porous paper, air space, insulator, metal jacket

Electrochemical Cell Setup

An electrochemical cell typically consists of two electrodes (e.g., zinc and copper) immersed in electrolyte solutions and connected by a salt bridge. A chemical reaction occurs when the electrodes are connected by an external circuit.

• Without external circuit: No cell reaction occurs.

• With external circuit: Electron flow enables the chemical reaction, lighting a bulb or powering a device.

Oxidation-Reduction (Redox) Reactions

Half-Reactions

Redox reactions are split into two half-reactions: one for oxidation and one for reduction.

• Oxidation: Loss of electrons or increase in oxidation number.

• Reduction: Gain of electrons or decrease in oxidation number.

• Example: $2\text{Na}(s) + \text{Cl}_2(g) \rightarrow 2\text{NaCl}(s)$ Oxidation: $2\text{Na} \rightarrow 2\text{Na}^+$ Reduction: $\text{Cl}_2 \rightarrow 2\text{Cl}^-$

Rules for Assigning Oxidation Numbers

Oxidation numbers are assigned based on a set of rules:

• Elements: Oxidation number is 0 (e.g., Cu).

• Monatomic ions: Oxidation number equals the ion's charge (e.g., F-: -1, Na+: +1).

• Oxygen: Usually -2; in peroxides (e.g., H2O2), -1.

• Hydrogen: +1 in most compounds; -1 in binary compounds with metals (e.g., CaH2); 0 in H2.

• Halogens: Fluoride is always -1; other halogens are -1 except when bonded to oxygen or a more electronegative halogen.

• Compounds and ions: The sum of oxidation numbers in a neutral compound is 0; in a polyatomic ion, it equals the ion's charge.

Examples of Oxidation Number Calculations

Determining the oxidation state of transition metals in compounds:

• Potassium permanganate (KMnO4): $1(+1) + 1(x) + 4(-2) = 0$ $x = +7$ (Mn)

• Potassium manganate (K2MnO4): $2(+1) + 1(x) + 4(-2) = 0$ $x = +6$ (Mn)

• Dichromate ion (Cr2O72-): $2(x) + 7(-2) = -2$ $x = +6$ (Cr)

Balancing Redox Reactions: Half-Reaction Method

Stepwise Procedure

Balancing redox reactions involves several steps:

1. Identify oxidation and reduction: Use oxidation numbers to determine which species are oxidized and reduced.

2. Write unbalanced half-reactions: Separate the oxidation and reduction processes.

3. Balance charges: Add electrons to balance the charge in each half-reaction.

4. Balance electron numbers: Multiply half-reactions by appropriate factors so the number of electrons lost equals those gained.

5. Add half-reactions: Combine to obtain the overall balanced equation.

Example 1: Zn and Ag+ Reaction

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

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

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

• Balanced overall: $\text{Zn}(s) + 2\text{Ag}^+(aq) \rightarrow \text{Zn}^{2+}(aq) + 2\text{Ag}(s)$

Example 2: Fe2I3 and Mg Reaction

• Reaction: $2\text{FeI}_3(aq) + 3\text{Mg}(s) \rightarrow 2\text{Fe}(s) + 3\text{MgI}_2(aq)$

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

• Reduction: $\text{Fe}^{3+}(aq) + 3e^- \rightarrow \text{Fe}(s)$

• Multiply: $3\text{Mg}(s) \rightarrow 3\text{Mg}^{2+}(aq) + 6e^-$ $2\text{Fe}^{3+}(aq) + 6e^- \rightarrow 2\text{Fe}(s)$

• Overall: $2\text{FeI}_3(aq) + 3\text{Mg}(s) \rightarrow 2\text{Fe}(s) + 3\text{MgI}_2(aq)$

Spectator Ions

Spectator ions are ions that do not participate directly in the chemical reaction. They appear unchanged on both sides of the ionic equation.

• Definition: An ion in an ionic equation that does not take part in the reaction.

• Example: In the reaction above, iodide (I-) is a spectator ion.

Summary Table: Rules for Assigning Oxidation Numbers

Rule	Description	Example
Element	Oxidation number is 0	Cu: 0
Monatomic ion	Equals ion charge	Na+: +1
Oxygen	-2 (except peroxides: -1)	H2O: -2, H2O2: -1
Hydrogen	+1 (most), -1 (with metals), 0 (H2)	HCl: +1, CaH2: -1
Halogens	F: -1; Cl, Br, I: -1 (except with O or higher halogen)	NaCl: -1
Compounds/ions	Sum is 0 (neutral) or equals ion charge (polyatomic)	SO42-: -2

Additional info:

• Electrochemistry is foundational for understanding batteries, corrosion, and energy conversion in chemical systems.

• Redox reactions are central to many biological and industrial processes.