5.1 Redox Reactions, Oxidation Numbers & Electrochemical Cells

5.1 Redox Reactions, Oxidation Numbers & Electrochemical Cells

Electrochemistry is the branch of physical chemistry that investigates the relationship between chemical reactions and electrical energy. It encompasses two primary phenomena: the generation of electricity from spontaneous chemical transformations (galvanic cells) and the driving of non-spontaneous chemical changes using external electrical power (electrolytic cells). A rigorous mastery of oxidation-reduction (redox) principles, cell notation, electrode potentials, and electrolysis calculations is vital for success in the Pakistan Army Medical Cadet (AMC) entrance examination.

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Fundamentals of Redox Reactions & Oxidation Numbers

Redox processes consist of two concurrent half-reactions: oxidation and reduction. Modern chemical definitions focus on electron transfer and oxidation state changes:

• Oxidation: Loss of electrons, addition of electronegative elements (or oxygen), removal of hydrogen, or an increase in oxidation state.
• Reduction: Gain of electrons, addition of electropositive elements (or hydrogen), removal of oxygen, or a decrease in oxidation state.
• Oxidizing Agent (Oxidant): A species that accepts electrons, undergoes reduction itself, and causes another species to be oxidized.
• Reducing Agent (Reductant): A species that donates electrons, undergoes oxidation itself, and causes another species to be reduced.

Rules for Assigning Oxidation Numbers

The oxidation number (or state) represents the apparent charge an atom acquires when bonding electrons are assigned to the more electronegative element. Candidates must strictly apply the following priority rules:

1. Free / Elementary State: The oxidation number of any uncombined element is zero (e.g., $Na$, $O_2$, $P_4$, $S_8$ all have an oxidation state of 0).
2. Monatomic Ions: Equal to the charge on the ion (e.g., $Fe^{3+}$ is $+3$, $Cl^-$ is $-1$).
3. Hydrogen: Assigned $+1$ when bonded to non-metals (e.g., $HCl$, $H_2O$), but assigned $-1$ in binary metal hydrides (e.g., $NaH$, $CaH_2$).
4. Oxygen: Assigned $-2$ in most compounds. Exceptions include:
   • Peroxides (e.g., $H_2O_2$, $Na_2O_2$): Oxygen is $-1$.
   • Superoxides (e.g., $KO_2$): Oxygen is $-\frac{1}{2}$.
   • Oxygen Fluorides (e.g., $OF_2$): Oxygen is $+2$ because fluorine is more electronegative.
5. Halogens: Fluorine is always assigned $-1$ in all its compounds. $Cl$, $Br$, and $I$ are $-1$ except when combined with oxygen or fluorine (e.g., in $ClO_3^-$, chlorine is $+5$).
6. Alkali & Alkaline Earth Metals: Group 1 metals are always $+1$; Group 2 metals are always $+2$.
7. Sum of Oxidation States: The sum of oxidation numbers in a neutral molecule is zero. In a polyatomic ion, the sum equals the net ionic charge.

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Balancing Redox Equations: Ion-Electron Method

To balance complex redox reactions in aqueous media, the ion-electron (half-reaction) method is used:

1. Divide the skeleton equation into two half-reactions: oxidation and reduction.
2. Balance main elements other than $H$ and $O$.
3. Balance Oxygen atoms: Add $H_2O$ molecules to the side deficient in oxygen.
4. Balance Hydrogen atoms:
   • Acidic Medium: Add $H^+$ ions to the side deficient in hydrogen.
   • Basic Medium: Add $H^+$ ions as above, then add an equal number of $OH^-$ ions to both sides of the equation (combining $H^+ + OH^- \rightarrow H_2O$), canceling excess water molecules.
5. Balance Electrical Charge: Add electrons ($e^-$) to the side with the higher positive charge.
6. Equalize Electrons: Multiply each half-reaction by suitable integers so the total electrons lost equal total electrons gained.
7. Add Half-Reactions: Sum the half-reactions and simplify by canceling identical species on both sides.

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Electrochemical Cells: Galvanic vs. Electrolytic

Electrochemical devices are categorized based on their energy conversion principles:

                    ┌────────────────────────────────────────┐
                    │          ELECTROCHEMICAL CELLS         │
                    └───────────────────┬────────────────────┘
                                        │
                  ┌─────────────────────┴─────────────────────┐
                  ▼                                           ▼
     ┌────────────────────────┐                  ┌────────────────────────┐
     │  GALVANIC / VOLTAIC    │                  │      ELECTROLYTIC      │
     ├────────────────────────┤                  ├────────────────────────┤
     │ Spontaneous (ΔG < 0)   │                  │ Non-spontaneous (ΔG>0) │
     │ Chemical ──► Electrical │                  │ Electrical ──► Chemical│
     │ Anode: Negative (-)    │                  │ Anode: Positive (+)    │
     │ Cathode: Positive (+)  │                  │ Cathode: Negative (-)  │
     └────────────────────────┘                  └────────────────────────┘

The Galvanic (Voltaic) Cell & Salt Bridge

A classic example of a galvanic cell is the Daniell Cell, composed of a zinc electrode immersed in $1.0\text{ M } ZnSO_4$ solution and a copper electrode in $1.0\text{ M } CuSO_4$ solution:

• Anode (Oxidation): $Zn_{(s)} \rightarrow Zn^{2+}_{(aq)} + 2e^-$ (Anode loses mass, electrode is negative).
• Cathode (Reduction): $Cu^{2+}{(aq)} + 2e^- \rightarrow Cu{(s)}$ (Cathode gains mass, electrode is positive).
• Overall Reaction: $Zn_{(s)} + Cu^{2+}{(aq)} \rightarrow Zn^{2+}{(aq)} + Cu_{(s)}$
• Cell Notation: $Zn_{(s)} \mid Zn^{2+}{(aq)} (1.0\text{ M}) \parallel Cu^{2+}{(aq)} (1.0\text{ M}) \mid Cu_{(s)}$

Functions of the Salt Bridge

The salt bridge is an inverted U-tube filled with an inert electrolyte (e.g., $KCl$, $KNO_3$, or $NH_4NO_3$) immobilized in agar-agar gel. Its primary roles are:

1. Completes the internal electrical circuit by allowing ionic migration.
2. Maintains electrical neutrality in both half-cells ($K^+$ ions migrate toward the cathode compartment to neutralize excess negative charge; $Cl^-$ or $NO_3^-$ ions migrate toward the anode to neutralize accumulating positive zinc cations).
3. Prevents liquid junction potential between the two electrolyte solutions.

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Standard Hydrogen Electrode (SHE) & Electrochemical Series

Because absolute single electrode potentials cannot be measured directly, standard reduction potentials ($E^\circ$) are defined relative to a standard reference electrode.

Standard Hydrogen Electrode (SHE)

• Construction: Platinized platinum foil coated with finely divided platinum black, immersed in a $1.0\text{ M } H^+$ solution ($HCl$), through which pure hydrogen gas is continuously bubbled at $1\text{ atm}$ pressure ($101.3\text{ kPa}$) at $298\text{ K}$ ($25^\circ\text{C}$).
• Assigned Potential: $E^\circ = 0.00\text{ V}$ at all temperatures.
• Half-Reaction: $2H^+{(aq)} (1.0\text{ M}) + 2e^- \rightleftharpoons H{2(g)} (1\text{ atm})$

The Electrochemical Series

The electrochemical series is an arrangement of elements in order of their standard reduction potentials ($E^\circ$) measured relative to the SHE at $298\text{ K}$.

Key Applications of the Electrochemical Series:

1. Predicting Feasibility (Spontaneity) of Redox Reactions: A cell reaction is spontaneous under standard conditions if the standard electromotive force ($E^\circ_{cell}$) is positive: $E^\circ_{cell} = E^\circ_{cathode (reduction)} - E^\circ_{anode (reduction)}$ $\Delta G^\circ = -n F E^\circ_{cell}$ where $n$ is the number of moles of electrons transferred and $F$ is Faraday's constant ($96,500\text{ C mol}^{-1}$). A positive $E^\circ_{cell}$ yields a negative $\Delta G^\circ$.
2. Displacement Reactions: Metals situated higher in the series (more negative $E^\circ$) have greater reducing power and will displace metals located lower in the series from their aqueous salt solutions. For example, $Zn$ displaces $Cu^{2+}$ from $CuSO_4$ solution.
3. Reactivity with Mineral Acids: Metals with negative $E^\circ$ values displace $H_2$ gas from dilute acids ($HCl$, $H_2SO_4$). Metals with positive $E^\circ$ values (e.g., $Cu, Ag, Au$) do not liberate hydrogen from dilute non-oxidizing acids.

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Quantitative Electrochemistry: Faraday's Laws of Electrolysis

Electrolysis involves driving non-spontaneous chemical reactions by passing an electric current through an electrolyte solution or molten salt.

Faraday's First Law of Electrolysis

The mass ($m$) of any substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte: $m \propto Q \implies m = Z \cdot Q = Z \cdot I \cdot t$ where:

• $m = \text{mass of substance in grams (g)}$
• $I = \text{electric current in amperes (A)}$
• $t = \text{time in seconds (s)}$
• $Q = I \times t = \text{charge in Coulombs (C)}$
• $Z = \text{Electrochemical Equivalent (ECE) in g C}^{-1}$

$\text{Electrochemical Equivalent } (Z) = \frac{\text{Molar Mass}}{n \times 96500} = \frac{\text{Equivalent Weight}}{96500}$

Faraday's Second Law of Electrolysis

When the same quantity of electricity is passed through solutions of different electrolytes connected in series, the masses of different substances deposited or liberated at the electrodes are directly proportional to their chemical equivalent weights ($E = \frac{\text{Molar Mass}}{\text{Valency}}$): $\frac{m_1}{m_2} = \frac{E_1}{E_2} = \frac{Z_1}{Z_2}$

Commercial Electrolytic Processes

• Downs Cell: Electrolysis of molten $NaCl$ (with $CaCl_2$ added to lower the melting point from $801^\circ\text{C}$ to $600^\circ\text{C}$) yields sodium metal at the cathode and chlorine gas at the anode.
• Nelson's (Diaphragm) Cell: Electrolysis of aqueous $NaCl$ (brine) produces $NaOH$, $H_2$ gas (at cathode), and $Cl_2$ gas (at anode).
• Electro-refining of Copper: Impure blister copper acts as the anode, pure copper strip acts as the cathode, and aqueous $CuSO_4$ with dilute $H_2SO_4$ serves as the electrolyte.