Electrochemistry revision notes for JEE

Key Concepts & Definitions

Electrochemistry:: The study of the production of electricity from the energy released during spontaneous chemical reactions, and the use of electrical energy to bring about non-spontaneous chemical transformations.
Galvanic (Voltaic) Cell:: A device that converts the chemical energy of a spontaneous redox reaction into electrical energy (e.g., Daniell cell).
Electrolytic Cell:: A device that uses electrical energy to carry out non-spontaneous chemical reactions.
Anode:: The electrode where oxidation takes place. In a galvanic cell, it has a negative potential.
Cathode:: The electrode where reduction takes place. In a galvanic cell, it has a positive potential.
Electrode Potential:: The potential difference that develops between the electrode and the electrolyte due to charge separation at equilibrium.
Standard Electrode Potential (E∘E^\circE∘):: The electrode potential when the concentrations of all species involved in a half-cell are unity. According to IUPAC convention, standard reduction potentials are now called standard electrode potentials.
Resistance (RRR):: Opposition to current flow, measured in ohms (Ω\OmegaΩ). R=ρ(l/A)R = \rho (l/A)R=ρ(l/A).
Resistivity (ρ\rhoρ):: Resistance of a substance when it is 1 meter long and its area of cross-section is 1 m2m^2m2. Units: Ω m\Omega\ mΩ m or Ω cm\Omega\ cmΩ cm.
Conductance (GGG):: Inverse of resistance (G=1/RG = 1/RG=1/R). Unit: siemens (SSS) or Ω−1\Omega^{-1}Ω−1 or mho.
Conductivity (κ\kappaκ):: Inverse of resistivity (κ=1/ρ\kappa = 1/\rhoκ=1/ρ). The conductance of a material 1 m long with a cross-section of 1 m2m^2m2. Unit: S m−1S\ m^{-1}S m−1 or S cm−1S\ cm^{-1}S cm−1.
Cell Constant (G∗G^*G∗):: The ratio of the distance between electrodes (lll) to their area of cross-section (AAA). G∗=l/AG^* = l/AG∗=l/A.
Molar Conductivity (Λm\Lambda_mΛm):: The conductance of the volume VVV of a solution containing one mole of electrolyte kept between two electrodes with an area of cross-section AAA and a distance of unit length.
Limiting Molar Conductivity (Λm∘\Lambda_m^\circΛm∘):: The molar conductivity of an electrolyte when the concentration approaches zero (infinite dilution).

Important Rules, Laws & Principles

Faraday's First Law of Electrolysis: The amount of chemical reaction occurring at any electrode during electrolysis by a current is directly proportional to the quantity of electricity ( $Q$ ) passed through the electrolyte (solution or melt).
Faraday's Second Law of Electrolysis: The amounts of different substances liberated by the same quantity of electricity passing through the electrolytic solution are proportional to their chemical equivalent weights (Atomic Mass of Metal $\div$ Number of electrons required to reduce the cation).
Kohlrausch Law of Independent Migration of Ions: The limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. Condition: Applies strictly at infinite dilution where inter-ionic forces are zero.
- $\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$ (where $\nu_+$ and $\nu_-$ are the number of cations and anions per formula unit).

Electrochemical & Galvanic Cells

Daniell Cell: Converts chemical energy to electrical energy via: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$ . Standard cell potential is 1.1 V (when concentrations are 1 M).
Effect of External Opposing Potential ( $E_{ext}$ ) on a Galvanic Cell:JEE TIPHighly tested concept regarding cell reversibility.
- $E_{ext} < 1.1\ V$ : Normal galvanic cell behavior. Electrons flow from Zn to Cu; current from Cu to Zn. Zn dissolves, Cu deposits.
- $E_{ext} = 1.1\ V$ : Equilibrium. No flow of electrons or current. Chemical reaction stops.
- $E_{ext} > 1.1\ V$ : Functions as an electrolytic cell. Direction is reversed: electrons flow from Cu to Zn. Cu dissolves at cathode, Zn deposits at anode.
Cell Representation: Anode is on the left, cathode on the right. A double vertical line ( $||$ ) represents the salt bridge. Example: $Cu(s)|Cu^{2+}(aq) || Ag^+(aq)|Ag(s)$ .
Standard Hydrogen Electrode (SHE): Assigned a zero potential at all temperatures. Consists of a platinum electrode coated with platinum black, dipped in 1 M $H^+$ $H^{+}$ solution, with pure $H_2$ $H_{2}$ gas bubbled at 1 bar.
- Reaction: $H^+(aq) + e^- \rightarrow \frac{1}{2}H_2(g)$
- Used as a reference to find standard potentials of other half-cells.

Nernst Equation & Thermodynamics of Cells

Nernst Equation: Defines the relationship between electrode potential and concentration.
- For $M^{n+}(aq) + ne^- \rightarrow M(s)$ : $E = E^\circ - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$
- For a general reaction: $aA + bB \rightleftharpoons cC + dD$ $a A + b B ⇌ c C + d D$ :
  - $E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln \frac{[C]^c[D]^d}{[A]^a[B]^b}$
- At 298 K, $\frac{2.303 RT}{F} = 0.059\ V$ .
- JEE TIPThe concentration of solid ( $M$ ) and pure liquids is strictly taken as unity. Do not include them in the Nernst reaction quotient $Q$ .
Equilibrium Constant from Nernst Equation: At equilibrium, $E_{cell} = 0$ $E_{ce ll} = 0$ (The cell is dead) and reaction quotient $Q = K_c$ $Q = K_{c}$ .
- $E^\circ_{cell} = \frac{2.303 RT}{nF} \log K_c$
Gibbs Free Energy and Cell Potential: Electrical work done in one second is electrical potential multiplied by total charge. Maximum work requires reversible charge passage.
- $\Delta_r G = -nF E_{cell}$
- $\Delta_r G^\circ = -nF E^\circ_{cell}$

Conductance of Electrolytic Solutions

Electronic (Metallic) Conductance: Through metals, due to electron movement. Depends on metal nature, structure, and valence electrons per atom.
Conducting Polymers & Superconductors (Novel Materials): Organic polymers like polyacetylene (exposed to iodine), polyaniline, polypyrrole, and polythiophene exhibit metallic conductance (Nobel Prize 2000). Superconductors have zero resistivity; mixed oxides and ceramics can now show this up to 150 K.
Ionic (Electrolytic) Conductance: Conductance by ions in solutions. Depends on electrolyte nature, ion size, solvation, solvent nature, viscosity, and concentration.
Measurement: Uses an alternating current (AC) source in a Wheatstone bridge to prevent DC from causing electrolysis and changing the solution's composition.JEE TIPThe AC power source operates in the audio frequency range of 550 to 5000 cycles per second (Hz).
Variation with Concentration:
- Conductivity ( $\kappa$ ): Always decreases with a decrease in concentration (for both weak and strong electrolytes) because the number of ions per unit volume carrying the current decreases.
- Molar Conductivity ( $\Lambda_m$ ): Always increases with a decrease in concentration. The total volume $V$ of solution containing one mole of electrolyte increases, which more than compensates for the decrease in $\kappa$ .
Strong Electrolytes: $\Lambda_m$ increases slowly with dilution following the equation $\Lambda_m = \Lambda_m^\circ - A c^{1/2}$ . The constant $A$ depends on the electrolyte type (1-1, 2-1, etc.).
Weak Electrolytes (e.g., Acetic Acid): $\Lambda_m$ $Λ_{m}$ increases steeply on dilution, especially near lower concentrations, due to an increase in the degree of dissociation ( $\alpha$ $α$ ).
- Degree of dissociation: $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$
- Dissociation constant: $K_c = \frac{c\alpha^2}{1-\alpha} = \frac{c \Lambda_m^2}{\Lambda_m^\circ (\Lambda_m^\circ - \Lambda_m)}$

Electrolysis & Products of Electrolysis

Criteria: Products depend on the nature of the material, type of electrodes (inert like Pt/Au vs reactive), and standard electrode potentials.
Rule of Preference:
- Cathode: Species with a higher (more positive) standard reduction potential gets reduced preferentially.
- Anode: Species with a lower standard reduction potential gets oxidized preferentially.
Aqueous NaCl Electrolysis:
- Cathode: $H_2O$ is reduced to $H_2(g)$ instead of $Na^+$ reducing to $Na(s)$ because $E^\circ(H_2O/H_2) > E^\circ(Na^+/Na)$ .
- Anode: $Cl^-$ is oxidized to $Cl_2(g)$ instead of $H_2O$ oxidizing to $O_2(g)$ due to overpotential.
- Net cell product: $H_2$ , $Cl_2$ , and $NaOH(aq)$ remaining in solution.
Sulfuric Acid Electrolysis ( $H_2SO_4$ ):
- Dilute $H_2SO_4$ : Water is oxidized at the anode: $2H_2O(l) \rightarrow O_2(g) + 4H^+(aq) + 4e^-$ .
- Concentrated $H_2SO_4$ : Sulfate is oxidized at the anode: $2SO_4^{2-}(aq) \rightarrow S_2O_8^{2-}(aq) + 2e^-$ (forms peroxodisulphate).

Commercial Cells & Batteries

Primary Batteries (Non-rechargeable):
- Dry Cell (Leclanche Cell): Anode: Zinc container. Cathode: Graphite rod surrounded by $MnO_2$ $M n O_{2}$ and Carbon. Electrolyte paste: $NH_4Cl$ $N H_{4} Cl$ and $ZnCl_2$ $Z n C l_{2}$ .
  - Anode Rxn: $Zn \rightarrow Zn^{2+} + 2e^-$
  - Cathode Rxn: $MnO_2 + NH_4^+ + e^- \rightarrow MnO(OH) + NH_3$
- Mercury Cell: For low current devices (hearing aids). Anode: Zn-Hg amalgam. Cathode: Paste of HgO and C. Electrolyte: Paste of KOH and ZnO.
  - Anode: $Zn(Hg) + 2OH^- \rightarrow ZnO(s) + H_2O + 2e^-$
  - Cathode: $HgO + H_2O + 2e^- \rightarrow Hg(l) + 2OH^-$
Secondary Batteries (Rechargeable):
- Lead Storage Battery: Automobiles/inverters. Anode: Lead. Cathode: Lead packed with $PbO_2$ $P b O_{2}$ . Electrolyte: 38% $H_2SO_4$ $H_{2} S O_{4}$ .
  - Discharge Anode: $Pb + SO_4^{2-} \rightarrow PbSO_4 + 2e^-$
  - Discharge Cathode: $PbO_2 + SO_4^{2-} + 4H^+ + 2e^- \rightarrow PbSO_4 + 2H_2O$
- Nickel-Cadmium Cell: Longer life, highly expensive. Manufactured in a unique "jelly roll" arrangement separated by a layer soaked in moist sodium/potassium hydroxide.
  - Discharge rxn: $Cd(s) + 2Ni(OH)_3(s) \rightarrow CdO(s) + 2Ni(OH)_2(s) + H_2O(l)$ .
Fuel Cells & The Hydrogen Economy: Galvanic cells directly converting combustion energy of fuels ( $H_2$ $H_{2}$ , $CH_4$ $C H_{4}$ , $CH_3OH$ $C H_{3} O H$ ) into electricity. The "Hydrogen Economy" is a vision where hydrogen is produced via solar water splitting and consumed in fuel cells, producing only water and zero pollution.
- $H_2-O_2$ Fuel Cell: Used in Apollo space program. Porous carbon electrodes with Pt/Pd catalyst in concentrated aqueous NaOH.
- Cathode: $O_2(g) + 2H_2O(l) + 4e^- \rightarrow 4OH^-(aq)$
- Anode: $2H_2(g) + 4OH^-(aq) \rightarrow 4H_2O(l) + 4e^-$
- Efficiency $\sim 70\%$ (compared to $\sim 40\%$ for thermal plants).

Corrosion

An electrochemical phenomenon where metal is oxidized to oxides/salts.
Rusting of Iron:
- Anode spot: $2Fe \rightarrow 2Fe^{2+} + 4e^-$ ( $E^\circ = -0.44\ V$ )
- Cathode spot: Electrons reduce $O_2$ in presence of $H^+$ : $O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l)$ ( $E^\circ = 1.23\ V$ )
- Overall: $2Fe + O_2 + 4H^+ \rightarrow 2Fe^{2+} + 2H_2O$ ( $E^\circ_{cell} = 1.67\ V$ )
- $Fe^{2+}$ further oxidizes to form rust: $Fe_2O_3 \cdot xH_2O$ .
Prevention: Paint, bisphenol, galvanizing (Sn, Zn), or using a sacrificial electrode (Mg, Zn) which corrodes instead of the target object.

Formulae & Equations

Cell Potential: $E_{cell} = E_{right} - E_{left} = E_{cathode} - E_{anode}$
Nernst Eq at 298 K: $E_{cell} = E^\circ_{cell} - \frac{0.059}{n} \log \frac{[Products]}{[Reactants]}$
Standard Gibbs Free Energy: $\Delta_r G^\circ = -nF E^\circ_{cell} = -RT \ln K_c$
Resistance: $R = \rho \frac{l}{A}$
Conductivity: $\kappa = \frac{1}{\rho} = \frac{1}{R} \times \frac{l}{A} = \frac{G^*}{R}$
Molar Conductivity (crucial conversion format): $\Lambda_m \ (S\ cm^2\ mol^{-1}) = \frac{\kappa\ (S\ cm^{-1}) \times 1000}{Molarity\ (mol\ L^{-1})}$
Kohlrausch's Law: $\Lambda_m^\circ (A_xB_y) = x\lambda_m^\circ (A^{y+}) + y\lambda_m^\circ (B^{x-})$
Degree of Dissociation: $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$
Charge/Faraday: $Q = It$ . 1 Faraday ( $F$ ) $= 96487\ C\ mol^{-1}$ (Approx $96500\ C$ ).

Trends & Comparisons

Strength of Oxidizing/Reducing Agents:
- Higher (more positive) $E^\circ$ $\rightarrow$ Stronger tendency to get reduced $\rightarrow$ Stronger Oxidizing Agent (e.g., $F_2$ ).
- Lower (more negative) $E^\circ$ $\rightarrow$ Stronger tendency to get oxidized $\rightarrow$ Stronger Reducing Agent (e.g., $Li$ metal).

⚠️ EXCEPTIONS & ANOMALIES

The Overpotential Exception (Electrolysis of aqueous NaCl): Thermodynamically, the oxidation of water to $O_2(g)$ at the anode ( $E^\circ = 1.23\ V$ ) is preferred over $Cl^-$ to $Cl_2(g)$ ( $E^\circ = 1.36\ V$ ). Anomaly: Kinetically, $O_2$ formation is incredibly slow, requiring an "overpotential" (extra applied voltage). Thus, $Cl_2$ gas is generated preferentially.
The Infinite Dilution Graphical Anomaly (Weak Electrolytes): For strong electrolytes, plotting $\Lambda_m$ against $c^{1/2}$ yields a straight line intercepting the y-axis at $\Lambda_m^\circ$ . Exception: For weak electrolytes (acetic acid), the curve is asymptotically steep near zero concentration. $\Lambda_m^\circ$ cannot be obtained by extrapolation; Kohlrausch’s law must be used.
The Constant Voltage Exception (Mercury Cell): Most batteries undergo a voltage drop as reactant ion concentrations decrease. Anomaly: The Mercury cell maintains a constant voltage (~1.35 V) throughout its life. Why: The overall cell reaction ( $Zn(Hg) + HgO(s) \rightarrow ZnO(s) + Hg(l)$ ) does not contain any ions in solution whose concentrations can change.
Opposite Temperature Dependence: Electronic (metallic) conductance decreases with an increase in temperature, whereas electrolytic (ionic) conductance increases with an increase in temperature.
Concentration-Dependent Anode Products ( $H_2SO_4$ ): Special Case: Dilute $H_2SO_4$ electrolysis yields $O_2$ gas. Concentrated $H_2SO_4$ yields peroxodisulphate ions, $S_2O_8^{2-}$ .
The Pressure-Build up Anomaly (Dry Cell): Reduction produces $NH_3$ gas at the cathode, which should burst the battery. Exception: The $NH_3$ instantly reacts with $Zn^{2+}$ to form the complex ion $[Zn(NH_3)_4]^{2+}$ , safely removing the gas.
Opposing External Voltage ( $E_{ext}$ ): Special case: If an exact external voltage of $1.1\ V$ opposes a Daniell cell, it does not reverse; it achieves a dead equilibrium ( $I = 0$ ). Only when $E_{ext} > 1.1\ V$ does it anomalously turn into an electrolytic cell.

Previous Year JEE Topics

Nernst Equation with pH/Ksp: Frequently, the concentration of $H^+$ is not given directly but via pH. ( $pH = -\log[H^+]$ ).
Calculations using Kohlrausch Law: Finding $\Lambda_m^\circ$ for weak acids (like $\Lambda_m^\circ(CH_3COOH)$ ) using a combination of strong electrolytes ( $\Lambda_m^\circ(CH_3COONa) + \Lambda_m^\circ(HCl) - \Lambda_m^\circ(NaCl)$ ).
Faraday's Laws Numericals: Determining the time required to deposit a certain mass, or mass deposited given current and time.
Predicting Products of Electrolysis: MCQ traps differentiating between molten salts (only one possible reduction/oxidation) and aqueous solutions (competition with water).
Conductivity Cell Constant: Back-calculating the cell constant $G^*$ using a reference $KCl$ solution, then applying it to an unknown solution.

Memory Aids & Top 11 JEE Traps

[JEE TIP] Trap 1 - The ΔG vs E° Scaling Divide:
- Misconception: Multiplying a stoichiometric cell reaction by a factor of 2 doubles the standard cell potential ( $E^\circ_{\text{cell}}$ ).
- Correct Understanding: $E^\circ_{\text{cell}}$ is an intensive property and remains completely unchanged regardless of the reaction coefficients. However, the Standard Gibbs Free Energy ( $\Delta_r G^\circ = -nFE^\circ_{\text{cell}}$ ) is an extensive property and will scale proportionally with the coefficients.
[JEE TIP] Trap 2 - The Divergent Dilution Trends:
- Misconception: Conductivity ( $\kappa$ ) and Molar Conductivity ( $\Lambda_m$ ) both increase symmetrically upon dilution.
- Correct Understanding: They behave inversely. Conductivity ( $\kappa$ ) decreases upon dilution because the total number of current-carrying ions per unit volume drops. Conversely, Molar Conductivity ( $\Lambda_m$ ) increases because the rapid expansion in solution volume completely offsets the decrease in $\kappa$ .
[JEE TIP] Trap 3 - Aqueous NaCl Cathodic Preference:
- Misconception: Metallic sodium ( $\text{Na}$ ) is deposited at the cathode during the electrolysis of an aqueous $\text{NaCl}$ solution.
- Correct Understanding: Because water has a higher standard reduction potential than $\text{Na}^+$ ions, water is preferentially reduced at the cathode. Instead of sodium metal, $\text{H}_2$ gas is liberated and the solution near the cathode becomes alkaline due to $\text{OH}^-$ accumulation.
[JEE TIP] Trap 4 - Pure Solids and Liquids in Nernst:
- Misconception: Active concentrations or terms for pure solids like $\text{Cu}(s)$ or $\text{Zn}(s)$ must be explicitly calculated and written inside the Nernst reaction quotient ( $Q$ ).
- Correct Understanding: The thermodynamic activity of all pure solids and pure liquids is strictly taken as unity (1). They are entirely omitted from the reaction quotient expression during Nernst equation calculations.
[JEE TIP] Trap 5 - The Cell Constant Invariance:
- Misconception: Changing the nature or the concentration of the electrolyte inside a conductivity cell alters the value of the cell constant ( $G^*$ ).
- Correct Understanding: The cell constant ( $G^* = l/A$ ) is a purely geometric property dependent solely on the physical distance between the electrodes ( $l$ ) and their cross-sectional area ( $A$ ). It remains absolutely constant regardless of the solution inside.
[JEE TIP] Trap 6 - The Fatal Molar Conductivity Unit Twist:
- Misconception: The formula $\Lambda_m = \frac{\kappa \times 1000}{M}$ is universal for converting conductivity to molar conductivity.
- Correct Understanding: This specific formula only works if $\kappa$ is provided in $\text{S cm}^{-1}$ . If $\kappa$ is given in SI units ( $\text{S m}^{-1}$ ), the correct conversion formula is $\Lambda_m = \frac{\kappa}{1000 \times M}$ . Note the conversion factor: $1\text{ S m}^2\text{ mol}^{-1} = 10^4\text{ S cm}^2\text{ mol}^{-1}$ .
[JEE TIP] Trap 7 - SHE Absolute Potential Fallacy:
- Misconception: The Standard Hydrogen Electrode (SHE) possesses a true, physically measured absolute electrode potential of exactly $0.00\text{ V}$ .
- Correct Understanding: Measuring the absolute potential of a single isolated half-cell is physically impossible. The value of $0.00\text{ V}$ assigned to the SHE is an arbitrary reference convention adopted at all temperatures to allow relative potential measurements.
[JEE TIP] Trap 8 - Negative E° Polar Opposites:
- Misconception: A highly negative standard reduction potential ( $E^\circ$ ) indicates that the chemical species acts as a highly powerful oxidizing agent.
- Correct Understanding: A highly negative standard reduction potential implies that the species strongly resists reduction. Instead, its reduced form (such as metallic $\text{Li}$ ) acts as an exceptionally powerful reducing agent.
[JEE TIP] Trap 9 - The Molar Conductivity Extrapolation Barrier:
- Misconception: You can determine the limiting molar conductivity ( $\Lambda_m^\circ$ ) at infinite dilution for any electrolyte by simply extrapolating its concentration graph to the y-axis.
- Correct Understanding: This linear extrapolation technique only works for strong electrolytes following the Debye-Hückel-Onsager equation. Weak electrolytes show a steep, near-asymptotic curve near zero concentration, requiring the application of Kohlrausch's Law instead.
[JEE TIP] Trap 10 - Lead Storage Battery Operational Inversion:
- Misconception: Discharging and recharging a lead storage battery are identical galvanic processes running at different operational speeds.
- Correct Understanding: Discharging functions as a Galvanic cell (spontaneous process that consumes $\text{H}_2\text{SO}_4$ and deposits solid $\text{PbSO}_4$ on both plates). Recharging acts as an Electrolytic cell (non-spontaneous process driven by an external voltage that regenerates $\text{H}_2\text{SO}_4$ and converts $\text{PbSO}_4$ back to $\text{Pb}$ and $\text{PbO}_2$ ).
[JEE TIP] Trap 11 - Faraday's Stoichiometric Electron Demands:
- Misconception: Calculating the mass of an element deposited requires only its molar mass without considering its specific ionic valence or $n$ -factor.
- Correct Understanding: The moles of electrons required to deposit an atom are exactly equal to its chemical $n$ -factor. For instance, reducing $1\text{ mole of }\text{Al}^{3+}$ ions to solid $\text{Al}(s)$ strictly demands 3 Faradays ( $3\text{ F}$ ) of total electric charge.