Electrochemistry for JEE Mains

Cheatsheet Content

1. Introduction to Electrochemistry Electrochemistry: Study of production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to bring about non-spontaneous chemical transformations. Electrochemical Cell (Galvanic/Voltaic Cell): Converts chemical energy into electrical energy (spontaneous reaction). Electrolytic Cell: Converts electrical energy into chemical energy (non-spontaneous reaction). 2. Electrochemical Cells (Galvanic Cells) Anode: Electrode where oxidation occurs (negative pole). Cathode: Electrode where reduction occurs (positive pole). Salt Bridge: Connects two half-cells, maintains electrical neutrality, prevents mixing of solutions. Contains inert electrolyte (e.g., KCl, KNO$_3$). Cell Notation: Anode | Anode ion || Cathode ion | Cathode Example: $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$ Electrode Potential ($E$): Tendency of an electrode to lose or gain electrons when in contact with its own ions. Standard Electrode Potential ($E^\circ$): Electrode potential when concentrations of all species are $1 M$ and pressure is $1 atm$ at $298 K$. Standard Hydrogen Electrode (SHE): Reference electrode, $E^\circ = 0 V$. Reaction: $2H^+(aq, 1M) + 2e^- \rightleftharpoons H_2(g, 1 atm)$ Cell Potential ($E_{cell}$): $E_{cell} = E_{cathode} - E_{anode}$ (both standard reduction potentials). For a spontaneous reaction, $E_{cell} > 0$. 3. Nernst Equation Relates electrode potential/cell potential to concentrations of species. For a half-cell reaction: $M^{n+}(aq) + ne^- \rightarrow M(s)$ $$E = E^\circ - \frac{RT}{nF} \ln \frac{[M]}{[M^{n+}]} = E^\circ - \frac{0.0592}{n} \log \frac{1}{[M^{n+}]}$$ (at $298 K$, assuming $[M]=1$) For a general cell reaction: $aA + bB \rightarrow cC + dD$ $$E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q = E^\circ_{cell} - \frac{0.0592}{n} \log Q$$ where $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (reaction quotient). 4. Relation between $E_{cell}$, $\Delta G$, and $K_{eq}$ Gibbs Free Energy ($\Delta G$): $\Delta G = -nFE_{cell}$ For standard conditions: $\Delta G^\circ = -nFE^\circ_{cell}$ For spontaneous reaction: $\Delta G 0$ Equilibrium Constant ($K_{eq}$): At equilibrium, $E_{cell} = 0$ and $Q = K_{eq}$. $E^\circ_{cell} = \frac{RT}{nF} \ln K_{eq} = \frac{0.0592}{n} \log K_{eq}$ (at $298 K$) 5. Electrolytic Cells Uses external electrical energy to drive non-spontaneous reactions. Anode: Positive pole (oxidation). Cathode: Negative pole (reduction). Electrolysis: Process of chemical decomposition by electric current. Products of Electrolysis: Depend on electrode potentials of competing species. At cathode: species with higher reduction potential gets reduced. At anode: species with lower oxidation potential (higher reduction potential for the reverse reaction) gets oxidized. 6. Faraday's Laws of Electrolysis First Law: The mass of a substance deposited or liberated at any electrode is directly proportional to the quantity of electricity passed through the electrolyte. $$W \propto Q \implies W = ZQ$$ where $Q = It$ (coulombs), $Z$ is electrochemical equivalent. Second Law: When the same quantity of electricity is passed through different electrolytes, the masses of substances deposited or liberated are directly proportional to their chemical equivalents (equivalent weights). $$\frac{W_1}{W_2} = \frac{E_1}{E_2}$$ Key relation: $W = \frac{E \cdot I \cdot t}{F}$ $E$: Equivalent weight (Molar mass / n-factor) $F$: Faraday's constant ($96485 C/mol$) $n$-factor: Number of electrons involved in the half-reaction. 1 Faraday = Charge of 1 mole of electrons. 7. Conductance of Electrolytic Solutions Resistance ($R$): $R = \rho \frac{l}{A}$ (units: Ohm, $\Omega$) Resistivity ($\rho$): Resistance of a conductor of unit length and unit cross-sectional area (units: $\Omega \cdot m$). Conductance ($G$): Reciprocal of resistance. $G = \frac{1}{R}$ (units: Siemens, $S = \Omega^{-1}$). Conductivity ($\kappa$ or $\sigma$): Reciprocal of resistivity. $\kappa = \frac{1}{\rho} = G \frac{l}{A}$ (units: $S \cdot m^{-1}$). Cell Constant ($G^* = \frac{l}{A}$): $\kappa = G \cdot G^*$ Molar Conductivity ($\Lambda_m$): Conductivity of a solution containing 1 mole of electrolyte placed between two electrodes 1 cm apart with sufficient area to contain all the solution. $$\Lambda_m = \frac{\kappa \times 1000}{C}$$ (units: $S \cdot cm^2 \cdot mol^{-1}$, if $\kappa$ in $S \cdot cm^{-1}$ and $C$ in $mol \cdot L^{-1}$) 8. Variation of Conductivity with Concentration Strong Electrolytes: $\Lambda_m$ increases slowly with dilution. Debye-Hückel-Onsager Equation: $\Lambda_m = \Lambda_m^\circ - A\sqrt{C}$ $\Lambda_m^\circ$: Molar conductivity at infinite dilution. Weak Electrolytes: $\Lambda_m$ increases steeply with dilution due to increased dissociation. 9. Kohlrausch's Law At infinite dilution, when dissociation is complete, each ion makes a definite contribution to the molar conductivity of the electrolyte, irrespective of the nature of the other ion. $$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$ where $\nu_+$ and $\nu_-$ are the number of cations and anions per formula unit of the electrolyte, and $\lambda_+^\circ$ and $\lambda_-^\circ$ are their molar ionic conductivities at infinite dilution. Applications: Determination of $\Lambda_m^\circ$ for weak electrolytes. Calculation of degree of dissociation ($\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$) Calculation of dissociation constant ($K_a = \frac{C\alpha^2}{1-\alpha}$) 10. Batteries (Primary & Secondary) Primary Batteries: Non-rechargeable (e.g., Dry cell, Mercury cell). Dry Cell (Leclanché cell): Anode: Zn, Cathode: Carbon rod in $MnO_2 + C$ paste, Electrolyte: $NH_4Cl + ZnCl_2$. Mercury Cell: Anode: Zn-Hg amalgam, Cathode: $HgO + C$ paste, Electrolyte: $KOH + ZnO$. Constant voltage. Secondary Batteries: Rechargeable (e.g., Lead-acid battery, Ni-Cd battery). Lead-Acid Battery: Anode: Pb, Cathode: $PbO_2$, Electrolyte: $38\% H_2SO_4$. Nickel-Cadmium Cell: Anode: Cd, Cathode: $NiO_2$ (hydrated), Electrolyte: KOH. 11. Fuel Cells Converts energy of combustion of fuels (e.g., H$_2$, CH$_4$, CH$_3OH$) directly into electrical energy. H$_2$-O$_2$ Fuel Cell: Anode: $H_2(g) + 2OH^-(aq) \rightarrow 2H_2O(l) + 2e^-$ Cathode: $O_2(g) + 2H_2O(l) + 4e^- \rightarrow 4OH^-(aq)$ Overall: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$ Environmentally friendly, high efficiency. 12. Corrosion Electrochemical phenomenon where metals are attacked by the environment. Rusting of Iron: Anode (Fe): $Fe(s) \rightarrow Fe^{2+}(aq) + 2e^-$ Cathode (O$_2$): $O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l)$ Overall: $2Fe(s) + O_2(g) + 4H^+(aq) \rightarrow 2Fe^{2+}(aq) + 2H_2O(l)$ $Fe^{2+}$ is further oxidized to $Fe^{3+}$ (hydrated ferric oxide, rust: $Fe_2O_3 \cdot xH_2O$). Prevention: Barrier protection (paint, oil, grease). Galvanization (coating with Zn, a more reactive metal). Cathodic protection (connecting to a more easily oxidized metal, sacrificial anode). Alloying (e.g., stainless steel).