How does a hydrogen fuel cell generate zero-emission electrical energy to propel urban city buses drinking only pure water from its exhaust pipe? Nernst Equation and Kohlrausch's Law govern electrochemical energy conversion.
यह अध्याय क्यों महत्वपूर्ण है
In Class 12 Chemistry, "Electrochemistry" provides an authoritative, curriculum-verified master resource aligned with the 2026–27 NCERT syllabus.
State and apply the Nernst Equation: $E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059}{n}\log Q$ at $298\text{ K}$.
Relate cell potential to Gibbs Free Energy: $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ and equilibrium constant: $\log K_c = \frac{nE^\circ_{\text{cell}}}{0.059}$.
Define Conductivity ($\kappa$), Molar Conductivity ($\Lambda_m = \frac{\kappa \times 1000}{M}$), and state Kohlrausch's Law of Independent Migration of Ions.
State Faraday's Laws of Electrolysis and explain commercial Batteries (Lead storage, Dry cell) and Corrosion.
अध्याय रूपरेखा एवं प्रगति
11. Nernst Equation & Thermodynamics
22. Kohlrausch's Law of Independent...
33. Batteries & Corrosion Prevention
सम्पूर्ण सैद्धांतिक एवं वैचारिक अध्ययन
1. Nernst Equation & Thermodynamics
For cell reaction $aA + bB \to cC + dD$, the cell potential at temperature $T=298\text{ K}$ is: $$\mathbf{E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n}\log_{10}\left(\frac{[C]^c [D]^d}{[A]^a [B]^b}\right)}$$ Maximum work equals electrical free energy: $\mathbf{\Delta G^\circ = -n F E^\circ_{\text{cell}}}$ ($F = 96,487\text{ C/mol}$). Equilibrium constant: $\mathbf{\log K_c = \frac{n E^\circ_{\text{cell}}}{0.0591}}$.
2. Kohlrausch's Law of Independent Migration
Kohlrausch's Law: Limiting molar conductivity of an electrolyte is the sum of the individual contributions of its anions and cations: $$\mathbf{\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ}$$ Crucial application: calculating limiting conductivity of weak electrolytes like acetic acid: $\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$!
3. Batteries & Corrosion Prevention
Lead Storage Battery: Spongy lead anode and $\text{PbO}_2$ cathode in $38\%$ $\text{H}_2\text{SO}_4$. In discharging: $\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \to 2\text{PbSO}_4 + 2\text{H}_2\text{O}$. Recharging reverses the process. Cathodic Protection: Sacrificial zinc blocks (Galvanization) protect steel ship hulls.
Keep an error log and revisit questions that exposed a misconception.
अवधारणात्मक हल उदाहरण एवं अनुप्रयोग (Solved Examples)
उदाहरण 1
Calculate the emf of the Daniell cell at $298\text{ K}$: $\text{Zn}(s) | \text{Zn}^{2+}(0.1\text{M}) || \text{Cu}^{2+}(0.01\text{M}) | \text{Cu}(s)$ given $E^\circ_{\text{cell}} = 1.10\text{ V}$.
State Kohlrausch's Law of independent migration of ions and state two of its applications.
विस्तृत समाधान / उत्तर:
Kohlrausch's law states that 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. Applications: (1) Determination of limiting molar conductivity ($\Lambda_m^\circ$) for weak electrolytes, (2) Determination of degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^\circ$) and dissociation constant $K_a$.
उदाहरण 3
Calculate $\Delta G^\circ$ for a cell having $E^\circ_{\text{cell}} = 1.1\text{ V}$ and $n = 2$ ($F = 96500\text{ C/mol}$).
मूल वैचारिक स्पष्टता की जांच के लिए नैदानिक प्रश्न। पहले स्वयं हल करें, फिर उत्तर देखें।
1
Calculate the emf of the Daniell cell at $298\text{ K}$: $\text{Zn}(s) | \text{Zn}^{2+}(0.1\text{M}) || \text{Cu}^{2+}(0.01\text{M}) | \text{Cu}(s)$ given $E^\circ_{\text{cell}} = 1.10\text{ V}$.
State Kohlrausch's Law of independent migration of ions and state two of its applications.
उत्तर एवं व्याख्या देखें
उत्तर: Kohlrausch's law states that 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. Applications: (1) Determination of limiting molar conductivity ($\Lambda_m^\circ$) for weak electrolytes, (2) Determination of degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^\circ$) and dissociation constant $K_a$. Additive ionic conductivities; finds weak electrolyte Λ0 and dissociation degree.
3
Calculate $\Delta G^\circ$ for a cell having $E^\circ_{\text{cell}} = 1.1\text{ V}$ and $n = 2$ ($F = 96500\text{ C/mol}$).
What is the effect of dilution on: (i) Conductivity ($\kappa$), (ii) Molar Conductivity ($\Lambda_m$)?
उत्तर एवं व्याख्या देखें
उत्तर: (i) Conductivity $\kappa$ decreases on dilution because the number of current-carrying ions per unit volume of solution decreases. (ii) Molar conductivity $\Lambda_m$ increases on dilution because the increase in volume ($V$) containing 1 mole of electrolyte vastly outweighs the decrease in $\kappa$. Conductivity decreases; Molar conductivity increases.
5
Write the chemical reactions taking place at the anode and cathode during the discharging of a lead-storage battery.
उत्तर एवं व्याख्या देखें
उत्तर: Anode: $\text{Pb}(s) + \text{SO}_4^{2-}(aq) \to \text{PbSO}_4(s) + 2e^-$. Cathode: $\text{PbO}_2(s) + \text{SO}_4^{2-}(aq) + 4\text{H}^+(aq) + 2e^- \to \text{PbSO}_4(s) + 2\text{H}_2\text{O}(l)$. Discharge forms PbSO4 at both electrodes.
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