Consider the following redox reaction taking place in acidic medium BH₄⁻(aq) + ClO₃⁻(aq) arrow H₂BO₃⁻(aq) + Cl⁻(aq)$BH_{4}^{-}(aq) + ClO_{3}^{-}(aq) \rightarrow H_{2}BO_{3}^{-}(aq) + Cl^{-}(aq)$ If the Nernst equation for the above balanced reaction is Ecell = Ecell° - (RT)/(nF) ln Q,$E_{\text{cell}} = E_{\text{cell}}^{\circ} - \frac{RT}{nF} \ln Q,$ Then the value of n is _____.

Core Logic

Matching applications to their respective electrochemical cells: * Transistors use standard dry cells: Anode is Zn container, Cathode is carbon rod coated with MnO₂$MnO_2$ arrow$\rightarrow$ (III). * Hearing aids require compact voltage outputs over time, matching Mercury cells: Anode Zn/Hg, Cathode HgO + C arrow$\rightarrow$ (I). * Invertors utilize rechargeable systems, matching Lead-storage batteries: Anode Pb, Cathode Pb | PbO₂$PbO_2$ arrow$\rightarrow$ (IV). * Apollo space ship dynamically powered via Hydrogen-Oxygen Fuel cells arrow$\rightarrow$ (II).

Pattern Recognition

Space missions universally trigger fuel cell pairs in standard test patterns due to the secondary requirement of gathering pure drinking water byproduct.

Chapter Mix

Class 12 Chemistry: Electrochemistry

Core Logic

Analyzing anodic reactions during electrolysis: * Case (A): With active Ag electrodes, silver oxidation occurs at the anode (Ag arrow Ag⁺ + e⁻$Ag \rightarrow Ag^{+} + e^{-}$). No oxygen is evolved. * Case (B): With inert Pt electrodes, oxidation of water occurs preferentially at the anode over NO₃^-$NO_3^-$ ions:2H₂O arrow O₂ + 4H⁺ + 4e⁻$$2H_2O \rightarrow O_2 + 4H^{+} + 4e^{-}$$

• Case (C): In dilute H₂SO₄$H_2SO_4$, water oxidation takes place, releasing O₂$O_2$ gas at the anode.
• Case (D): In concentrated H₂SO₄$H_2SO_4$, oxidation of SO₄²⁻$SO_4^{2-}$ creates peroxodisulphate ions (S₂O₈²⁻$S_2O_8^{2-}$), inhibiting oxygen evolution.

Pattern Recognition

Remember that active electrodes participate directly in redox reactions, whereas inert electrodes (Pt, Graphite) yield oxygen gas when water is oxidized in the presence of oxoanions like NO₃^-$NO_3^-$ or dilute SO₄²⁻$SO_4^{2-}$.

Chapter Mix

Class 12 Chemistry: Electrochemistry

Related Formula

Conductivity relationship with cell parameters:

where G^*$G^*$ represents the static cell constant.

Step 1: Setting Up Ratios

Using concentration subscripts c$c$ (concentrated) and d$d$ (dilute):

Expressing conductivity through molar conductivity values:

Substituting the graphical read coordinates (Cc = 0.15², Cd = 0.1²$C_c = 0.15^2, C_d = 0.1^2$ with scaled λm$\lambda_m$ parameters):

Pattern Recognition

Sees: Resistance correlation across specific graph coordinates. Shortcut: Equate cell parameters through κ ∝ (1)/(R)$\kappa \propto \frac{1}{R}$ and solve for the target resistance directly.

Chapter Mix

Class 12 Chemistry: Electrochemistry

Related Formula

Core Logic

Standard limiting ionic molar conductivities (λ^°$\lambda^\circ$) in aqueous solution at 298~K$298\mathrm{~K}$:

• H^+: 349.8 ~S~cm²~mol⁻¹$\mathrm{H^+}: 349.8\mathrm{~S~cm^2~mol^{-1}}$ (exceptionally high due to Grotthuss proton-jumping mechanism)
• Ca²⁺: 119.0 ~S~cm²~mol⁻¹$\mathrm{Ca^{2+}}: 119.0\mathrm{~S~cm^2~mol^{-1}}$
• Mg²⁺: 106.1 ~S~cm²~mol⁻¹$\mathrm{Mg^{2+}}: 106.1\mathrm{~S~cm^2~mol^{-1}}$
• K^+: 73.5 ~S~cm²~mol⁻¹$\mathrm{K^+}: 73.5\mathrm{~S~cm^2~mol^{-1}}$
• Na^+: 50.1 ~S~cm²~mol⁻¹$\mathrm{Na^+}: 50.1\mathrm{~S~cm^2~mol^{-1}}$

Step 1: Final Order

Arranging in decreasing order:

Pattern Recognition

Hydration effects: Smaller univalent cations (Na^+$\mathrm{Na^+}$) are more heavily hydrated than larger ones (K^+$\mathrm{K^+}$), so λ^°(K^+) > λ^°(Na^+)$\lambda^\circ(\mathrm{K^+}) > \lambda^\circ(\mathrm{Na^+})$. Divalent ions have higher ionic charge density and higher molar conductivities than alkali metal ions.

Chapter Mix

Class 12 Chemistry: Electrochemistry

Related Formula

Core Logic

• Find the limiting molar conductance of NH₄^+$NH_4^+$ using the NH₄Cl$NH_4Cl$ data:

• Calculate Λm^°$\Lambda_m^\circ$ for the weak electrolyte ammonium hydroxide (NH₄OH$NH_4OH$):

• Evaluate the degree of dissociation (α$\alpha$):

Comparing with the format x × 10⁻¹$\mathbf{x} \times 10^{-1}$, the value of x$\mathbf{x}$ is 3.

Pattern Recognition

Kohlrausch's law allows direct algebraic recombination of ion conductances. Always construct the targeted weak base compound value by filtering out the spectator chloride contribution from the initial salt parameters.

Chapter Mix

Class 12 Chemistry: Electrochemistry