Given below is the plot of the molar conductivity vs concentration$\sqrt{\text{concentration}}$ for KCl in aqueous solution.

If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100Ω$100\Omega$ then the resistance of the same cell with the dilute solution is xΩ$\mathrm{x}\Omega$ The value of x$\mathbf{x}$ is (Nearest integer)

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

Core Logic

Limiting molar conductivity relies heavily on the charge and hydrodynamic radius of the hydrated ion. Let us verify the standard experimental limiting molar ionic conductivities (λ°$\lambda^{\circ}$) at 298 K$298\text{ K}$:

• H⁺: 349.8 S cm² mol⁻¹$H^{+}: 349.8\text{ S cm}^2\text{ mol}^{-1}$ (exhibits Grotthuss proton-hopping conduction mechanism)
• Ca²⁺: 119.0 S cm² mol⁻¹$Ca^{2+}: 119.0\text{ S cm}^2\text{ mol}^{-1}$
• Mg²⁺: 106.1 S cm² mol⁻¹$Mg^{2+}: 106.1\text{ S cm}^2\text{ mol}^{-1}$
• K⁺: 73.5 S cm² mol⁻¹$K^{+}: 73.5\text{ S cm}^2\text{ mol}^{-1}$
• Na⁺: 50.1 S cm² mol⁻¹$Na^{+}: 50.1\text{ S cm}^2\text{ mol}^{-1}$

Step 1: Trend Layout

Arranging these values in descending order yields:

Pattern Recognition

Shortcut: H⁺$H^{+}$ always has the absolute highest value due to its unique proton-hopping transport system. For metal ions, a higher ionic charge boosts conductivity (M²⁺ > M⁺$M^{2+} > M^{+}$), and within a group, a smaller hydrated radius (larger bare ion) increases mobility (K⁺ > Na⁺$K^{+} > Na^{+}$).

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