Conductance of Electrolytic Solutions ⚡

Electricity moves through solutions when ions carry charge. Understanding how easily this happens is key for batteries, sensors, and NEET questions. Let’s unpack the ideas step-by-step 🙂.

1. Basic Terms

  • Resistance (R) – opposition to current, measured in ohm (Ω). It follows \(R = \rho \dfrac{l}{A}\) where l is length and A is cross-sectional area :contentReference[oaicite:0]{index=0}.
  • Resistivity (ρ) – resistance of a 1 m × 1 m2 specimen; units Ω m. \(1\;Ω m = 100\;Ω cm\) :contentReference[oaicite:1]{index=1}.
  • Conductance (G) – ease of current flow, \(G = \dfrac{1}{R}\) (Si). Units = siemens (S) :contentReference[oaicite:2]{index=2}.
  • Conductivity (κ) – inverse of ρ, units S m-1. \(1\;S cm^{-1}=100\;S m^{-1}\) :contentReference[oaicite:3]{index=3}.

2. Electronic vs Ionic Conductance

Metals conduct by electron flow, while solutions conduct by ion motion. Ionic conductivity depends on:

  • Type of electrolyte
  • Ion size & solvation
  • Solvent viscosity
  • Concentration
  • Temperature (↑T ⇒ ↑κ) :contentReference[oaicite:4]{index=4}

3. Measuring Conductivity 📏

  • A conductivity cell has platinised Pt electrodes separated by l and area A. Resistance is \(R = \rho\dfrac{l}{A}\) (2.17) :contentReference[oaicite:5]{index=5}.
  • The cell constant \(G^* = \dfrac{l}{A} = Rκ\) (2.18). Calibrate \(G^*\) with standard KCl solutions :contentReference[oaicite:6]{index=6}.
  • With \(G^*\) known, conductivity is \(κ = \dfrac{G^*}{R}\) (2.20). Modern meters display κ directly :contentReference[oaicite:7]{index=7}.

4. Molar Conductivity (Λm)

\(\Lambda_m = \dfrac{κ}{c}\) (2.21); units S m2 mol-1.
1 S m2 mol-1 = 104 S cm2 mol-1 :contentReference[oaicite:8]{index=8}.

4.1 How κ and Λm change with dilution 💧

  • Conductivity (κ) decreases because fewer ions per unit volume carry current :contentReference[oaicite:9]{index=9}.
  • Molar conductivity (Λm) increases since one mole now occupies a larger volume: \(Λ_m = κV\) (2.22) :contentReference[oaicite:10]{index=10}.

4.2 Strong vs Weak Electrolytes

For strong electrolytes: \(Λ_m = Λ_m^{\circ} – A\sqrt{c}\) (2.23) gives a straight line when Λm is plotted against √c :contentReference[oaicite:11]{index=11}.

For weak electrolytes, Λm rises sharply on dilution. Degree of dissociation is \(\alpha = \dfrac{Λ_m}{Λ_m^{\circ}}\) (2.26) :contentReference[oaicite:12]{index=12}.

5. Kohlrausch’s Law 🧮

At infinite dilution, ion contributions add independently: \(Λ_m^{\circ} = n_+λ_+^{\circ} + n_-λ_-^{\circ}\) (2.25) :contentReference[oaicite:13]{index=13}.
Example: \(Λ_m^{\circ}(\text{CaCl}_2)=119.0+2(76.3)=271.6\;S cm^2 mol^{-1}\) :contentReference[oaicite:14]{index=14}.

6. Unit Tips 📝

  • Ω m → Ω cm: ×100 or ÷100 as needed.
  • S cm-1 → S m-1: ×100.
  • S m2 mol-1 → S cm2 mol-1: ×104 :contentReference[oaicite:15]{index=15}.

7. Sample Calculations 🔍

  1. 0.02 mol L-1 KCl: using \(G^*=129\;m^{-1}\) gives \(κ=0.248\;S m^{-1}\) and \(Λ_m=1.24×10^{-2}\;S m^{2} mol^{-1}\) :contentReference[oaicite:16]{index=16}.
  2. 0.05 mol L-1 NaOH column: ρ = 87.135 Ω cm; κ = 0.01148 S cm-1; Λm = 229.6 S cm2 mol-1 :contentReference[oaicite:17]{index=17}.

Important Concepts for NEET ⭐

  1. The master relation \(R=\rho\dfrac{l}{A}\) and its conversion to \(G\) and \(κ\).
  2. Calibrating the cell constant with standard KCl before measuring unknown solutions.
  3. Trend with dilution: κ decreases, Λm increases; understand why for strong vs weak electrolytes.
  4. Kohlrausch’s law lets you compute Λm◦ and the degree of dissociation (α) of weak acids/bases.
  5. Quick unit conversions (Ω m ↔ Ω cm, S m-1 ↔ S cm-1, S m2 mol-1 ↔ S cm2 mol-1).