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Q.(a)(i) State Kohlrausch's law.

(ii) Why does the conductivity of a solution decrease with dilution?
(b) If the molar conductivity of a 1.5(M) KCl solution is 138.9 S.cm^2.mol^-1, determine the value of the conductivity of the solution.
(c) How many faradays of electricity would be required to obtain 20.0 g of Ca from molten CaCl2? ((1+1)+2+1=5) OR
(a) 2Al(s) + 3Cu2+(0.01M) --> 2Al3+(0.01M) + 3Cu(s). Calculate the EMF of the given cell at 298K. Given: E-cell(standard) = 1.98 V.
(b)(i) What type of cell is the lead storage battery?
(ii) What is corrosion? (3+(1+1)=5)
Tripura TbseHigher Secondary (+2 Stage) Examination 2025Subjective· 5mImportance★★★★★
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Concept understanding — Molar Conductivity

From Resistance to Conductance: Flipping the Idea

You already know resistance (RR) — it tells you how much a material opposes the flow of current. A high resistance means the wire fights the current; a low resistance means it lets current through easily.

Now flip that thought. Instead of asking "how much does it resist?", ask "how easily does it let current flow?" That's exactly what conductance measures.

Note

Conductance (GG) is the reciprocal of resistance:

G=1RG = \frac{1}{R}

Unit: siemens (S) — named after Werner von Siemens. 1 S = 1 A/V (ampere per volt).

If a wire has R=10 ΩR = 10\ \Omega, its conductance is G=0.1 SG = 0.1\ \text{S}. If R=0.5 ΩR = 0.5\ \Omega, G=2 SG = 2\ \text{S} — it conducts twice as well.

Ohm's Law in Conductance Form

You know V=IRV = IR. Rearranging:

I=VR=GVI = \frac{V}{R} = G V

So current = conductance × voltage. A high-conductance material draws a large current for the same voltage — it's a "good conductor."

Now, Conductivity: The Material's Intrinsic Property

Resistance depends on two things: the material itself (its "resistivity" ρ\rho) and the geometry (length LL, cross-sectional area AA):

R=ρLAR = \rho \frac{L}{A}

Conductance also depends on geometry. A thicker wire (larger AA) or a shorter wire (smaller LL) has higher conductance. To isolate the material's inherent ability to conduct, we define conductivity (σ\sigma):

σ=1ρ\sigma = \frac{1}{\rho}

And for a uniform wire:

G=σALG = \sigma \frac{A}{L}

Conductivity is the reciprocal of resistivity. It tells you how well the material itself conducts, independent of shape and size.

  • Unit: siemens per metre (S/m).
  • High σ\sigma → good conductor (copper: ≈5.8×107 S/m\approx 5.8 \times 10^7\ \text{S/m}).
  • Low σ\sigma → poor conductor / insulator (glass: ≈10−12 S/m\approx 10^{-12}\ \text{S/m}).
Watch out

Don't confuse conductance (property of a specific object, depends on geometry) with conductivity (property of the material, independent of geometry). A short thick copper wire has high conductance; a long thin copper wire has lower conductance — but both have the same conductivity.

The Big Picture in One Table

QuantitySymbolDefinitionDepends onUnit
ResistanceRRV/IV/IMaterial + geometryΩ\Omega
Resistivityρ\rhoRA/LR A / LMaterial onlyΩ⋅m\Omega \cdot \text{m}
ConductanceGG1/R1/RMaterial + geometryS
Conductivityσ\sigma1/ρ1/\rhoMaterial onlyS/m

Intuitive Analogy

Think of a water pipe:

  • Resistance = how hard it is to push water through (narrow, long pipe).
  • Conductance = how easily water flows (wide, short pipe). …

Why this formula?

Conductance and Conductivity: Why the Formulas Hold

Let's build this from first principles — understanding the why before the what.

1. The Core Idea: How Easily Does Current Flow?

Think of a conductor (like a copper wire). When you apply a voltage across it, electrons drift through the material. Two questions arise:

  • How much current flows for a given voltage? → This is conductance (GG).
  • How well does the material itself allow current? → This is conductivity (σ\sigma).

The key distinction: Conductance depends on the size and shape of the object. Conductivity is an intrinsic property of the material.

2. Ohm's Law in Terms of Conductance

You know Ohm's law:

V=IRV = IR

But we can rewrite it as:

I=VRI = \frac{V}{R}

Define conductance GG as the reciprocal of resistance:

G=1RG = \frac{1}{R}

So:

I=GVI = G V

Why this makes sense:

  • A larger GG means more current for the same voltage — the conductor "conducts" better.
  • GG has units of siemens (S) = A/V\text{A/V}.

3. From Resistance to Conductivity: The Geometry Factor

Resistance of a uniform conductor depends on:

  • Length LL (longer → more resistance)
  • Cross-sectional area AA (thicker → less resistance)
  • Material property ρ\rho (resistivity)

The formula:

R=ρLAR = \rho \frac{L}{A}

Now, conductivity σ\sigma is the reciprocal of resistivity:

σ=1ρ\sigma = \frac{1}{\rho}

So:

R=1σ⋅LAR = \frac{1}{\sigma} \cdot \frac{L}{A}

Why this form?

  • If you double the length, electrons have to travel twice as far, colliding more → resistance doubles.
  • If you double the area, there's twice as many "lanes" for electrons → resistance halves.

4. The Key Formula: Conductance in Terms of Conductivity

Since G=1/RG = 1/R, we get:

G=σALG = \sigma \frac{A}{L}

This is the central relationship. Let's see why it holds:

  • σ\sigma tells you how well the material conducts (intrinsic).
  • A/LA/L tells you how the geometry amplifies or reduces that.

Intuition:

  • A fat, short wire (AA large, LL small) has high conductance.
  • A thin, long wire (AA small, LL large) has low conductance.
  • A material with high σ\sigma (like copper) gives higher GG than one with low σ\sigma (like iron), for the same shape.

5. Microscopic Derivation (Why σ\sigma Exists)

At the microscopic level, conductivity arises from electron motion:

σ=neμ\sigma = n e \mu

Where:

  • nn = number of free electrons per unit volume
  • ee = electron charge …
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