JEE Mains Chemistry · Electrochemistry

Conductivity, Cell Constant and Molar Conductivity

From a measured resistance to conductivity through the cell constant, then to molar conductivity, with the units and the factors that change how well a solution conducts.

All Electrochemistry notes JEE Mains Chemistry strategy

Why this matters

Fourteen PYQs, nine of them numerical, and one from 2026. Ten turn a resistance, resistivity or ppm figure into κ and Λm through the cell constant, often with a unit change on the way; four ask what affects conductance and how fast different ions move. Two ideas cover the page.

Concept 1 of 2: Cell constant, conductivity and molar conductivity

A conductivity cell measures resistance. The cell constant turns that into conductivity, which belongs to the solution, not the cell. Dividing conductivity by concentration then gives molar conductivity: how well one mole of electrolyte conducts.

Definition

Conductance $G=\frac{1}{R}$ (S). Resistivity $\rho=\frac{1}{\kappa}$ .
Cell constant $G^*=\frac{l}{A}$ , in cm⁻¹ or m⁻¹. Then $\kappa=\frac{G^*}{R}=G\times G^*$ .
$\Lambda_m=\frac{1000\,\kappa}{c}$ with $\kappa$ in S cm⁻¹ and $c$ in mol L⁻¹ gives S cm² mol⁻¹.
In SI, $\Lambda_m=\frac{\kappa}{c}$ with $\kappa$ in S m⁻¹ and $c$ in mol m⁻³ gives S m² mol⁻¹.
$1$ S cm² mol⁻¹ $=10^{-4}$ S m² mol⁻¹. $1$ S m² $=10^{5}$ mS dm².
ppm to molarity: 74.5 ppm KCl is 74.5 mg L⁻¹, which is $10^{-3}$ M.
One cell, two solutions: $G^*$ is the same, so $\kappa_1R_1=\kappa_2R_2$ .
Units to match: cell constant m⁻¹; $\kappa$ S m⁻¹ ( $\Omega^{-1}$ m⁻¹); $\Lambda_m$ S cm² mol⁻¹; degree of dissociation, none.

From resistance to molar conductivity

\kappa=\frac{G^*}{R},\qquad \Lambda_m=\frac{1000\,\kappa}{c}

G^*cell constant l/A (cm⁻¹)
cconcentration in mol L⁻¹

Worked example

A cell filled with a standard solution of

\kappa=0.0040

S cm⁻¹ reads 250 Ω. Filled with a 0.05 M solution it reads 400 Ω. Find the cell constant and the molar conductivity of the 0.05 M solution.

Practice this conceptself-check · 5 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 5 Apr 2026 Shift 2 · Q49Moderate

Example 1 · Electrochemistry · Conductivity, Cell Constant and Molar Conductivity

At 298 K , the molar conductivity of

x\%(w/w)

MX solution (aqueous) is

123.5\text{ }S{\text{ }cm}^{2}{\text{ }mol}^{- 1}

. The conductance of same solution is

1.9 \times 10^{- 3}\text{ }S

. The value of

x

\_\_\_\_

\times 10^{- 2}

. (Given : cell constant

= 1.3{\text{ }cm}^{- 1}

; molar mass of MX is

75\text{ }g{\text{ }mol}^{- 1}

, density of aqueous solution of MX at 298 K is

1.0\text{ }g{\text{ }mL}^{- 1}

)

Mixing unit systems

The factor 1000 belongs with S cm⁻¹ and mol L⁻¹. In SI, convert

c

to mol m⁻³ (multiply mol L⁻¹ by 1000) and drop the factor.

Resistivity used as conductivity

A resistivity in Ω cm must be inverted to get

\kappa

before anything else.

Drill 9 more on cell constant, conductivity and molar conductivity

Concept 2 of 2: What conductance depends on

Current in a solution is carried by moving ions. Anything that changes how many ions there are, or how fast they move, changes the conductance. The electrodes only collect the current.

Definition

Affects conductance: the nature of the electrolyte, the size and hydration of its ions, the solvent and its viscosity, the concentration, and the temperature (conductance rises with temperature).
Does not: the material of the electrodes.
On dilution $\kappa$ FALLS, because there are fewer ions per unit volume. $\Lambda_m$ RISES, because each mole of ions moves more freely.
$\mathrm{H^+}$ and $\mathrm{OH^-}$ are much faster than any other ion: they pass along chains of hydrogen-bonded water (the Grotthuss mechanism).
Within a group, a smaller BARE ion holds more water, so its hydrated ion is larger and slower: $\mathrm{Li^+<Na^+<K^+}$ .

Ion	λ° at 298 K (S cm² mol⁻¹)	Why
$\mathrm{H^+}$	$349.6$	Proton hopping along hydrogen bonds
$\mathrm{OH^-}$	$199.1$	Proton hopping, in reverse
$\mathrm{SO_4^{2-}}$	$160.0$	Double charge carries twice the current
$\mathrm{Ca^{2+}}$	$119.0$	Double charge
$\mathrm{Mg^{2+}}$	$106.0$	Double charge, but a smaller ion is more hydrated than Ca²⁺
$\mathrm{Br^-}$	$78.1$	Large anion, lightly hydrated
$\mathrm{Cl^-}$	$76.3$	Close to K⁺, which is why KCl is the standard
$\mathrm{K^+}$	$73.5$	Least hydrated of Li⁺, Na⁺, K⁺
$\mathrm{Na^+}$	$50.1$	More hydrated than K⁺
$\mathrm{CH_3COO^-}$	$40.9$	Large, bulky organic anion
$\mathrm{Li^+}$	$38.7$	Smallest bare ion, largest hydrated ion

Values are per mole of the ion as written.

Practice this conceptself-check · 5 quick reps

The same idea in a real exam question:

JEE Mains · 2025 · 3 Apr 2025 · Q45Moderate

Example 2 · Electrochemistry · Conductivity, Cell Constant and Molar Conductivity

Correct order of limiting molar conductivity for cations in water at 298 K is :

Bare size against hydrated size

\mathrm{Li^+}

is the smallest bare ion but the slowest in water. What moves is the ion with its shell of water.

κ and Λm move opposite ways

"Conductivity always decreases on dilution" is true. "Molar conductivity decreases on dilution" is false.

Drill 3 more on what conductance depends on

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Cell constant, conductivity and molar conductivity
From resistance to molar conductivity
$\kappa=\frac{G^*}{R},\qquad \Lambda_m=\frac{1000\,\kappa}{c}$

Reference tables (1)

What conductance depends on11 rows

Ion	λ° at 298 K (S cm² mol⁻¹)	Why
$\mathrm{H^+}$	$349.6$	Proton hopping along hydrogen bonds
$\mathrm{OH^-}$	$199.1$	Proton hopping, in reverse
$\mathrm{SO_4^{2-}}$	$160.0$	Double charge carries twice the current
$\mathrm{Ca^{2+}}$	$119.0$	Double charge
$\mathrm{Mg^{2+}}$	$106.0$	Double charge, but a smaller ion is more hydrated than Ca²⁺
$\mathrm{Br^-}$	$78.1$	Large anion, lightly hydrated
$\mathrm{Cl^-}$	$76.3$	Close to K⁺, which is why KCl is the standard
$\mathrm{K^+}$	$73.5$	Least hydrated of Li⁺, Na⁺, K⁺
$\mathrm{Na^+}$	$50.1$	More hydrated than K⁺
$\mathrm{CH_3COO^-}$	$40.9$	Large, bulky organic anion
$\mathrm{Li^+}$	$38.7$	Smallest bare ion, largest hydrated ion

Values are per mole of the ion as written.

Watch out for (4)

Mixing unit systems
→ Cell constant, conductivity and molar conductivity
Resistivity used as conductivity
→ Cell constant, conductivity and molar conductivity
Bare size against hydrated size
→ What conductance depends on
κ and Λm move opposite ways
→ What conductance depends on

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