Which of the statements about solutions of electrolytes is not correct? (i) Conductivity of solution depends u

NCERT Exemplar · Q7

Q. Which of the statements about solutions of electrolytes is not correct?

(i) Conductivity of solution depends upon size of ions.

(ii) Conductivity depends upon viscosity of solution.

(iii) Conductivity does not depend upon solvation of ions present in solution.

(iv) Conductivity of solution increases with temperature.

Madhya Pradesh MpbseMCQ· 1mImportance★★★★★

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Concept understanding — Molar Conductivity

From Resistance to Conductance: Flipping the Idea

You already know resistance ( $R$ ) — 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 ( $G$ ) is the reciprocal of resistance:

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

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

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

Ohm's Law in Conductance Form

You know $V = IR$ . Rearranging:

I = \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" $\rho$ ) and the geometry (length $L$ , cross-sectional area $A$ ):

R = \rho \frac{L}{A}

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

\sigma = \frac{1}{\rho}

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 $\sigma$ → good conductor (copper: $\approx 5.8 \times 10^7\ \text{S/m}$ ).
Low $\sigma$ → poor conductor / insulator (glass: $\approx 10^{-12}\ \text{S/m}$ ).

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

Quantity	Symbol	Definition	Depends on	Unit
Resistance	$R$	$V/I$	Material + geometry	$\Omega$
Resistivity	$\rho$	$R A / L$	Material only	$\Omega \cdot \text{m}$
Conductance	$G$	$1/R$	Material + geometry	S
Conductivity	$\sigma$	$1/\rho$	Material only	S/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 ( $G$ ).
How well does the material itself allow current? → This is conductivity ( $\sigma$ ).

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 = IR

But we can rewrite it as:

I = \frac{V}{R}

Define conductance $G$ as the reciprocal of resistance:

G = \frac{1}{R}

So:

I = G V

Why this makes sense:

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

3. From Resistance to Conductivity: The Geometry Factor

Resistance of a uniform conductor depends on:

Length $L$ (longer → more resistance)
Cross-sectional area $A$ (thicker → less resistance)
Material property $\rho$ (resistivity)

The formula:

R = \rho \frac{L}{A}

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

\sigma = \frac{1}{\rho}

So:

R = \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 $G = 1/R$ , we get:

G = \sigma \frac{A}{L}

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

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

Intuition:

A fat, short wire ( $A$ large, $L$ small) has high conductance.
A thin, long wire ( $A$ small, $L$ large) has low conductance.
A material with high $\sigma$ (like copper) gives higher $G$ than one with low $\sigma$ (like iron), for the same shape.

5. Microscopic Derivation (Why $\sigma$ Exists)

At the microscopic level, conductivity arises from electron motion:

\sigma = n e \mu

Where:

$n$ = number of free electrons per unit volume
$e$ = electron charge …

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The key idea is that molar conductivity depends on ion mobility, which is affected by ion size, solvation (which changes effective size), and viscosity — but the statement that conductivity does not depend on solvation is false. The incorrect statement is (iii).

Let’s start with the core concept. When we talk about conductivity of an electrolyte solution, we’re really talking about how easily ions move through the solution under an electric field. This movement — called ionic mobility — is what determines conductivity. Anything that slows ions down or speeds them up will affect conductivity.

The factors that influence ionic mobility are:

Size of the ion — larger ions move slower (all else equal).
Solvation — when ions get surrounded by solvent molecules, their effective size increases, reducing mobility.
Viscosity of the solution — a more viscous medium offers more resistance to ion movement.
Temperature — higher temperature reduces viscosity and increases kinetic energy, so ions move faster.

Now, let’s examine each statement one by one.

Statement (i): Conductivity depends upon size of ions.

This is correct. Smaller ions (like $K^+$ ) move faster than larger ones (like $Cs^+$ ) in the same solvent, so conductivity is higher for smaller ions — provided solvation effects are similar.
Statement (ii): Conductivity depends upon viscosity of solution.

Correct. Higher viscosity means greater frictional drag on ions. For example, adding glycerol to water increases viscosity and lowers conductivity.
Statement (iii): Conductivity does not depend upon solvation of ions present in solution.

This is the suspect one. Solvation actually does affect conductivity. When an ion gets solvated, it becomes effectively larger — a hydrated $Li^+$ ion, for instance, moves slower than a bare $Li^+$ would. So solvation reduces ionic mobility and hence conductivity. The statement says the opposite — that conductivity does not depend on solvation — which is false.
Statement (iv): Conductivity of solution increases with temperature. …

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Method: Conceptual Elimination Using the Definition of Molar Conductivity

Step 1 — Recall the core idea

Molar conductivity ( $\Lambda_m$ ) is the conductivity of all ions produced from one mole of electrolyte in a given volume of solution.

It depends on:

Number of ions (degree of dissociation)
Speed of ions (mobility)
Interionic interactions

Step 2 — Analyse each statement

Statement	Correct or not?	Reason
(i) Conductivity depends on size of ions	✓ Correct	Smaller ions move faster → higher conductivity
(ii) Conductivity depends on viscosity	✓ Correct	Higher viscosity → slower ion movement → lower conductivity
(iii) Conductivity does not depend on solvation	✗ Incorrect	Solvation increases effective size of ions, slowing them down → affects conductivity

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Here are the common mistakes students make on this question, along with how to avoid each.

Mistake 1: Confusing "Conductivity" with "Molar Conductivity"

The Error: Students read the question and immediately think of molar conductivity ( $\Lambda_m$ ), and then reason loosely about which factors matter, without pinning down exactly what each statement claims.
Why it happens: Conductivity ( $\kappa$ ) and molar conductivity ( $\Lambda_m$ ) are related ( $\Lambda_m = 1000\kappa/C$ ) but are affected by different combinations of factors, so it's easy to blur them together.
How to avoid: Always check the exact term the statement uses, and treat ionic mobility (which both $\kappa$ and $\Lambda_m$ depend on) as the common underlying driver.

Mistake 2: Thinking Solvation Has No Effect on Conductivity

The Error: Students reason "solvation only changes molar conductivity, not bulk conductivity," and conclude that statement (iii)/(iii) ("Conductivity does not depend upon solvation of ions") is actually TRUE.
Why it's wrong: Solvation directly changes an ion's effective size, and larger effective size means lower ionic mobility (by the Stokes–Einstein relation, mobility $\propto 1/r_{effective}$ ). Since conductivity is built from ionic mobility multiplied by ion concentration and charge, anything that changes mobility — including solvation — changes conductivity too. The classic textbook example is that hydrated $Li^+$ (heavily solvated, large effective radius) has LOWER ionic conductivity than $Na^+$ or $K^+$ , even though bare $Li^+$ is the smallest alkali metal ion.
How to avoid: Remember: solvation slows ions down by making them effectively bigger, and slower ions carry current less efficiently — so solvation DOES affect conductivity. Statement (iii)/(iii), which claims conductivity "does not depend" on solvation, is therefore the FALSE statement, i.e. it is the "not correct" statement the question is asking for.

Mistake 3: Misinterpreting the Effect of Temperature

The Error: Some students think conductivity of an electrolyte solution decreases with temperature (like metals), so they mark statement (iv)/(iv) as the incorrect one.
Why it happens: They confuse electrolytic solutions with metallic conductors. In metals, resistance increases with temperature. In solutions, the opposite happens.
How to avoid: Remember the kinetic picture for solutions: as temperature increases, viscosity decreases and ion mobility increases, so more ions move faster and conductivity increases. Statement (iv)/(iv) is therefore a TRUE statement, not the answer.

Mistake 4: Overlooking the "Not Correct" Wording …

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Q.Which of the statements about solutions of electrolytes is not correct?

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