Variations of Conductivity with Concentration

Q: Why does specific conductivity decrease with dilution for both strong and weak electrolytes?

Specific conductivity ($\kappa$) is a measure of the conductance of a unit volume of the solution. When a solution is diluted, the total number of ions remains the same, but they are spread out over a larger volume. This means that the number of ions present in any given unit volume (e.g., 1 cm$^3$) decreases. Since fewer charge carriers are available in that specific volume to transport electricity, the specific conductivity of the solution decreases. This holds true regardless of whether the electrolyte is strong or weak, as the fundamental principle of reduced ion density per unit volume applies to both.

Q: What is the significance of molar conductivity at infinite dilution ($\Lambda_m^\circ$)?

Molar conductivity at infinite dilution ($\Lambda_m^\circ$) represents the maximum possible molar conductivity an electrolyte can achieve. At infinite dilution, inter-ionic attractions become negligible, and ions move completely independently of each other. For strong electrolytes, $\Lambda_m^\circ$ can be determined by extrapolating the $\Lambda_m$ vs. $\sqrt{c}$ plot. For weak electrolytes, it cannot be found by extrapolation but is crucial for calculating the degree of dissociation and dissociation constant using Kohlrausch's Law. It provides a benchmark for the intrinsic conducting ability of an electrolyte's ions.

Q: How is the degree of dissociation ($\alpha$) related to molar conductivity for weak electrolytes?

For weak electrolytes, the degree of dissociation ($\alpha$) is directly related to its molar conductivity. The ratio of the molar conductivity at a given concentration ($\Lambda_m$) to the molar conductivity at infinite dilution ($\Lambda_m^\circ$) gives the degree of dissociation. The formula is $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$. This relationship is extremely useful because it allows us to calculate how much of a weak electrolyte has dissociated into ions at a particular concentration, provided we know its molar conductivity at that concentration and its molar conductivity at infinite dilution (which can be determined using Kohlrausch's Law).

Updated 22 Mar 2026

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The conductivity of an electrolytic solution, which is its ability to conduct electricity, is fundamentally dependent on the concentration of ions present within it. This relationship is not straightforward, as two distinct measures, specific conductivity ( $\kappa$ ) and molar conductivity ( $\Lambda_m$ ), exhibit contrasting trends with changes in concentration. Specific conductivity, representing t…

Quick Summary

Electrolytic solutions conduct electricity due to the movement of ions. The ability to conduct is quantified by specific conductivity ( $\kappa$ ) and molar conductivity ( $\Lambda_m$ ). Specific conductivity, the conductance of a unit volume, decreases with dilution for both strong and weak electrolytes because the number of ions per unit volume reduces.

Molar conductivity, the conductance of one mole of electrolyte, increases with dilution for both types. For strong electrolytes, this increase is due to reduced inter-ionic attractions and increased ionic mobility, following the Debye-Hückel-Onsager equation ( $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$ ).

For weak electrolytes, the increase is much steeper and primarily due to an increase in the degree of dissociation ( $\alpha$ ) as per Ostwald's Dilution Law, which produces more ions. Molar conductivity at infinite dilution ( $\Lambda_m^\circ$ ) is the maximum conductivity, obtainable by extrapolation for strong electrolytes, but requiring Kohlrausch's Law for weak electrolytes.

Understanding these variations is crucial for characterizing electrolytes and solving related numerical problems in NEET.

Full explanation

Electrolytic conductance is the ability of a solution containing ions to conduct electric current. This phenomenon is fundamental to electrochemistry and is critically influenced by the concentration of the electrolyte. To understand this variation, we must first distinguish between two key measures of conductivity: specific conductivity and molar conductivity.

Conceptual Foundation: Factors Affecting Electrolytic Conductance

Electrolytic conductance depends primarily on two factors:

Number of Ions — The more ions present in a solution, the greater its capacity to carry charge, and thus higher its conductivity.

Mobility of Ions — Ions must be able to move freely through the solution to transport charge. Factors like inter-ionic attraction, viscosity of the solvent, and temperature affect ionic mobility. Higher mobility leads to higher conductivity.

Key Principles and Laws

Specific Conductivity ($\kappa$) — Also known as conductivity, it is defined as the conductance of a solution of unit volume (e.g., 1 cm

^3

) placed between two electrodes of unit area (1 cm

^2

) separated by unit distance (1 cm). Its unit is Siemens per centimeter (S cm

^{-1}

) or Siemens per meter (S m

^{-1}

). It is an intensive property, meaning it depends on the concentration of ions in a specific volume.

\kappa = \frac{1}{R} \times \frac{l}{A}

where

R

is resistance,

l

is the distance between electrodes, and

A

is the area of the electrodes. The term

l/A

is the cell constant (

G^*

). So,

\kappa = G/G^*

, where

G

is conductance.

Molar Conductivity ($\Lambda_m$) — It is defined as the conductance of the volume of solution containing one mole of electrolyte placed between two electrodes with unit area of cross-section and separated by unit distance. Alternatively, it is the specific conductivity divided by the molar concentration (

c

) of the electrolyte. Its unit is Siemens centimeter squared per mole (S cm

^2

mol

^{-1}

) or Siemens meter squared per mole (S m

^2

mol

^{-1}

). It is an extensive property, reflecting the total conducting power of one mole of electrolyte.

\Lambda_m = \frac{\kappa}{c}

\kappa

is in S cm

^{-1}

and

c

is in mol L

^{-1}

(which is mol/1000 cm

^3

), then:

\Lambda_m = \frac{\kappa \times 1000}{c}

where

c

is in mol L

^{-1}

and

\Lambda_m

is in S cm

^2

mol

^{-1}

Variations of Conductivity with Concentration

1. Specific Conductivity ($\kappa$)

For both strong and weak electrolytes, specific conductivity ( $\kappa$ ) decreases with dilution (decrease in concentration). This trend is straightforward to understand:

When a solution is diluted, the total volume of the solution increases, but the total number of ions remains constant (assuming complete dissociation for strong electrolytes, or a fixed degree of dissociation for weak electrolytes at a given concentration).

Consequently, the number of ions present per unit volume (e.g., 1 cm

^3

) decreases.

Since specific conductivity measures the conductance of a unit volume, a reduction in the number of charge carriers within that unit volume directly leads to a decrease in specific conductivity.

2. Molar Conductivity ($\Lambda_m$)

For both strong and weak electrolytes, molar conductivity ( $\Lambda_m$ ) increases with dilution (decrease in concentration), but the reasons and the magnitude of increase differ significantly.

a) For Strong Electrolytes:

Strong electrolytes, such as NaCl, KCl, or strong acids like HCl, dissociate almost completely into ions in solution, even at high concentrations. Therefore, the number of ions produced by one mole of a strong electrolyte remains constant regardless of dilution.

The increase in $\Lambda_m$ with dilution for strong electrolytes can be attributed to two main factors: * Reduced Inter-ionic Attractions: At higher concentrations, ions are closer to each other, leading to significant electrostatic attractive forces between oppositely charged ions (ion-ion interactions).

These attractions hinder the free movement of ions, reducing their effective mobility. Upon dilution, the ions move further apart, inter-ionic attractions weaken, and the ions become freer to move, thus increasing their mobility and contributing more to the overall conductance.

* Reduced Viscous Drag: As the concentration decreases, the solution becomes less viscous, reducing the frictional drag experienced by the moving ions. This also contributes to increased ionic mobility.

The relationship between molar conductivity and concentration for strong electrolytes is often described by the Debye-Hückel-Onsager equation:

\Lambda_m = \Lambda_m^\circ - A\sqrt{c}

where: *

\Lambda_m

is the molar conductivity at concentration

c

* $\Lambda_m^\circ$ (Lambda naught or Lambda infinity) is the molar conductivity at infinite dilution (or zero concentration). This is the maximum possible molar conductivity, where inter-ionic interactions are negligible, and ions move freely.

* $A$ is a constant that depends on the nature of the solvent, temperature, and the type of electrolyte (e.g., 1:1, 2:1 electrolyte). It incorporates factors related to inter-ionic attraction and electrophoretic effect.

* $\sqrt{c}$ is the square root of the concentration.

A plot of $\Lambda_m$ versus $\sqrt{c}$ for strong electrolytes yields a straight line. Extrapolating this line to $\sqrt{c} = 0$ (i.e., infinite dilution) allows us to determine $\Lambda_m^\circ$ for strong electrolytes.

b) For Weak Electrolytes:

Weak electrolytes, such as acetic acid (CH $_3$ COOH) or ammonia (NH $_3$ ), dissociate only partially in solution. The degree of dissociation ( $\alpha$ ) increases significantly upon dilution. The increase in $\Lambda_m$ with dilution for weak electrolytes is primarily due to: * **Increased Degree of Dissociation ( $\alpha$ )**: According to Ostwald's Dilution Law, as a weak electrolyte solution is diluted, its degree of dissociation increases.

This means that more molecules of the electrolyte break down into ions, leading to a greater number of charge carriers in the solution. This increase in the number of ions is the dominant factor for the sharp increase in $\Lambda_m$ for weak electrolytes upon dilution.

* Increased Ionic Mobility: Similar to strong electrolytes, reduced inter-ionic attractions and viscous drag also contribute to increased ionic mobility, but this effect is secondary compared to the increase in the number of ions.

A plot of $\Lambda_m$ versus $\sqrt{c}$ for weak electrolytes does not yield a straight line. Instead, it shows a steep, non-linear increase, especially at very low concentrations, and does not extrapolate to a definite value of $\Lambda_m^\circ$ at $\sqrt{c} = 0$ .

This is because the degree of dissociation continues to increase even at very low concentrations, making it difficult to determine $\Lambda_m^\circ$ by simple extrapolation. For weak electrolytes, $\Lambda_m^\circ$ is determined using Kohlrausch's Law of Independent Migration of Ions.

\Lambda_m = \alpha \Lambda_m^\circ

where

\alpha

is the degree of dissociation. This equation highlights that the molar conductivity at any concentration is a fraction of the molar conductivity at infinite dilution, with the fraction being the degree of dissociation.

Real-World Applications

Water Purity — The conductivity of water is a direct indicator of its purity. Pure water has very low conductivity, while water with dissolved salts (ions) has higher conductivity. This principle is used in water purification systems and environmental monitoring.

Conductometric Titrations — The change in conductivity during an acid-base titration can be monitored to determine the equivalence point. For example, in the titration of a strong acid with a strong base, the conductivity initially decreases (H

^+

ions replaced by less mobile Na

^+

ions) and then increases (excess OH

^-

ions).

Characterization of Electrolytes — By studying the variation of molar conductivity with concentration, one can distinguish between strong and weak electrolytes and determine their dissociation constants.

Common Misconceptions

Confusing Specific and Molar Conductivity Trends — A common mistake is to assume that both specific and molar conductivity follow the same trend with dilution. Remember, specific conductivity decreases with dilution, while molar conductivity increases with dilution.

Assuming Complete Dissociation for Weak Electrolytes — Weak electrolytes never fully dissociate, even at infinite dilution. Their degree of dissociation approaches 1 only at infinite dilution.

Extrapolating for Weak Electrolytes — Students often try to extrapolate the

\Lambda_m

vs.

\sqrt{c}

plot for weak electrolytes to find

\Lambda_m^\circ

, which is incorrect. This method only works for strong electrolytes.

NEET-Specific Angle

For NEET, understanding the qualitative trends (increase/decrease) for both $\kappa$ and $\Lambda_m$ with dilution is crucial. Be prepared to interpret graphs of $\Lambda_m$ vs. $\sqrt{c}$ for strong and weak electrolytes.

Numerical problems often involve calculating $\Lambda_m$ using $\kappa$ and concentration, or determining the degree of dissociation ( $\alpha$ ) for weak electrolytes using $\Lambda_m$ and $\Lambda_m^\circ$ (where $\Lambda_m^\circ$ is usually given or calculated using Kohlrausch's law).

The Debye-Hückel-Onsager equation is important for strong electrolytes, particularly its graphical representation and the concept of infinite dilution. For weak electrolytes, the concept of increasing degree of dissociation with dilution and its impact on $\Lambda_m$ is key.

Key Concepts

Specific Conductivity (

\kappa

) and Dilution

Specific conductivity, $\kappa$ , is an intensive property, representing the conductance of a fixed volume of…

Molar Conductivity (

\Lambda_m

) for Strong Electrolytes

Molar conductivity, $\Lambda_m$ , considers the total conductance of one mole of electrolyte. For strong…

Molar Conductivity (

\Lambda_m

) and Degree of Dissociation for Weak Electrolytes

For weak electrolytes, the increase in $\Lambda_m$ with dilution is much more pronounced and primarily driven…

Often confused with

Side-by-side differences the NEET paper likes to test.

Variations of Conductivity with Concentration vs Strong Electrolytes vs. Weak Electrolytes (Conductivity Variation)

Aspect	Variations of Conductivity with Concentration	Strong Electrolytes vs. Weak Electrolytes (Conductivity Variation)
Specific Conductivity ($\kappa$) with Dilution	Decreases (due to reduced ion density per unit volume)	Decreases (due to reduced ion density per unit volume)
Molar Conductivity ($\Lambda_m$) with Dilution	Increases moderately (due to reduced inter-ionic attractions and increased ionic mobility)	Increases sharply (primarily due to increased degree of dissociation, producing more ions)
Plot of $\Lambda_m$ vs. $\sqrt{c}$	Linear, allows extrapolation to find $\Lambda_m^\circ$ (Debye-Hückel-Onsager equation)	Non-linear, steep curve, extrapolation not possible to find $\Lambda_m^\circ$
Primary factor for $\Lambda_m$ increase on dilution	Increased ionic mobility (reduced inter-ionic forces)	Increased degree of dissociation (more ions formed)
Degree of Dissociation ($\alpha$)	Approaches 1 (complete dissociation) even at moderate concentrations	Increases significantly with dilution, approaches 1 only at infinite dilution

While specific conductivity decreases with dilution for both strong and weak electrolytes due to reduced ion concentration per unit volume, their molar conductivity trends diverge significantly. Strong electrolytes show a moderate increase in molar conductivity with dilution, primarily due to enhanced ionic mobility as inter-ionic attractions diminish.

In contrast, weak electrolytes exhibit a much sharper increase in molar conductivity upon dilution, predominantly because their degree of dissociation increases, generating a greater number of charge-carrying ions.

This fundamental difference is also reflected in their respective $\Lambda_m$ vs. $\sqrt{c}$ plots and the methods used to determine their molar conductivity at infinite dilution.

Why it is tested: This comparison is highly relevant for NEET as it forms the basis for understanding electrolyte behavior. Questions frequently test the qualitative and quantitative differences in conductivity variations, the underlying reasons, and the applicability of laws like Debye-Hückel-Onsager and Ostwald's Dilution Law to each type of electrolyte. It's crucial for solving problems related to degree of dissociation and determining $\Lambda_m^\circ$.

Questions students ask

5 answered on this topic.

Why does specific conductivity decrease with dilution for both strong and weak electrolytes?

Specific conductivity ( $\kappa$ ) is a measure of the conductance of a unit volume of the solution. When a solution is diluted, the total number of ions remains the same, but they are spread out over a larger volume.

This means that the number of ions present in any given unit volume (e.g., 1 cm $^3$ ) decreases. Since fewer charge carriers are available in that specific volume to transport electricity, the specific conductivity of the solution decreases.

This holds true regardless of whether the electrolyte is strong or weak, as the fundamental principle of reduced ion density per unit volume applies to both.

Why does molar conductivity increase with dilution for strong electrolytes?

For strong electrolytes, which are already fully dissociated, dilution primarily affects the inter-ionic interactions. At higher concentrations, ions are closer, leading to stronger attractive forces between oppositely charged ions.

These forces hinder their movement. Upon dilution, ions move further apart, reducing these inter-ionic attractions and increasing their effective mobility. Additionally, the viscous drag on ions decreases in a more dilute solution.

The combined effect of increased ionic mobility and reduced hindrance outweighs the decrease in ion density per unit volume, leading to an overall increase in molar conductivity.

Why does molar conductivity increase significantly with dilution for weak electrolytes?

The primary reason for the significant increase in molar conductivity ( $\Lambda_m$ ) for weak electrolytes upon dilution is the increase in their degree of dissociation ( $\alpha$ ). Weak electrolytes only partially dissociate into ions.

According to Ostwald's Dilution Law, as the solution is diluted, the equilibrium shifts to favor more dissociation, producing a greater number of ions. Since molar conductivity is directly proportional to the number of ions produced by one mole of electrolyte, this increase in ion count leads to a sharp rise in $\Lambda_m$ .

Increased ionic mobility due to reduced inter-ionic attractions also plays a role, but the increase in the number of charge carriers is the dominant factor.

What is the significance of molar conductivity at infinite dilution ($\Lambda_m^\circ$)?

Molar conductivity at infinite dilution ( $\Lambda_m^\circ$ ) represents the maximum possible molar conductivity an electrolyte can achieve. At infinite dilution, inter-ionic attractions become negligible, and ions move completely independently of each other.

For strong electrolytes, $\Lambda_m^\circ$ can be determined by extrapolating the $\Lambda_m$ vs. $\sqrt{c}$ plot. For weak electrolytes, it cannot be found by extrapolation but is crucial for calculating the degree of dissociation and dissociation constant using Kohlrausch's Law.

It provides a benchmark for the intrinsic conducting ability of an electrolyte's ions.

How is the degree of dissociation ($\alpha$) related to molar conductivity for weak electrolytes?

For weak electrolytes, the degree of dissociation ( $\alpha$ ) is directly related to its molar conductivity. The ratio of the molar conductivity at a given concentration ( $\Lambda_m$ ) to the molar conductivity at infinite dilution ( $\Lambda_m^\circ$ ) gives the degree of dissociation.

The formula is $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$ . This relationship is extremely useful because it allows us to calculate how much of a weak electrolyte has dissociated into ions at a particular concentration, provided we know its molar conductivity at that concentration and its molar conductivity at infinite dilution (which can be determined using Kohlrausch's Law).

Revise in 30 seconds

Specific Conductivity ($\kappa$) — Conductance of unit volume. Unit: S cm

^{-1}

Trend with Dilution —

\kappa

decreases for both strong & weak electrolytes (fewer ions per unit volume).

Molar Conductivity ($\Lambda_m$) — Conductance of 1 mole electrolyte. Unit: S cm

^2

mol

^{-1}

Trend with Dilution —

\Lambda_m

increases for both strong & weak electrolytes.

Strong Electrolytes —

\Lambda_m

increases moderately due to reduced inter-ionic attractions. Follows Debye-Hückel-Onsager:

\Lambda_m = \Lambda_m^\circ - A\sqrt{c}

. Plot

\Lambda_m

vs.

\sqrt{c}

is linear.

Weak Electrolytes —

\Lambda_m

increases sharply due to increased degree of dissociation (

\alpha

). Plot

\Lambda_m

vs.

\sqrt{c}

is non-linear.

Degree of Dissociation ($\alpha$) — For weak electrolytes,

\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}

\alpha

increases with dilution.

Specific Conductivity Decreases, Molar Conductivity Increases (with dilution). Strong Electrolytes are Linear, Weak Electrolytes Sharp (on $\Lambda_m$ vs. $\sqrt{c}$ plot). Weak Dissociate More (on dilution).