Variations of Conductivity with Concentration — Revision Notes

⚡ 30-Second Revision

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.

2-Minute Revision

The conductivity of an electrolytic solution changes significantly with concentration. We consider two main types: specific conductivity ($kappa$) and molar conductivity ($Lambda_m$). Specific conductivity, which is the conductance of a unit volume of solution, always decreases upon dilution for both strong and weak electrolytes. This is because diluting the solution reduces the number of ions present in that fixed unit volume.

Molar conductivity, on the other hand, always increases upon dilution for both strong and weak electrolytes, but for different reasons. For strong electrolytes, which are already fully dissociated, the increase is moderate and primarily due to reduced inter-ionic attractions and increased ionic mobility as ions move further apart.

This behavior is described by the linear Debye-Hückel-Onsager equation. For weak electrolytes, the increase in molar conductivity is much sharper and is predominantly caused by an increase in the degree of dissociation ($alpha$) upon dilution, leading to a greater number of charge-carrying ions.

The degree of dissociation can be calculated as the ratio of molar conductivity at a given concentration to that at infinite dilution ($\alpha = \Lambda_m / \Lambda_m^\circ$). Understanding these distinct trends and their underlying reasons is crucial for NEET.

5-Minute Revision

Variations of conductivity with concentration are a core concept in electrochemistry. We differentiate between specific conductivity ($kappa$) and molar conductivity ($Lambda_m$).

**Specific Conductivity ($kappa$)**: This measures the conductance of a fixed unit volume (e.g., 1 cm$^3$) of the solution. For *both* strong and weak electrolytes, $kappa$ decreases with dilution.

The reason is simple: when you add more solvent, the total number of ions remains constant (for a given amount of electrolyte), but they are spread over a larger volume. Thus, the number of ions in any given 1 cm$^3$ volume decreases, leading to lower specific conductivity.

For example, if a 0.1 M KCl solution has $\kappa = 0.0129$ S cm$^{-1}$, a 0.01 M KCl solution will have $\kappa = 0.00141$ S cm$^{-1}$.

**Molar Conductivity ($Lambda_m$)**: This measures the total conductance produced by one mole of an electrolyte. For *both* strong and weak electrolytes, $Lambda_m$ increases with dilution, but the mechanisms differ.

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Strong Electrolytes — These dissociate completely. The number of ions from one mole is constant. The increase in $Lambda_m$ with dilution is moderate and primarily due to:

* Reduced Inter-ionic Attractions: Ions are further apart, reducing electrostatic forces that hinder their movement. * Increased Ionic Mobility: Ions move more freely and faster. This relationship is described by the Debye-Hückel-Onsager equation: $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$.

A plot of $Lambda_m$ vs. $sqrt{c}$ is linear, allowing extrapolation to find $Lambda_m^\circ$ (molar conductivity at infinite dilution). * *Example*: If $\Lambda_m$ for 0.1 M KCl is $129$ S cm$^2$ mol$^{-1}$, for 0.

01 M KCl it might be $141$ S cm$^2$ mol$^{-1}$.

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Weak Electrolytes — These dissociate partially. The increase in $Lambda_m$ with dilution is sharp and primarily due to:

* **Increased Degree of Dissociation ($alpha$)**: According to Ostwald's Dilution Law, dilution shifts the dissociation equilibrium to produce more ions from the undissociated molecules. This significantly increases the number of charge carriers.

* The degree of dissociation is given by $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$. A plot of $Lambda_m$ vs. $sqrt{c}$ is non-linear and steep, making extrapolation to find $Lambda_m^\circ$ impossible.

$Lambda_m^\circ$ for weak electrolytes is determined using Kohlrausch's Law. * *Example*: For 0.1 M acetic acid, $\Lambda_m = 5.2$ S cm$^2$ mol$^{-1}$. If $\Lambda_m^\circ = 390.5$ S cm$^2$ mol$^{-1}$, then $\alpha = 5.

2/390.5 \approx 0.013$. Upon dilution to 0.01 M,$\Lambda_m$might increase to$16.2$S cm$^2$mol$^{-1}$, and$\alpha$to$16.2/390.5 \approx 0.041$. The increase in$alpha$ is substantial.

Key Formulas: $\Lambda_m = \frac{\kappa \times 1000}{c}$ (for $kappa$ in S cm$^{-1}$, $c$ in mol L$^{-1}$); $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$.

Remember the contrasting trends and the specific reasons for each, especially for NEET conceptual questions and numerical problems.

Prelims Revision Notes

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Specific Conductivity ($kappa$) — Conductance of a unit volume (1 cm$^3$) of solution. Unit: S cm$^{-1}$ or S m$^{-1}$.

* Trend with Dilution: Always decreases for both strong and weak electrolytes. * Reason: Number of ions per unit volume decreases upon dilution.

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Molar Conductivity ($Lambda_m$) — Conductance of the volume containing one mole of electrolyte. Unit: S cm$^2$ mol$^{-1}$ or S m$^2$ mol$^{-1}$.

* Formula: $\Lambda_m = \frac{\kappa \times 1000}{c}$ (if $kappa$ in S cm$^{-1}$, $c$ in mol L$^{-1}$). Or $\Lambda_m = \frac{\kappa}{c}$ (if $kappa$ in S m$^{-1}$, $c$ in mol m$^{-3}$). Note: 1 M = 1 mol L$^{-1}$ = 1000 mol m$^{-3}$. * Trend with Dilution: Always increases for both strong and weak electrolytes.

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Strong Electrolytes (e.g., NaCl, HCl)

* Dissociation: Almost complete dissociation into ions. * **$Lambda_m$ Trend: Increases moderately** with dilution. * Reason: Reduced inter-ionic attractions and increased ionic mobility as ions move further apart. * Debye-Hückel-Onsager Equation: $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$. * **Plot of $Lambda_m$ vs. $sqrt{c}$**: Linear, allows extrapolation to find $Lambda_m^\circ$ (molar conductivity at infinite dilution).

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Weak Electrolytes (e.g., CH$_3$COOH, NH$_4$OH)

* Dissociation: Partial dissociation; exists in equilibrium. * **$Lambda_m$ Trend: Increases sharply** with dilution. * Reason: Primarily due to a significant increase in the **degree of dissociation ($alpha$)** (Ostwald's Dilution Law), leading to more ions.

* Degree of Dissociation: $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$. * **Plot of $Lambda_m$ vs. $sqrt{c}$**: Non-linear, steep curve; extrapolation to find $Lambda_m^\circ$ is not possible. * **$Lambda_m^\circ$ for Weak Electrolytes**: Determined using Kohlrausch's Law of Independent Migration of Ions.

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Infinite Dilution ($Lambda_m^\circ$) — Maximum molar conductivity where inter-ionic interactions are negligible.

Key Points for NEET:

Qualitative trends of $kappa$ and $Lambda_m$ with dilution.
Distinguishing reasons for $Lambda_m$ increase in strong vs. weak electrolytes.
Graphical interpretation of $Lambda_m$ vs. $sqrt{c}$ plots.
Numerical calculations involving $kappa$, $Lambda_m$, $c$, and $alpha$.

Vyyuha Quick Recall

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).