Conductance Of Electrolytic Solutions

Conductivity: The ability of a solution to conduct electric current is called conductivity. This ability is due to the presence of ions in the solution.

Electrolytes: Substances that produce ions when dissolved in a solvent (usually water) and thus conduct electricity are called electrolytes. They can be strong electrolytes (dissociate completely) or weak electrolytes (dissociate partially).

Factors Affecting Conductivity:

Nature of the Electrolyte: Strong electrolytes conduct better than weak electrolytes.
Concentration of Ions: Higher concentration of ions generally leads to higher conductivity.
Temperature: Conductivity generally increases with temperature because the kinetic energy of ions increases, leading to more frequent and energetic collisions, and often increased dissociation for weak electrolytes.
Nature of the Solvent: The solvent's ability to dissolve the electrolyte and solvate the ions affects conductivity.
Mobility of Ions: Ions that are smaller and have weaker intermolecular forces tend to have higher mobility and contribute more to conductivity.

Measurement Of The Conductivity Of Ionic Solutions

Resistance (R): The opposition to the flow of electric current. Measured in Ohms ($\Omega$).

Conductance (G): The reciprocal of resistance. It is a measure of how easily current flows.

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

Units: Siemens (S) or ohm$^{-1}$ ($\Omega^{-1}$).

Cell Constant (l/A): The ratio of the distance between the electrodes ($l$) to the area of the electrodes ($A$). Its units are typically $m^{-1}$ or $cm^{-1}$.

Conductivity ($\kappa$): The fundamental property of the solution, independent of the cell dimensions. It is defined as the conductance of a solution contained in a cell with unit length and unit cross-sectional area.

$$ \kappa = G \times \frac{l}{A} $$

Units: Siemens per meter (S/m) or Siemens per centimeter (S/cm).

Conductivity Meter: Conductivity is measured using a conductivity meter. This instrument typically uses two electrodes immersed in the solution. An alternating current (AC) is applied to avoid polarization effects (build-up of ions at the electrodes). The resistance of the solution is measured, and the conductivity is calculated using the cell constant.

Conductance Bridge: A Wheatstone bridge circuit is often used for accurate measurement of resistance.

Measurement Steps:

A conductivity cell with a known cell constant is used.
The cell is cleaned and dried.
The conductivity meter is calibrated using standard solutions of known conductivity.
The conductivity cell is immersed in the solution to be measured.
The resistance ($R$) is measured.
Conductivity ($\kappa$) is calculated using $\kappa = \frac{1}{R} \times \text{cell constant}$.

Variation Of Conductivity And Molar Conductivity With Concentration

1. Conductivity ($\kappa$):

Trend: Conductivity generally increases with an increase in the concentration of the electrolyte.

Reason: As the concentration of ions in the solution increases, there are more charge carriers available to conduct electricity, leading to higher conductivity.

2. Molar Conductivity ($\Lambda_m$):

Definition: Molar conductivity is the conductivity of an electrolyte solution divided by the molar concentration of the electrolyte. It represents the efficiency of ion transport per mole of electrolyte.

$$\Lambda_m = \frac{\kappa}{C}$$

Where:

$\Lambda_m$ is the molar conductivity (Units: S m$^2$ mol$^{-1}$ or S cm$^2$ mol$^{-1}$).
$\kappa$ is the conductivity.
$C$ is the molar concentration of the electrolyte.

Variation of Molar Conductivity with Concentration:

Strong Electrolytes: Molar conductivity ($\Lambda_m$) increases with increasing concentration, but the rate of increase slows down at higher concentrations. This is because while the number of ions increases, the inter-ionic attraction and solvation effects become more pronounced, hindering ion mobility. However, the effect of increasing ion number dominates initially.

Kohlrausch's Law: For strong electrolytes, the molar conductivity at infinite dilution ($\Lambda_m^\circ$) can be extrapolated. Kohlrausch's law states that at infinite dilution, the molar conductivity of an electrolyte is the sum of the contributions of its individual ions, each moving independently.

$\Lambda_m = \Lambda_m^\circ - A\sqrt{C}$

Where $A$ is a constant dependent on the electrolyte and solvent, and $\Lambda_m^\circ$ is the molar conductivity at infinite dilution.

Weak Electrolytes: Molar conductivity ($\Lambda_m$) increases sharply with increasing concentration, especially at low concentrations. This is because weak electrolytes are only partially ionized at low concentrations. As concentration increases, the degree of ionization increases (due to the common ion effect being less dominant at very low concentrations), leading to a higher molar conductivity. The curve for weak electrolytes is much steeper than for strong electrolytes.

Molar Conductivity at Infinite Dilution ($\Lambda_m^\circ$): This is the hypothetical molar conductivity of an electrolyte if it were completely dissociated and the ions moved independently, with no inter-ionic interactions. It can be determined by extrapolation from conductivity data at low concentrations for strong electrolytes or by using Kohlrausch's law with data from other electrolytes.