For a specific weak monobasic acid, the limiting molar conductivity at infinite dilution is 4.00×10−2 ohm−1m2mol−1.
The limiting molar conductivity of an electrolyte represents its maximum conductivity when completely dissociated and at infinite dilution. For weak acids, this value is particularly important as their observed molar conductivity at practical concentrations is significantly lower due to incomplete dissociation.
Understanding Limiting Molar Conductivity ($\Lambda_m^0$)
Molar conductivity ($\Lambda_m$) is a measure of the conducting power of all the ions produced by one mole of an electrolyte in a solution. As a solution is diluted, the molar conductivity generally increases because interionic attractions decrease, allowing ions to move more freely. For weak electrolytes like weak acids, dilution also increases the degree of dissociation, leading to a much sharper increase in molar conductivity compared to strong electrolytes.
The limiting molar conductivity at infinite dilution ($\Lambda_m^0$) is the theoretical maximum conductivity reached when the electrolyte is completely dissociated and the ions are so far apart that interionic interactions are negligible. It is an intrinsic property of the electrolyte's ions.
According to Kohlrausch's Law of Independent Migration of Ions, the limiting molar conductivity of an electrolyte is the sum of the limiting ionic conductivities of its constituent cations and anions. For a weak acid (HA), this would be:
$\Lambda_m^0 (\text{HA}) = \lambda_m^0 (\text{H}^+) + \lambda_m^0 (\text{A}^-)$
where $\lambda_m^0 (\text{H}^+)$ is the limiting molar conductivity of the hydrogen ion and $\lambda_m^0 (\text{A}^-)$ is that of the conjugate base anion. To learn more about this principle, you can explore resources on Kohlrausch's Law.
A Specific Example for a Weak Acid
As an illustrative example, for a particular weak monobasic acid, its limiting molar conductivity at infinite dilution has been determined to be 4.00×10−2 ohm−1m2mol−1. This same weak acid demonstrates characteristics typical of weak electrolytes, being only 5% dissociated in a 0.01 mol dm−3 solution, highlighting the significant difference between its observed conductivity at a given concentration and its maximum possible conductivity.
Factors Influencing Limiting Molar Conductivity
Several factors can influence the limiting molar conductivity of an electrolyte:
- Nature of the Ions: This includes the size, charge, and the extent of solvation (hydration) of the ions. Smaller, less solvated ions with higher charges generally have higher limiting ionic conductivities due to greater mobility. For instance, H$^+$ ions have exceptionally high mobility.
- Temperature: Increasing temperature generally increases the kinetic energy of ions, leading to higher mobility and thus higher limiting molar conductivity.
- Viscosity of Solvent: A less viscous solvent allows ions to move more freely, resulting in higher limiting molar conductivity.
Importance and Applications
Understanding the limiting molar conductivity of weak acids is crucial for several chemical and practical applications:
- Determining Dissociation Constants (Ka): The degree of dissociation ($\alpha$) for a weak electrolyte can be calculated using the ratio of its observed molar conductivity ($\Lambda_m$) at a specific concentration to its limiting molar conductivity ($\Lambda_m^0$): $\alpha = \Lambda_m / \Lambda_m^0$. This degree of dissociation is then used to calculate the acid dissociation constant (Ka), a fundamental property of weak acids.
- Characterizing Electrolytes: It provides a method to characterize the intrinsic conducting ability of the ions of a specific acid, independent of concentration effects.
- Analytical Chemistry: Conductivity measurements, relying on the principles of molar conductivity, are used in various analytical techniques for determining the concentration of ions in solutions.
The table below summarizes the conceptual components of limiting molar conductivity:
| Component | Description | Impact on $\Lambda_m^0$ |
|---|---|---|
| Cation ($\text{H}^+$) | Limiting ionic conductivity of the hydrogen ion. Highly mobile. | Significant Contribution |
| Anion ($\text{A}^-$) | Limiting ionic conductivity of the conjugate base anion. Varies by acid. | Varies by Acid |
| Weak Acid ($\text{HA}$) | Sum of $\lambda_m^0 (\text{H}^+) + \lambda_m^0 (\text{A}^-)$ at infinite dilution. | Total Intrinsic Value |
