Kohlrausch's Law, a fundamental principle in electrochemistry, describes how the conductivity of electrolyte solutions behaves at infinite dilution.
Understanding Kohlrausch's Law
Kohlrausch's law, also known as the Law of Independent Migration of Ions, states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations in the electrolyte at constant concentration. This law is most applicable when an electrolyte is diluted to the point where the ions are so far apart they do not interact with each other.
Key Concepts
- Equivalent Conductivity: This refers to the conductivity of a solution containing one gram equivalent of an electrolyte.
- Infinite Dilution: This theoretical state occurs when an electrolyte is dissolved in a very large amount of solvent, effectively minimizing interactions between ions.
- Independent Migration: At infinite dilution, each ion behaves independently and its contribution to the overall conductivity of the solution is solely based on its own inherent ionic conductance.
Mathematical Representation
Kohlrausch's law can be mathematically expressed as:
λm∞ = ν+λ+ + ν-λ-
Where:
- λm∞ represents the molar conductivity of the electrolyte at infinite dilution
- λ+ represents the ionic conductivity of the cation at infinite dilution
- λ- represents the ionic conductivity of the anion at infinite dilution
- ν+ is the number of cations per formula unit of the electrolyte
- ν- is the number of anions per formula unit of the electrolyte
Practical Applications
- Determining Ionic Conductivities: It helps in determining the limiting molar conductivities of individual ions. These values can be used to calculate the conductivity of any solution made of these ions.
- Calculating Dissociation Constants: By using the law it is possible to determine the degree of dissociation of weak electrolytes.
- Understanding Electrolyte Behavior: The law gives insights into how different electrolytes behave in solution.
Examples
Let's take the example of Sodium Chloride (NaCl). According to Kohlrausch's law:
λm∞(NaCl) = λ∞(Na+) + λ∞(Cl-)
This equation implies that the molar conductivity of NaCl at infinite dilution equals the sum of the molar conductivities of the Na+ and Cl- ions at infinite dilution.
- For example, if you know the values of λ∞(Na+) and λ∞(Cl-), you can calculate the molar conductivity of NaCl at infinite dilution.
- Similarly, it allows the determination of molar conductivity of weak electrolytes where it cannot be easily determined through extrapolation.
- In practical measurements, the values of ionic conductivities at infinite dilutions for strong electrolytes can be determined experimentally and then used for calculations involving weaker ones.
Table: Ionic Conductivities
| Ion | Conductivity at Infinite Dilution (S cm2 mol-1) |
|---|---|
| H+ | 349.6 |
| Na+ | 50.1 |
| K+ | 73.5 |
| Cl- | 76.3 |
| OH- | 198.0 |
Conclusion
Kohlrausch's law is an important tool in electrochemistry to understand the behavior of ions in electrolyte solutions, particularly in the context of infinite dilution. It allows for the determination of ionic conductivities and dissociation constants, which are crucial in various applications.
