Q.In a plot of against the square root of concentration () for strong and weak electrolyte, the value of limiting molar conductivity of a weak electrolyte cannot be obtained graphically. Suggest a way to obtain this value. Also state the related law, if any.
The limiting molar conductivity of a weak electrolyte cannot be found by direct extrapolation of its vs. plot because the curve is steep and nonlinear. Instead, we use Kohlrausch’s law of independent migration of ions: add the known limiting molar conductivities of the constituent ions (obtained from strong electrolytes) to get the weak electrolyte’s .
Why the graph fails for weak electrolytes
For a strong electrolyte, decreases linearly with at low concentrations (Kohlrausch’s empirical law). You can extrapolate that straight line back to to read directly from the intercept.
For a weak electrolyte (like acetic acid), the plot is completely different. As you dilute the solution, dissociation increases sharply — so rises steeply at very low concentrations. The curve never becomes linear near , and you cannot reliably extend it to the vertical axis. Any graphical extrapolation would give a value far below the true .
A common mistake is to try drawing a tangent or fitting a straight line to the weak electrolyte’s data. The plot is not linear at any concentration — the curvature is severe because dissociation changes rapidly with dilution. Extrapolation here is guesswork, not science.
The way forward: Kohlrausch’s law
The solution is to avoid the graph entirely and use a theoretical law that works for all electrolytes.
Kohlrausch’s law of independent migration of ions
where and are the numbers of cations and anions per formula unit, and , are their limiting molar conductivities (at infinite dilution).
The key insight: at infinite dilution, each ion moves independently of its counterion. So the total conductivity is simply the sum of the contributions from each ion — no matter which electrolyte the ion came from.
Step-by-step method
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Identify the ions of the weak electrolyte.
For example, acetic acid () dissociates into and .
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Find the limiting molar conductivities of these ions from strong electrolytes that are fully dissociated.
- is obtained from a strong acid like HCl:
Since $\Lambda_m^0(\text{HCl})$ and $\lambda^0(\text{Cl}^-)$ are known from experiments, you solve for $\lambda^0(\text{H}^+)$.
- is obtained from a strong salt like sodium acetate ():
Again, $\Lambda_m^0$ of the salt and $\lambda^0(\text{Na}^+)$ are known, so $\lambda^0(\text{CH}_3\text{COO}^-)$ is found.
3. Add the ionic contributions for the weak electrolyte:
You never need to measure the weak electrolyte itself at infinite dilution. The ionic values are tabulated for common ions — once you have them, you can compute for any weak electrolyte by simple addition. This is the power of Kohlrausch’s law.
The law stated
The related law is Kohlrausch’s law of independent migration of ions (1900). It states that at infinite dilution, each ion contributes a fixed amount to the molar conductivity of an electrolyte, independent of the other ion present. Mathematically:
where runs over all ions in the formula unit.
This law is exact at infinite dilution. It fails at finite concentrations because ion-ion interactions become significant — but for the limiting value, it is the only reliable method for weak electrolytes.
The limiting molar conductivity of a weak electrolyte is obtained by applying Kohlrausch’s law: add the known limiting molar conductivities of its constituent ions, which are determined from strong electrolytes. The value is .
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