The correct answer is Option (3) → (A), (B), (C) and (D)
Kohlrausch's law states that at infinite dilution (or limiting molar conductivity, $\Lambda_m^\circ$), each ion contributes a definite amount to the total molar conductivity of the electrolyte, irrespective of the nature of the other ion.
$\Lambda_m^\circ = \lambda^\circ_{+} + \lambda^\circ_{-}$
Where $\Lambda_m^\circ$ is the limiting molar conductivity, and $\lambda^\circ_{+}$ and $\lambda^\circ_{-}$ are the limiting ionic conductivities of the cation and anion, respectively.
This law is applied to determine several properties:
(A) Molar conductivity of a weak electrolyte
- Since the $\Lambda_m$ of a weak electrolyte cannot be accurately determined by extrapolation of the $\Lambda_m$ vs. $\sqrt{C}$ plot, Kohlrausch's law is used.
- The $\Lambda_m^\circ$ of a weak electrolyte (e.g., $\text{CH}_3\text{COOH}$) can be calculated from the $\Lambda_m^\circ$ values of three strong electrolytes (e.g., $\text{HCl}$, $\text{NaCl}$, and $\text{CH}_3\text{COONa}$).
$\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$
(B) Degree of dissociation of a weak electrolyte
- The degree of dissociation ($\alpha$) of a weak electrolyte at a given concentration ($C$) can be calculated using the ratio of its molar conductivity ($\Lambda_m$) at that concentration to its limiting molar conductivity ($\Lambda_m^\circ$):
$\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$
- Since $\Lambda_m^\circ$ is calculated using Kohlrausch's law, $\alpha$ is determined indirectly using this law.
- Once the degree of dissociation ($\alpha$) is known, the dissociation constant ($K_a$) for a weak electrolyte (like a weak acid, $\text{HA}$) can be calculated using Ostwald's dilution law:
(C) Dissociation constant
$K_a = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 \quad (\text{if } \alpha \text{ is small})$
- Thus, the dissociation constant is determined using the results obtained from Kohlrausch's law.
- Sparingly soluble salts (like $\text{AgCl}$ or $\text{BaSO}_4$) are considered strong electrolytes at saturation, which is essentially infinite dilution since their concentration is very low.
- Therefore, the molar conductivity at saturation ($\Lambda_m$) is taken as $\Lambda_m^\circ$.
- The conductivity ($\kappa$) of the saturated solution is measured, and the solubility ($S$, which is the concentration $C$ at saturation) can be calculated:
(D) Solubility of sparingly soluble salts
- Sparingly soluble salts (like $\text{AgCl}$ or $\text{BaSO}_4$) are considered strong electrolytes at saturation, which is essentially infinite dilution since their concentration is very low.
- Therefore, the molar conductivity at saturation ($\Lambda_m$) is taken as $\Lambda_m^\circ$.
- The conductivity ($\kappa$) of the saturated solution is measured, and the solubility ($S$, which is the concentration $C$ at saturation) can be calculated:
$\Lambda_m^\circ = \frac{\kappa \times 1000}{S}⇒S = \frac{\kappa \times 1000}{\Lambda_m^\circ}$
- $\Lambda_m^\circ$ is determined by summing the $\lambda^\circ$ values for the ions of the salt using Kohlrausch's law.
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