Question

What is Kohlrausch's law? If \( \lambda^{\circ}_m \) for NaCl, HCl and NaAc are 126.4, 425.9 and 91.0 S cm² mol^-1 respectively, find the value of \( \lambda^{\circ}_m \) for HAc. (2+2)

Hint:

Kohlrausch's law: at infinite dilution \( \lambda^{\circ}_m \) is the sum of independent ionic conductivities. Combine the salts as \( \lambda^{\circ}_m(\text{HAc}) = \lambda^{\circ}_m(\text{HCl}) + \lambda^{\circ}_m(\text{NaAc}) - \lambda^{\circ}_m(\text{NaCl}) \).

Answer 1

Part 1: Kohlrausch's law
Statement: Kohlrausch's law of independent migration of ions states that, at infinite dilution (when dissociation is complete), the limiting molar conductivity of an electrolyte is the sum of the individual contributions of its cation and anion, each ion migrating independently of the other.
\[ \lambda^{\circ}_m = \nu_+\,\lambda^{\circ}_+ + \nu_-\,\lambda^{\circ}_- \]
where \( \nu_+ \) and \( \nu_- \) are the numbers of cations and anions per formula unit, and \( \lambda^{\circ}_+ \), \( \lambda^{\circ}_- \) are their limiting ionic molar conductivities.

Part 2: Calculation for HAc (acetic acid)
Step 1 (Set up the ion balance): Write each salt as its ions.
\[ \lambda^{\circ}_m(\text{HCl}) = \lambda^{\circ}_{H^+} + \lambda^{\circ}_{Cl^-} \]
\[ \lambda^{\circ}_m(\text{NaAc}) = \lambda^{\circ}_{Na^+} + \lambda^{\circ}_{Ac^-} \]
\[ \lambda^{\circ}_m(\text{NaCl}) = \lambda^{\circ}_{Na^+} + \lambda^{\circ}_{Cl^-} \]
Step 2 (Combine to eliminate the spectator ions): Add HCl and NaAc, then subtract NaCl. The Na⁺ and Cl^- cancel, leaving H⁺ and Ac^-, which is exactly HAc:
\[ \lambda^{\circ}_m(\text{HAc}) = \lambda^{\circ}_m(\text{HCl}) + \lambda^{\circ}_m(\text{NaAc}) - \lambda^{\circ}_m(\text{NaCl}) \]
Step 3 (Substitute the data):
\[ \lambda^{\circ}_m(\text{HAc}) = 425.9 + 91.0 - 126.4 \]
Step 4 (Arithmetic):
\[ = 516.9 - 126.4 = 390.5\ \text{S cm}^2\text{mol}^{-1} \]
\[ \boxed{\lambda^{\circ}_m(\text{HAc}) = 390.5\ \text{S cm}^2\text{mol}^{-1}} \]
This value is found indirectly because acetic acid is a weak electrolyte and its \( \lambda^{\circ}_m \) cannot be obtained by direct extrapolation.