Question #44787

A liquid junction is formed between Solution I ($10^{-3}\text{ M } \ce{KCl}$) and Solution II ($3.0\text{ M } \ce{KCl}$) at $298\text{ K}$. A student calculates the expected Liquid Junction Potential ($E_{LJP, \text{ideal}}$) assuming Kohlrausch's law of independent migration holds, using limiting molar conductivities: $\lambda^\infty_{\ce{K^+}} = 73.5\text{ S cm}^2\text{ mol}^{-1}$ and $\lambda^\infty_{\ce{Cl^-}} = 76.5\text{ S cm}^2\text{ mol}^{-1}$.

However, in the highly concentrated Solution II, Debye-Hückel-Onsager relaxation and electrophoretic effects severely retard the $\ce{K^+}$ ion. Consequently, the actual average transference number of $\ce{K^+}$ across the junction drops to $\bar{t}_+ = 0.40$.

Given the ratio of mean ionic activities $a_{II}/a_I = 10^3$ and $\frac{2.303 RT}{F} = 0.06\text{ V}$, calculate the magnitude of the unexpected shift in the liquid junction potential, $\Delta E = |E_{LJP, \text{actual}} - E_{LJP, \text{ideal}}|$.