[Single-digit Integer] A dilute solution of was placed between two platinum electrodes, 12 cm apart, — Electrochemistry Chemistry Question

💡 Solution & Explanation

\textbf{Step 1: Find ionic mobility of K⁺.} \[ u(\text{K}^+) = \frac{\lambda^\circ(\text{K}^+)}{F} = \frac{7.5 \times 10^{-3}\ \text{mho m}^2\text{mol}^{-1}}{96500\ \text{C mol}^{-1}} = 7.77 \times 10^{-8}\ \text{m}^2\text{V}^{-1}\text{s}^{-1} \] Converting to cm$^2$ V$^{-1}$ s$^{-1}$: $\times 10^4$: \[ u = 7.77 \times 10^{-4}\ \text{cm}^2\text{V}^{-1}\text{s}^{-1} \] \textbf{Step 2: Find electric field.} \[ \mathcal{E} = \frac{V}{d} = \frac{1.93}{12} = 0.1608\ \text{V cm}^{-1} \] \textbf{Step 3: Find drift velocity of K⁺.} \[ v = u \times \mathcal{E} = 7.77 \times 10^{-4} \times 0.1608 = 1.25 \times 10^{-4}\ \text{cm s}^{-1} \] \textbf{Step 4: Find distance in 20 h.} \[ t = 20 \times 3600 = 72000\ \text{s} \] \[ d = v \times t = 1.25 \times 10^{-4} \times 72000 = \boxed{9.0\ \text{cm}} \]