During the high-temperature industrial electrolysis of molten (fused) sodium chloride (), the time s — Electrochemistry Chemistry Question
Question
During the high-temperature industrial electrolysis of molten (fused) sodium chloride ($NaCl$), the time strictly required to produce exactly $0.10\text{ moles}$ of pure chlorine gas ($Cl_2$) at the anode using a constant steady current of $3.0\text{ A}$ is $x$ minutes. What is the value of $x$ rounded to the nearest integer? (Use Faraday's Constant $1\text{ F} = 96500\text{ C}$)
💡 Solution & Explanation
The balanced anodic oxidation half-reaction is $2Cl^- \rightarrow Cl_2 + 2e^-$. Thus, 1 mole of $Cl_2$ rigorously requires 2 moles of electrons. $0.10$ moles of $Cl_2$ requires $0.20$ moles of electrons. Total charge required $Q = 0.20\text{ mol} \times 96500\text{ C/mol} = 19300\text{ C}$. Given $I = 3.0\text{ A}$, time $t = Q / I = 19300 / 3.0 = 6433.33\text{ seconds}$. Converting to minutes: $6433.33 / 60 = 107.22\text{ minutes}$. Rounded to the nearest integer, $x = 107$.