A chemist wants to produce Cl2(g) by the electrolysis of molten NaCl. What mass of Cl2 is produced if a steady current of 2 A is passed for 2.5 minutes? (1 F = 96500 C mol−1; molar mass of Cl2 = 71 g mol−1)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.110 g
By Faraday’s first law, the amount of product is proportional to the charge passed (Q = I × t). At the anode, chloride ions of the molten salt are oxidised:
\( \displaystyle \ce{2Cl^- -> Cl2(g) + 2e^-} \)
So 1 mol of \( \ce{Cl2} \) needs 2 mol of electrons (2 F).
Charge passed (t = 2.5 min = 150 s):
\( \displaystyle Q=I\times t=2\,\mathrm{A}\times150\,\mathrm{s}=300\,\mathrm{C} \)
Moles of electrons:
\( \displaystyle n_{e^-}=\frac{300\,\mathrm{C}}{96500\,\mathrm{C\,mol^{-1}}}=3.11\times10^{-3}\,\mathrm{mol} \)
Moles of \( \ce{Cl2} \):
\( \displaystyle n_{\ce{Cl2}}=\frac{3.11\times10^{-3}}{2}=1.55\times10^{-3}\,\mathrm{mol} \)
Mass of \( \ce{Cl2} \):
\( \displaystyle m=1.55\times10^{-3}\,\mathrm{mol}\times71\,\mathrm{g\,mol^{-1}}=0.110\,\mathrm{g} \)