Electrolytic cells and electrolysis Knowledge-Based Study

Study notes

1. An electrolytic cell is an electrochemical system that uses electrical energy from an external direct current (DC) power source to drive a non-spontaneous chemical reaction ($\Delta G > 0$). This process of chemical decomposition induced by an electric current is known as electrolysis.

   Unlike galvanic (voltaic) cells, which convert chemical potential energy into electrical energy spontaneously, electrolytic cells require an input of voltage greater than the opposing cell potential to force electrons in the reverse direction.

   An electrolytic cell consists of three primary components:

   • Power Source: A DC supply (such as a battery) that pumps electrons onto one electrode and pulls them away from the other.
   • Electrodes: Conductors, usually inert materials such as platinum ($\text{Pt}$) or graphite ($\text{C}$), submerged in the electrolyte.
   • Electrolyte: A molten ionic salt or an aqueous solution containing mobile ions that conduct charge through the bulk liquid.

   The conventions for electrode designation in an electrolytic cell are:

   • Anode: Connected to the positive terminal of the power supply. Oxidation occurs here: electrons are removed from species in the electrolyte. Hence, the anode is positively charged ($+$).
   • Cathode: Connected to the negative terminal of the power supply. Reduction occurs here: electrons are delivered to species in the electrolyte. Hence, the cathode is negatively charged ($-$).

   Mnemonic: Oxidation always occurs at the Anode (An Ox), and Reduction always occurs at the Cathode (Red Cat), regardless of whether the cell is galvanic or electrolytic.

   In a molten ionic liquid, only two types of ions are present: cations and anions. There is no water to compete at the electrodes.

   Consider the electrolysis of molten sodium chloride ($\text{NaCl}$):

   • Cathode (Reduction): $2\text{Na}^+(\text{l}) + 2e^- \rightarrow 2\text{Na}(\text{l})$
   • Anode (Oxidation): $2\text{Cl}^-(\text{l}) \rightarrow \text{Cl}_2(\text{g}) + 2e^-$
   • Overall Reaction: $2\text{NaCl}(\text{l}) \rightarrow 2\text{Na}(\text{l}) + \text{Cl}_2(\text{g})$

   Liquid sodium metal forms at the negative cathode, while chlorine gas bubbles evolve at the positive anode.

   When an aqueous salt solution is electrolyzed, water molecules can also be oxidized or reduced, leading to competitive reactions at both electrodes.

   Cathode Competition (Reduction)

   At the cathode, the metal cation competes with water for reduction:

   • $2\text{H}_2\text{O}(\text{l}) + 2e^- \rightarrow \text{H}_2(\text{g}) + 2\text{OH}^-(\text{aq})\quad (E^\circ = -0.83\text{ V at pH 7: } -0.41\text{ V})$

   If the cation belongs to an active metal (such as $\text{Na}^+$, $\text{K}^+$, $\text{Ca}^{2+}$, or $\text{Al}^{3+}$), water is reduced preferentially, producing hydrogen gas ($\text{H}_2$). Less reactive metal cations, such as $\text{Cu}^{2+}$ or $\text{Ag}^+$, have higher standard reduction potentials than water and are reduced to elemental metal instead.

   Anode Competition (Oxidation)

   At the anode, the anion competes with water for oxidation:

   • $2\text{H}_2\text{O}(\text{l}) \rightarrow \text{O}_2(\text{g}) + 4\text{H}^+(\text{aq}) + 4e^-\quad (E^\circ = +1.23\text{ V at pH 7: } +0.82\text{ V})$

   Polyatomic oxoanions like $\text{SO}_4^{2-}$ and $\text{NO}_3^-$ are extremely difficult to oxidize because the central atom is already in its maximum oxidation state; in these cases, water is oxidized to produce oxygen gas ($\text{O}_2$). Halide ions (such as $\text{Cl}^-$, $\text{Br}^-$, $\text{I}^-$) can be oxidized instead of water, often influenced by kinetic factors like overpotential.

   Michael Faraday established the quantitative relationship between the amount of electricity consumed and the amount of substance transformed during electrolysis:

   1. First Law: The mass of a substance deposited or liberated at an electrode is directly proportional to the total electric charge passed through the cell.
   2. Second Law: When the same quantity of electric charge is passed through different electrolytes, the masses of substances altered are proportional to their chemical equivalent weights.

   Key Equations

   The total electric charge ($Q$) in coulombs is related to current ($I$) in amperes and time ($t$) in seconds by:

   $$Q = I \times t$$

   The number of moles of electrons ($n_{e^-}$) transferred is:

   $$n_{e^-} = \frac{Q}{F} = \frac{I \times t}{F}$$

   where $F$ is Faraday\'s constant ($F \approx 96{,}485\text{ C/mol } e^-$). The mass ($m$) of substance produced is determined by:

   $$m = \frac{I \times t \times M}{z \times F}$$

   where $M$ is the molar mass of the substance and $z$ is the number of moles of electrons transferred per mole of substance.