Electrochemical Cells: Electrolytic Cells and Principles of Electrolysis

Fundamentals of Redox Spontaneity and Electrolysis

• Redox reaction spontaneity is determined by the sign of the calculated cell potential:

  • A positive calculated voltage ($E^\circ_{\text{cell}} > 0$) indicates that the oxidation-reduction reaction is thermodynamically spontaneous.

  • A negative calculated voltage ($E^\circ_{\text{cell}} < 0$) indicates that the oxidation-reduction reaction is non-spontaneous under standard conditions.

• Electrolysis is the process in which electrical energy from an external power source is supplied to drive an otherwise non-spontaneous chemical reaction.

• Electrolytic cells are classified into three primary categories:

  • Electrolysis of aqueous salts ($\text{H}_2\text{O}$ solution) using reactive (active) electrodes.

  • Electrolysis of molten salts (in the absence of $\text{H}_2\text{O}$) using unreactive (inert) electrodes.

  • Electrolysis of aqueous salts ($\text{H}_2\text{O}$ solution) using unreactive (inert) electrodes.

Architecture and Electrode Polarity of Electrolytic Cells

• The polarity and operational mechanism of electrodes in an electrolytic cell (ELC) operate as follows:

  • Anode:

  • Connected directly to the positive ($+$\text{) terminal} of the external direct current (DC) power supply.

  • The external power supply pulls electrons ($\text{e}^-$) away from the anode.

  • Oxidation (the loss of electrons) occurs at the anode.

  • Cathode:

  • Connected directly to the negative ($-$\text{) terminal} of the external DC power supply.

  • The external power supply forces electrons ($\text{e}^-$) onto the cathode.

  • Reduction (the gain of electrons) occurs at the cathode.

• Electron transfer pathway:

  • Electrons move through the external circuit from the positive anode toward the positive terminal of the power supply, and from the negative terminal of the power supply onto the negative cathode.

  • Inside the electrolyte bath, current is carried by the physical migration of ions: anions migrate toward the positive anode, and cations migrate toward the negative cathode.

Electrolysis of Aqueous Salts with Reactive Electrodes

• In systems with reactive (active) electrodes, the electrode material participates directly in the chemical reaction rather than serving merely as an inert conductor.

• Mechanism of electroplating a metal object (such as an iron spoon in a nickel sulfate solution):

  • Electrolyte solution contains nickel ions ($\text{Ni}^{2+}$), sulfate ions ($\text{SO}_4^{2-}$), and water molecules ($\text{H}_2\text{O}$).

  • The object to be plated (iron spoon, $\text{Fe}$) is connected to the negative terminal and acts as the cathode.

  • The active plating metal (nickel plate, $\text{Ni}$) is connected to the positive terminal and acts as the anode.

• Electrode reactions:

  • Cathode reaction (Reduction):     $\text{Ni}^{2+}_{(aq)} + 2\text{e}^- \rightarrow \text{Ni}_{(s)}$

  • Dissolved nickel cations accept electrons at the surface of the spoon, precipitating as solid nickel atoms ($\text{Ni}$) that form a thin, adherent metallic coating.

  • Anode reaction (Oxidation):     $\text{Ni}_{(s)} \rightarrow \text{Ni}^{2+}_{(aq)} + 2\text{e}^-$

  • Nickel metal atoms from the active anode give up electrons to the external circuit and dissolve into the electrolyte solution as $\text{Ni}^{2+}$ cations.

• Ion depletion dynamics:

  • The concentration of $\text{Ni}^{2+}$ cations in the electrolyte solution remains constant over time.

  • Nickel ions are replenished by the dissolving nickel anode at the exact stoichiometric rate that they are deposited onto the cathode, preventing depletion of the plating bath.

Industrial Applications: Electroplating and Electrorefining

• Electroplating:

  • Definition: The deposition of a thin protective or decorative layer of one metal onto the conductive surface of another substrate through electrolysis.

  • Cell arrangement:

  • Cathode: The object to be coated.

  • Anode: The metal being deposited.

  • Electrolyte: A solution containing a low concentration of the ions of the plating metal.

  • Metals commonly used in electroplating:

  • Gold ($\text{Au}$)

  • Silver ($\text{Ag}$)

  • Copper ($\text{Cu}$)

  • Nickel ($\text{Ni}$)

  • Chromium ($\text{Cr}$)

  • Engineering functions of electroplated coatings:

  • Corrosion protection: Providing a sacrificial or barrier layer of a corrosion-resistant metal to shield base metals prone to oxidation.

  • Aesthetic/decorative enhancement (e.g., gold-plated watches, silver-plated teapots and goblets, copper-plated mugs, chrome-plated taps).

  • Electrical conductivity improvement on contacts and circuits.

  • Friction reduction and mechanical wear resistance on moving components.

  • Radiation shielding.

  • Barrel plating:

  • An industrial technique where small conductive parts (such as fasteners, bolts, or small components) are placed inside a slowly rotating perforated barrel immersed in an electrolytic plating bath with a DC power supply, ensuring an even metallic coating.

• Electrorefining:

  • Definition: The industrial electrolytic purification of crude metals extracted from ores or chemical concentrates.

  • Electrorefining of copper:

  • Anode: Cast slabs of impure, blister copper ($\text{Cu}$) containing elemental impurities.

  • Cathode: Thin starter sheets of high-purity copper ($\text{Cu}$).

  • Electrolyte: Acidified aqueous copper(II) sulfate ($\text{CuSO}_4$ and $\text{H}_2\text{SO}_4$).

  • Fate of copper and impurities during refining:

  • Copper dissolves at the anode and plates out at the cathode:       $\text{Anode: } \text{Cu}_{(s, \text{ impure})} \rightarrow \text{Cu}^{2+}_{(aq)} + 2\text{e}^-$       $\text{Cathode: } \text{Cu}^{2+}_{(aq)} + 2\text{e}^- \rightarrow \text{Cu}_{(s, \text{ pure})}$

  • More active metal impurities (such as zinc, $\text{Zn}$, and iron, $\text{Fe}$) are more easily oxidized than copper and dissolve into the solution as cations ($\text{Zn}^{2+}$, $\text{Fe}^{2+}$), remaining in the electrolyte without plating onto the cathode.

  • Less active (noble) impurities (such as silver, $\text{Ag}$, gold, $\text{Au}$, and platinum, $\text{Pt}$) are not oxidized at the operating potential; they slough off the anode and accumulate at the base of the cell as "anode mud" (anode slime), which is recovered for valuable precious metals.

Quantitative Relationships: Faraday's Laws of Electrolysis

• Michael Faraday's Law of Electrolysis states:

  • "The amount of electrical charge introduced to the nonspontaneous system is proportional to the chemical change produced and that a quantity of electricity produces a corresponding amount of substance being electrolyzed."

• Stoichiometric pathway for quantitative electrolysis calculations:   $\text{Current } (I) \text{ and time } (t) \rightarrow \text{Quantity of charge } (Q) \rightarrow \text{Moles of electrons } (n_{\text{e}^-}) \rightarrow \text{Moles of substance} \rightarrow \text{Mass of substance } (g)$

• Fundamental quantities, governing relations, and conversion factors:

  • Electrical Charge ($Q$):

  • Unit: Coulomb ($\text{C}$).

  • Defining relation: $1\,\text{C} = 1\,\text{A} \cdot \text{s} = 1\,\text{J/V}$.

  • Faraday constant ($F$): The electric charge carried by one mole of electrons:       $1\,\text{mol e}^- = 96{,}485\,\text{C}$       $1\,\text{Faraday} = 96{,}485\,\text{C}\,\text{mol}^{-1}\text{ of e}^-$       (Alternatively approximated as $9.648 \times 10^4\,\text{C}$).

  • Current Flow ($I$):

  • Unit: Ampere ($\text{A}$).

  • Defining relation: $I = \frac{Q}{t}$, where $1\,\text{A} = 1\,\text{C/s}$.

  • Electrical Potential ($V$):

  • Unit: Volt ($\text{V}$).

  • Defining relation: $1\,\text{V} = 1\,\text{J/C}$.

  • Electrical Power ($P$):

  • Unit: Watt ($\text{W}$).

  • Defining relation: $1\,\text{W} = 1\,\text{J/s}$.

  • Electrical Energy ($E$):

  • Unit: Joule ($\text{J}$).

  • Defining relation: $E = Q \times V$, where $1\,\text{J} = 1\,\text{V} \cdot \text{C}$.

  • Commercial energy unit: Kilowatt-hour ($\text{kWh}$):       $1\,\text{kWh} = 3.600 \times 10^6\,\text{J}$

• Stoichiometry of electron transfer based on balanced reduction half-reactions:

  • Silver reduction: $\text{Ag}^+_{(aq)} + \text{e}^- \rightarrow \text{Ag}_{(s)}$

  • Yields the ratio: $1\,\text{mol e}^- \rightarrow 1\,\text{mol Ag}$ ($107.9\,\text{g}$\text{ of }$\text{Ag}$\text{ per }96{,}485\,\text{C}$).\n - Copper(II) reduction: \text{Cu}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Cu}{(s)}\n - Yields the ratio: 2\,\text{mol e}^- \rightarrow 1\,\text{mol Cu}$($63.55\,\text{g}$\text{ of }$\text{Cu}$\text{ per }$2 \times 96{,}485\,\text{C}).\n\n# Worked Quantitative Examples\n\n- **Problem 1: Chromium Electroplating from Potassium Dichromate**\n - Half-reaction: \text{Cr}2\text{O}_7^{2-}{(aq)} + 14\text{H}^+{(aq)} + 12\text{e}^- \rightarrow 2\text{Cr}{(s)} + 7\text{H}2\text{O}{(l)}\n - Molar mass of chromium: M_{\text{Cr}} = 52.00\,\text{g/mol}.\n - Stoichiometric ratio: 12\,\text{mol e}^- \rightarrow 2\,\text{mol Cr}$, or$6\,\text{mol e}^- \rightarrow 1\,\text{mol Cr}.\n - *(a) Mass of chromium plated by 1 \times 10^4\,\text{C}*:\n    n_{\text{e}^-} = \frac{1 \times 10^4\,\text{C}}{96{,}485\,\text{C/mol}} = 0.10365\,\text{mol e}^-\n    n_{\text{Cr}} = 0.10365\,\text{mol e}^- \times \left(\frac{2\,\text{mol Cr}}{12\,\text{mol e}^-}\right) = 0.017275\,\text{mol Cr}\n    m_{\text{Cr}} = 0.017275\,\text{mol} \times 52.00\,\text{g/mol} = 0.898\,\text{g}\n - *(b) Time required to plate 1.00\,\text{g}$of chromium using a current of$6\,\text{A}*:\n    n_{\text{Cr}} = \frac{1.00\,\text{g}}{52.00\,\text{g/mol}} = 0.01923\,\text{mol Cr}\n    n_{\text{e}^-} = 0.01923\,\text{mol Cr} \times 6 = 0.11538\,\text{mol e}^-\n    Q = 0.11538\,\text{mol e}^- \times 96{,}485\,\text{C/mol} = 11{,}133\,\text{C}\n    t = \frac{Q}{I} = \frac{11{,}133\,\text{C}}{6\,\text{A}} = 1{,}855\,\text{s} = 30.9\,\text{minutes}\n - *(c) Energy required in kilowatt-hours (\text{kWh}$) at an applied potential of$4.5\,\text{V}$to plate$1.00\,\text{g} of chromium*:\n    E = Q \times V = 11{,}133\,\text{C} \times 4.5\,\text{V} = 50{,}099\,\text{J}\n    E_{\text{kWh}} = \frac{50{,}099\,\text{J}}{3.600 \times 10^6\,\text{J/kWh}} = 0.0139\,\text{kWh}\n\n- **Problem 2: Operating Duration of an Industrial Electroplating Run**\n - Given parameters: V = 0.25\,\text{V}$, energy expended$E = 10.3\,\text{kWh}$, current$I = 3\,\text{A}.\n - Total energy in joules:\n    E = 10.3\,\text{kWh} \times (3.600 \times 10^6\,\text{J/kWh}) = 3.708 \times 10^7\,\text{J}\n - Total electrical charge:\n    Q = \frac{E}{V} = \frac{3.708 \times 10^7\,\text{J}}{0.25\,\text{V}} = 1.4832 \times 10^8\,\text{C}\n - Operating time in seconds and minutes:\n    t = \frac{Q}{I} = \frac{1.4832 \times 10^8\,\text{C}}{3\,\text{A}} = 4.944 \times 10^7\,\text{s}\n    t_{\text{min}} = \frac{4.944 \times 10^7\,\text{s}}{60\,\text{s/min}} = 8.24 \times 10^5\,\text{minutes}\n\n- **Problem 3: Thickness of Silver Plated on a Baby's Spoon**\n - Given parameters: Area A = 6.25\,\text{cm}^2$, current$I = 2\,\text{A}$, time$t = 2\,\text{hours and } 25\,\text{minutes}$, density of silver$\rho = 10.5\,\text{g/cm}^3$, molar mass of silver$M_{\text{Ag}} = 107.9\,\text{g/mol}.\n - Elapsed time in seconds:\n    t = (2 \times 3{,}600) + (25 \times 60) = 7{,}200 + 1{,}500 = 8{,}700\,\text{s}\n - Total charge delivered:\n    Q = I \times t = 2\,\text{A} \times 8{,}700\,\text{s} = 17{,}400\,\text{C}\n - Moles and mass of silver deposited (\text{Ag}^+ + \text{e}^- \rightarrow \text{Ag}):\n    n_{\text{e}^-} = \frac{17{,}400\,\text{C}}{96{,}485\,\text{C/mol}} = 0.18034\,\text{mol e}^- = n_{\text{Ag}}\n    m_{\text{Ag}} = 0.18034\,\text{mol} \times 107.9\,\text{g/mol} = 19.46\,\text{g}\n - Volume of silver deposit:\n    V_{\text{deposit}} = \frac{m}{\rho} = \frac{19.46\,\text{g}}{10.5\,\text{g/cm}^3} = 1.853\,\text{cm}^3\n - Thickness (d) of deposit layer:\n    d = \frac{V_{\text{deposit}}}{A} = \frac{1.853\,\text{cm}^3}{6.25\,\text{cm}^2} = 0.296\,\text{cm} = 2.96\,\text{mm}\n\n- **Practice Activity Problems**:\n - *Activity 1: Silver plating on a brass pendant*:\n - Current I = 1.20\,\text{A}$, time$t = 1.50\,\text{h} = 5{,}400\,\text{s}$, active$\text{Ag}$anode in$\text{AgNO}3$bath ($M{\text{Ag}} = 107.87\,\text{g/mol}).\n - Q = 1.20\,\text{A} \times 5{,}400\,\text{s} = 6{,}480\,\text{C}\n - n_{\text{e}^-} = \frac{6{,}480\,\text{C}}{96{,}485\,\text{C/mol}} = 0.06716\,\text{mol e}^-\n - Since \text{Ag}^+ + \text{e}^- \rightarrow \text{Ag}$,$n_{\text{Ag}} = 0.06716\,\text{mol}.\n - m_{\text{Ag}} = 0.06716\,\text{mol} \times 107.87\,\text{g/mol} = 7.24\,\text{g}\n - *Activity 2: Nickel plating of a surgical instrument*:\n - Target mass m_{\text{Ni}} = 3.25\,\text{g}$, current$I = 3.50\,\text{A}$, potential$V = 4.5\,\text{V}$, bath:$\text{NiCl}2$($M{\text{Ni}} = 58.69\,\text{g/mol}).\n - Half-reaction: \text{Ni}^{2+} + 2\text{e}^- \rightarrow \text{Ni}\n - n_{\text{Ni}} = \frac{3.25\,\text{g}}{58.69\,\text{g/mol}} = 0.05538\,\text{mol}\n - n_{\text{e}^-} = 2 \times 0.05538\,\text{mol} = 0.11075\,\text{mol e}^-\n - Q = 0.11075\,\text{mol} \times 96{,}485\,\text{C/mol} = 10{,}686\,\text{C}\n - (a) Required time in minutes:\n      t = \frac{10{,}686\,\text{C}}{3.50\,\text{A}} = 3{,}053\,\text{s} = 50.9\,\text{minutes}\n - (b) Electrical energy consumed:\n      E = Q \times V = 10{,}686\,\text{C} \times 4.5\,\text{V} = 48{,}087\,\text{J} = 4.81 \times 10^4\,\text{J}\n      E_{\text{kWh}} = \frac{48{,}087\,\text{J}}{3.600 \times 10^6\,\text{J/kWh}} = 0.0134\,\text{kWh}\n - *Activity 3: Copper plating of a circuit component*:\n - Area A = 12.0\,\text{cm}^2$, volume$V = 0.150\,\text{cm}^3$, time$t = 25.0\,\text{min}$, density$\rho_{\text{Cu}} = 8.96\,\text{g/cm}^3.\n - Mass of copper needed:\n      m_{\text{Cu}} = V \times \rho = 0.150\,\text{cm}^3 \times 8.96\,\text{g/cm}^3 = 1.344\,\text{g}\n\n# Electrolysis of Molten Salts with Unreactive Electrodes\n\n\n\n- In molten salt electrolysis, the ionic compound is heated until it liquefies; no water is present, eliminating solvent competition at the electrodes.\n- **Electrolysis of Molten Zinc Chloride (\text{ZnCl}{2(l)})**:\n - Electrodes: Inert carbon (graphite) electrodes.\n - Mobile species: \text{Zn}^{2+}$and$\text{Cl}^- ions in liquid state.\n - Anode reaction (Oxidation):\n    2\text{Cl}^- \rightarrow \text{Cl}{2(g)} + 2\text{e}^-\n - Bubbles of chlorine gas (\text{Cl}2) evolve at the positive anode.\n - Cathode reaction (Reduction):\n    \text{Zn}^{2+} + 2\text{e}^- \rightarrow \text{Zn}{(s)}\n - Solid zinc metal (\text{Zn}) deposits onto the negative cathode.\n\n\n\n- **Industrial Production of Sodium Metal (Downs Cell)**:\n - Molten sodium chloride (\text{NaCl}{(l)}$) is electrolyzed at approximately$600^\circ\text{C}.\n - Cell reactions:\n    \text{Anode (Oxidation): } 2\text{Cl}^- \rightarrow \text{Cl}{2(g)} + 2\text{e}^- \quad (E^\circ = +1.36\,\text{V})\n    \text{Cathode (Reduction): } 2\text{Na}^+ + 2\text{e}^- \rightarrow 2\text{Na}{(l)} \quad (E^\circ = -2.71\,\text{V})\n    \text{Overall cell reaction: } 2\text{NaCl}{(l)} \rightarrow 2\text{Na}{(l)} + \text{Cl}{2(g)}\n - Overall cell potential:\n    E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = -2.71\,\text{V} - 1.36\,\text{V} = -4.07\,\text{V}\n - Engineering design features of the Downs Cell:\n - Carbon (graphite) anode centrally positioned to collect chlorine gas.\n - Cylindrical iron cathode surrounding the anode.\n - An iron mesh/steel screen separator positioned between the anode and cathode chambers to prevent molten sodium and chlorine gas from coming into contact, preventing an explosive recombination reaction.\n - Molten sodium has a lower density than the molten salt mixture, causing it to float to the surface where it is collected in a riser pipe and siphoned off safely.\n\n# Standard Reduction Potentials Reference Data\n\n- Standard reduction potentials (E^\circ$at$25^\circ\text{C}$,$1\,\text{atm}$,$1\,\text{M}):\n - \text{F}{2(g)} + 2\text{e}^- \rightarrow 2\text{F}^-{(aq)}$:$+2.87\,\text{V}\n - \text{H}2\text{O}{2(aq)} + 2\text{H}^+{(aq)} + 2\text{e}^- \rightarrow 2\text{H}_2\text{O}{(l)}$:$+1.78\,\text{V}\n - \text{MnO}{4(aq)}^- + 8\text{H}^+{(aq)} + 5\text{e}^- \rightarrow \text{Mn}^{2+}{(aq)} + 4\text{H}_2\text{O}{(l)}$:$+1.51\,\text{V}\n - \text{Cl}{2(g)} + 2\text{e}^- \rightarrow 2\text{Cl}^-{(aq)}$:$+1.36\,\text{V}\n - \text{Cr}2\text{O}{7(aq)}^{2-} + 14\text{H}^+{(aq)} + 6\text{e}^- \rightarrow 2\text{Cr}^{3+}{(aq)} + 7\text{H}2\text{O}{(l)}$:$+1.33\,\text{V}\n - \text{O}{2(g)} + 4\text{H}^+{(aq)} + 4\text{e}^- \rightarrow 2\text{H}2\text{O}{(l)}$:$+1.23\,\text{V}\n - \text{Br}{2(l)} + 2\text{e}^- \rightarrow 2\text{Br}^-{(aq)}$:$+1.09\,\text{V}\n - \text{Ag}^+{(aq)} + \text{e}^- \rightarrow \text{Ag}{(s)}$:$+0.80\,\text{V}\n - \text{Fe}^{3+}{(aq)} + \text{e}^- \rightarrow \text{Fe}^{2+}{(aq)}$:$+0.77\,\text{V}\n - \text{O}{2(g)} + 2\text{H}^+{(aq)} + 2\text{e}^- \rightarrow \text{H}2\text{O}{2(aq)}$:$+0.70\,\text{V}\n - \text{I}{2(s)} + 2\text{e}^- \rightarrow 2\text{I}^-{(aq)}$:$+0.54\,\text{V}\n - \text{O}{2(g)} + 2\text{H}_2\text{O}{(l)} + 4\text{e}^- \rightarrow 4\text{OH}^-{(aq)}$:$+0.40\,\text{V}\n - \text{Cu}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Cu}{(s)}$:$+0.34\,\text{V}\n - \text{Sn}^{4+}{(aq)} + 2\text{e}^- \rightarrow \text{Sn}^{2+}{(aq)}$:$+0.15\,\text{V}\n - 2\text{H}^+{(aq)} + 2\text{e}^- \rightarrow \text{H}{2(g)}$:$0.00\,\text{V}\n - \text{Pb}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Pb}{(s)}$:$-0.13\,\text{V}\n - \text{Ni}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Ni}{(s)}$:$-0.26\,\text{V}\n - \text{Cd}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Cd}{(s)}$:$-0.40\,\text{V}\n - \text{Fe}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Fe}{(s)}$:$-0.45\,\text{V}\n - \text{Zn}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Zn}{(s)}$:$-0.76\,\text{V}\n - 2\text{H}_2\text{O}{(l)} + 2\text{e}^- \rightarrow \text{H}{2(g)} + 2\text{OH}^-{(aq)}$:$-0.83\,\text{V}\n - \text{Al}^{3+}{(aq)} + 3\text{e}^- \rightarrow \text{Al}{(s)}$:$-1.66\,\text{V}\n - \text{Mg}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Mg}{(s)}$:$-2.37\,\text{V}\n - \text{Na}^+{(aq)} + \text{e}^- \rightarrow \text{Na}{(s)}$:$-2.71\,\text{V}\n - \text{Li}^+{(aq)} + \text{e}^- \rightarrow \text{Li}{(s)}$:$-3.04\,\text{V}\n\n# Electrolysis of Aqueous Salts with Unreactive Electrodes\n\n\n\n- In aqueous solutions containing unreactive (inert) electrodes, water molecules (\text{H}2\text{O}) can participate in redox reactions, competing with the dissolved salt ions:\n - **Cathodic Competition (Reduction)**:\n - Cation reduction: \text{M}^{n+}{(aq)} + n\text{e}^- \rightarrow \text{M}{(s)}\n - Water reduction: 2\text{H}_2\text{O}{(l)} + 2\text{e}^- \rightarrow \text{H}{2(g)} + 2\text{OH}^-{(aq)} \quad (E^\circ = -0.83\,\text{V})\n - The species with the more positive (less negative) reduction potential is reduced preferentially.\n - **Anodic Competition (Oxidation)**:\n - Anion oxidation: 2\text{X}^-{(aq)} \rightarrow \text{X}{2} + 2\text{e}^-\n - Water oxidation: 2\text{H}2\text{O}{(l)} \rightarrow \text{O}{2(g)} + 4\text{H}^+{(aq)} + 4\text{e}^- \quad (E^\circ_{\text{ox}} = -1.23\,\text{V}, \text{ where } E^\circ_{\text{red}} = +1.23\,\text{V})\n - The species with the more positive oxidation potential (less positive reduction potential) is oxidized preferentially, subject to kinetic overpotentials.\n- **Electrolysis of Pure/Acidified Water**:\n - Pure water has low electrical conductivity; a non-reactive electrolyte such as sulfuric acid (\text{H}2\text{SO}_4) is added to provide mobile ions.\n - Anode half-reaction:\n    2\text{H}_2\text{O}{(l)} \rightarrow \text{O}{2(g)} + 4\text{H}^+{(aq)} + 4\text{e}^- \quad (E^\circ_{\text{anode}} = +1.229\,\text{V})\n - Cathode half-reaction:\n    2\text{H}^+{(aq)} + 2\text{e}^- \rightarrow \text{H}{2(g)} \quad (E^\circ_{\text{cathode}} = 0.000\,\text{V})\n - Net cell reaction:\n    2\text{H}2\text{O}{(l)} \rightarrow 2\text{H}{2(g)} + \text{O}{2(g)}\n - Standard cell potential:\n    E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = 0\,\text{V} - (+1.229\,\text{V}) = -1.229\,\text{V}\n - Stoichiometry of gases:\n - Hydrogen gas evolves at the cathode and oxygen gas evolves at the anode in a 2:1 volumetric ratio.\n\n\n\n- **Electrolysis of 1\,\text{M}$Aqueous Copper(II) Chloride ($\text{CuCl}{2(aq)}) with Inert Carbon Electrodes**:\n - Competing species present: \text{Cu}^{2+}$,$\text{Cl}^-$, and$\text{H}_2\text{O}.\n - Cathode evaluation (Reduction possibilities):\n    \text{Cu}^{2+}{(aq)} + 2\text{e}^- \rightarrow \text{Cu}{(s)} \quad (E^\circ = +0.34\,\text{V})\n    2\text{H}_2\text{O}{(l)} + 2\text{e}^- \rightarrow \text{H}{2(g)} + 2\text{OH}^-{(aq)} \quad (E^\circ = -0.83\,\text{V})\n - Because +0.34\,\text{V} > -0.83\,\text{V}, copper(II) ions are reduced more easily than water.\n - Product at cathode: Solid copper metal (\text{Cu}{(s)}).\n - Anode evaluation (Oxidation possibilities):\n    2\text{Cl}^-{(aq)} \rightarrow \text{Cl}{2(g)} + 2\text{e}^- \quad (E^\circ{\text{red}} = +1.36\,\text{V})\n    2\text{H}2\text{O}{(l)} \rightarrow \text{O}{2(g)} + 4\text{H}^+{(aq)} + 4\text{e}^- \quad (E^\circ_{\text{red}} = +1.23\,\text{V})\n - Although water oxidation has a slightly lower thermodynamic reduction potential (+1.23\,\text{V}$vs.$+1.36\,\text{V}), the significant overpotential required for oxygen gas evolution favors the oxidation of chloride ions in concentrated solution.\n - Product at anode: Chlorine gas (\text{Cl}{2(g)}).\n - Overall cell potential:\n    E^\circ{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.34\,\text{V} - (+1.36\,\text{V}) = -1.02\,\text{V}\n\n# Kinetics of Electrolytic Cells: Activation Energy and Overpotential\n\n- **Activation Energy (E_a)**:\n - The minimum threshold amount of energy required to bring reacting atoms or molecules to an active transition state in which they can undergo chemical transformation or physical transport.\n- **Overpotential (Overvoltage)**:\n - The difference between the actual applied cell voltage required to drive an electrolytic reaction at a practical rate and the theoretical thermodynamic cell potential (E_{\text{cell}}).\n - Characteristics and operational consequences:\n - Directly dictates the voltage efficiency of an electrolytic cell.\n - The additional energy supplied to overcome overpotential is not converted to chemical bonds; it dissipates into the solution and surroundings as waste heat.\n - Overpotential is particularly high (often exceeding 0.5\,\text{V}$) for electrode processes that produce gases (such as$\text{O}{2(g)}$or$\text{H}{2(g)}$$) due to the slow kinetics of gas bubble nucleation and complex multi-electron transfer pathways.