Electrochemical Cells, Redox Potentials, and Electrolysis Principles

Introduction to Electrochemistry

• Electrochemistry Definition: The study of the inter-conversion between electrical energy and chemical energy.
• Electrochemical Cell: A specific cell consisting of electrodes that are dipped into electrolyte.
  • Types: There are two primary types of cells: Galvanic (Voltaic) cells and Electrolytic cells.
• Redox Reaction: A chemical reaction where oxidation and reduction occur simultaneously.
  • Oxidation occurs at the Anode.
  • Reduction occurs at the Cathode.
  • OIL RIG Mnemonic:
    • OIL: Oxidation Is Loss (of electrons).
    • RIG: Reduction Is Gain (of electrons).

Cell Components and Mechanisms

• Electrode: Represented by the anode and the cathode of the cell.
• Salt Bridge: A U-shaped tube containing a gel permeated with a solution of an inert electrolyte, such as $KCl$.
  • The ions in the salt bridge will not react with other ions in the solution or with the electrodes.
  • Function: It keeps the charges balanced between the two beakers to allow the flow of electrons to continue.
  • Ion Movement:
    • Cations move toward the Cathode.
    • Anions move toward the Anode.
• Half-Cell Reactions: Chemical reactions occurring specifically at the anode and cathode.
  • The combination of two half-cells results in the overall redox reaction.

Galvanic (Voltaic) vs. Electrolytic Cells

• Voltaic Cell (Galvanic Cell):
  • Energy: Chemical energy is converted to electrical energy; energy is released from a spontaneous redox reaction.
  • Work: The system does work on the surroundings.
  • Spontaneity: The reaction is spontaneous ($\Delta G < 0$).
  • Cell Potential: $E_{cell} > 0$.
  • Electrode Polarity: Anode is negative ($-$); Cathode is positive ($+$).
• Electrolytic Cell:
  • Energy: Electrical energy is used to drive a chemical reaction; energy is absorbed to drive a nonspontaneous redox reaction.
  • Work: The surroundings (power supply) do work on the system (cell).
  • Spontaneity: The reaction is non-spontaneous ($\Delta G > 0$).
  • Electrode Polarity: Anode is positive ($+$); Cathode is negative ($-$).
  • Mechanism: Electrons flow from the anode to the cathode through an external circuit.

Voltage of Common Voltaic Cells

• Common alkaline flashlight battery: $1.5\,V$
• Lead-acid car battery (6 cells): $2.0\,V$ per cell ($12\,V$ total)
• Calculator battery (mercury): $1.3\,V$
• Lithium-ion laptop battery: $3.7\,V$
• Electric eel: Approximately $5000$ cells in a $6\text{-ft}$ eel produce $750\,V$ ($0.15\,V$ per cell)
• Nerve of giant squid (across cell membrane): $0.070\,V$

Standard Reduction Potentials (SRP)

• Electromotive Force (EMF): Designated as $E^\circ_{cell}$, it is the potential difference between the anode and cathode measured in volts ($V$).
• Standard Conditions:
  • Concentration of electrolyte: $1.0\,M$
  • Temperature: $25^\circ C$
  • Pressure: $1\,atm$
• Formulas for Cell Potential:
  • $E^\circ_{cell} = E^\circ(\text{cathode}) - E^\circ(\text{anode})$
  • $E_{cell} = E^\circ(\text{oxidation}) + E^\circ(\text{reduction})$
• Standard Hydrogen Electrode (SHE):
  • Used as a reference for SRP values.
  • By definition, the reduction potential for hydrogen is $0\,V$.
  • Reaction: $2H^+(aq, 1\,M) + 2e^- \rightarrow H_2(g, 1\,atm)$
• Interpreting SRP Values:
  • More Positive $E^\circ$: Indicates reduction (cathode); the species adds electrons more easily, is more easily reduced, and acts as a better oxidizing agent.
  • More Negative $E^\circ$: Indicates oxidation (anode); the species loses electrons more easily, is more easily oxidized, and acts as a better reducing agent.

Cell Notation (Cell Diagram)

• The notation follows the order of components in the anode compartment (oxidation) followed by the cathode compartment (reduction).
• Structure: $\text{Electrode} | \text{Phase of lower oxidation state} | \text{Phase of higher oxidation state} || \text{Phase of higher oxidation state} | \text{Phase of lower oxidation state} | \text{Electrode}$
• Example 1: $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$
  • Anode: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
  • Cathode: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
• Example 2: $\text{graphite} | I^-(aq) | I_2(s) || H^+(aq), MnO_4^-(aq) | Mn^{2+}(aq) | \text{graphite}$
  • Contains inert graphite electrodes.
  • Anode: $2I^-(aq) \rightarrow I_2(s) + 2e^-$
  • Cathode: $MnO_4^-(aq) + 8H^+(aq) + 5e^- \rightarrow Mn^{2+}(aq) + 4H_2O$.

Free Energy and Spontaneity

• Gibbs Free Energy ($\Delta G$) Formulas:
  • $\Delta G = -nFE_{cell}$
  • Standard Conditions: $\Delta G^\circ = -nFE^\circ_{cell}$
  • Relationship with Equilibrium Constant: $\Delta G^\circ = RT \ln(Q)$
  • $E^\circ_{cell} = -\frac{RT}{nF} \ln(Q)$
• Constants:
  • $n$ = number of moles of electrons transferred.
  • $F$ (Faraday’s constant) = $96,500\,C/mol$.
  • $R$ (Gas Constant) = $8.314\,J/mol \cdot K$.
• Spontaneity Rules:
  • Spontaneous: $E_{cell} > 0$ and $\Delta G < 0$.
  • Nonspontaneous: $E_{cell} < 0$ and $\Delta G > 0$.

The Nernst Equation

• Factors Affecting Cell Potential ($E_{cell}$):
  1. Position of ions in the standard reduction potential table.
  2. Concentration of ions in electrolytes.
  3. Temperature of the reaction.
  4. Pressure of gases involved in the reaction.
• General Nernst Equation:
  • $E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln(Q)$
• At $T = 25^\circ C$ ($298\,K$) and $P = 1\,atm$:
  • $E_{cell} = E^\circ_{cell} - \frac{0.0592\,V}{n} \log(Q)$
• Reaction Quotient ($Q$):
  • $Q = \frac{[\text{Product}]^x}{[\text{Reactant}]^y} \times P_{gas}$, where $x$ and $y$ are stoichiometric coefficients.

Concentration Cells

• Definition: An electrochemical cell composed of two identical half-cells with different ion concentrations.
• Nernst Equation for Concentration Cells at $25^\circ C$:
  • $E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log\left(\frac{[M^{n+}]_{\text{dilute}}}{[M^{n+}]_{\text{conc}}}\right)$
  • Since the electrodes are identical, $E^\circ_{cell}$ is usually $0\,V$.

Factors Affecting Redox Potential

1. Concentration of Ions: Cell potential decreases as the concentration of ions in the cell decreases.
2. Temperature: Cell potential is temperature dependent according to the Nernst Equation ($E_{cell} = E^\circ_{cell} + \frac{2.303RT}{nF} \log(Q)$). Generally, $E_{cell}$ decreases with increasing temperature.

Electrolysis and Electrolytic Cells

• Electrolysis Definition: A process of dissociation or decomposition of an electrolyte to produce elements using an electric current to force a chemical reaction.
• Steps of Electrolysis:
  1. Ion movement towards electrodes.
  2. Ions discharged at electrodes.
• Electrochemical Series: Cations move toward the cathode ($-$); Anions move toward the anode ($+$).
• Electrodes: Often uses inert electrodes like Platinum ($Pt$) or graphite.
• Electrolytes: Can be molten salts or aqueous salt solutions.
• Factors Affecting Selective Discharge:
  • Position of ions in the electrochemical series: Ions at lower positions are selectively discharged.
  • Concentration of electrolytes: A particular ion with a significantly higher concentration may be selectively discharged.
  • Types of electrodes:
    • Inert: Carbon (graphite), Platinum; do not participate in the reaction.
    • Active: Metals that do participate in the reaction if the solution consists of the same element (e.g., copper electrodes in $CuSO_4$ solution).

Quantitative Aspects of Electrolysis (Faraday's Laws)

• First Law: The mass of a substance formed at an electrode is directly proportional to the quantity of electric charge ($Q$) that has flowed in the circuit.
• Second Law: For a given quantity of electric charge, the amount of metal formed is proportional to its equivalent weight.
• Formulas:
  • $Q = It$
    • $Q$ = electric charge in coulombs ($C$).
    • $I$ = current in amperes ($A$); represented as $1\,A = 1\,J/C$ or $1\,A = 1\,C/s$.
    • $t$ = time in seconds ($s$).
  • $n_{e^-} = \frac{Q}{F}$
    • $n_{e^-}$ = moles of electrons transferred.
    • $F$ = Faraday's constant ($96,500\,C/mol$).
• Conversion and Stoichiometry:
  • Mass of substance = $n_{\text{substance}} \times \text{molar mass}$.
  • Molar volume at STP = $22.4\,dm^3\,mol^{-1}$.

Applications of Electrolysis

• Electro-refining: Purification of a metal.
  • Example: Purification of Copper.
    • Anode (Impure Cu): $Cu \rightarrow Cu^{2+} + 2e^-$. The anode becomes thinner.
    • Cathode: $Cu^{2+} + 2e^- \rightarrow Cu$. Pure copper deposits on the cathode.
    • Impurities like $Au$, $Ag$, and $Pt$ (less reactive) fall as anode sludge. More reactive impurities like $Zn$ dissolve as aqueous ions.
• Electroplating: Coating one metal onto the surface of another to provide protection from corrosion.
  • Example: Electroplating Chromium onto Iron using an aqueous solution of Chromium ($III$) chloride ($CrCl_3$).
• Manufacture of Chemicals (Chlor-alkali process):
  • Produced: Chlorine ($Cl_2$), Hydrogen ($H_2$), and Sodium Hydroxide ($NaOH$).
  • Process: Brine enters the compartment. Chloride ions are oxidized at the anode to produce $Cl_2$ gas. Water is electrolyzed at the cathode to produce $H_2$ gas. Sodium ions move through a permeable plastic membrane to react with hydroxide ions, forming $NaOH$ solution.

Step-by-Step Calculation Examples

Example: Electrochemical Cell Potential ($Zn/Cu$)

• Given: $E^\circ_{\text{red}} Zn/Zn^{2+} = -0.76\,V$ and $E^\circ_{\text{red}} Cu/Cu^{2+} = +0.34\,V$.
• Solution:
  • $E^\circ_{cell} = E^\circ(\text{cathode}) - E^\circ(\text{anode})$
  • $E^\circ_{cell} = +0.34\,V - (-0.76\,V) = 1.10\,V$

Example: Nernst Equation (Zn and H+ reference)

• Cell: $Zn/Zn^{2+}(0.010\,M)$ and $H_2(0.30\,atm)/H^+(2.5\,M)$.
• Anode ($Zn \rightarrow Zn^{2+} + 2e^-$): $E^\circ = -0.76\,V$
• Cathode ($2H^+ + 2e^- \rightarrow H_2$): $E^\circ = 0.00\,V$
• $E^\circ_{cell} = 0.76\,V$
• Calculation: $E_{cell} = 0.76 - \frac{0.0592}{2} \log \left(\frac{[0.01][0.3]}{[2.5]^2}\right) = 0.76 - (-0.10) = 0.86\,V$.

Example: Mass of Calcium from Molten $CaCl_2$

• Current: $0.452\,A$ for $1.5\,h$ ($5400\,s$).
• $Q = 0.452 \times 5400 = 2,440.8\,C$
• $n_{e^-} = 2440.8 / 96500 = 0.0253\,mol$
• Reaction: $Ca^{2+} + 2e^- \rightarrow Ca$
• $n_{Ca} = 0.0253 / 2 = 0.0126\,mol$
• Mass: $0.0126\,mol \times 40\,g/mol = 0.504\,g$.

Example: Electroplating a Silver Spoon

• Mass required: $2.00\,g$ of $Ag$. Time: $12.0\,h$ ($43,200\,s$).
• $n_{Ag} = 2.00 / 107.87 = 0.0185\,mol$
• $n_{e^-} = n_{Ag} = 0.0185\,mol$
• $Q = 0.0185 \times 96500 = 17891.19\,C$
• $I = Q / t = 17891.19 / 43,200 = 0.4141\,A$.