Comprehensive Notes on Electrical Potential and Voltaic Cells

Electrical Potential and Voltaic Cells

Introduction to Electrical Potential

• Electrical potential relates to a voltaic cell's capacity to generate electric current.
• It is measured in volts (V).
• Voltage is related to electric current flow; voltmeters measure current flow, which is then related to voltage.
• Early instruments (galvanometers) used electrical laws to measure voltage but were heavy and difficult to use.
• Multimeters emerged in the 1920s, becoming truly portable with printed circuits and transistors.
• Electrical potential is the difference between half-cells; you cannot measure an isolated half-cell.
• Example: A zinc half-cell alone cannot produce a measurable electrical potential without being combined with another half-cell to allow a complete redox reaction.

Redox Reactions and Cell Potential

• Cell potential arises from the competition for electrons between two half-cells.
• In a zinc-copper voltaic cell, copper(II) ions (Cu2+) are reduced to copper metal because they have a stronger attraction for electrons than zinc ions (Zn2+).
• Zinc metal is oxidized in this process.

Reduction Potential

• Reduction potential measures the tendency of a half-reaction to occur as a reduction in an electrochemical cell.
• The half-cell with a higher reduction potential undergoes reduction, while the one with a lower reduction potential undergoes oxidation.

Cell Potential Calculation

• Cell potential ($E<em>{cell}$) is the difference in reduction potential between the two half-cells: $E</em>{cell} = E<em>{red} - E</em>{oxid}$
• $E_{cell}$ is the cell potential.
• $E_{red}$ is the reduction potential of the half-cell where reduction occurs.
• $E_{oxid}$ is the reduction potential of the half-cell where oxidation occurs.

Standard Electrode Potential

• Standard electrode potential ($E^{\circ}_{cell}$) is measured under standard conditions:
  • 1M concentration in half-cells.
  • 101 kPa pressure for gases.
  • 25 °C temperature.
• $E^{\circ}<em>{red}$ and $E^{\circ}</em>{oxid}$ represent standard reduction potentials for reduction and oxidation half-cells, respectively.

Standards for Comparison

• Standards provide a universal basis for comparison.
• Example: One meter is the same distance everywhere, allowing for consistent comparisons (e.g., 100-meter tracks).

Standard Hydrogen Electrode (SHE)

• The activity series predicts the relative reactivities in oxidation-reduction processes.
• Voltage measures the electric current flow, also known as electromotive force or potential difference.
• The standard hydrogen electrode is the baseline for measuring electron flow in chemical systems.

SHE Setup

• A platinum wire conducts electricity.
• The wire is immersed in a 1.0 M strong acid solution.
• Hydrogen gas (H2) is bubbled in at 1 atm pressure and 25°C.
• Half-reaction: $H_2 \rightarrow 2H^+ + 2e^-$
• The potential for hydrogen reduction under these conditions is defined as exactly zero ($E^\circ = 0$).

Measuring Potentials with SHE

• The SHE is used to measure the potentials of other electrodes in half-cells, often with a metal and its salt (e.g., sulfate).
• Example: Zinc half-cell.

Zinc Half-Cell Reaction

• Observation: Solid zinc mass decreases.
• Half-cell reaction: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
• Overall process:
  • $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$ (anode - oxidation)
  • $2H^+ + 2e^- \rightarrow H_2$ (cathode - reduction)
• Measured cell voltage: 0.76 V.

Standard EMF Calculation with Zinc

• Standard EMF: $E^\circ<em>{cell} = E^\circ</em>{cathode} - E^\circ_{anode}$
• $0.76 V = 0 - E^\circ_{anode}$
• $E^\circ_{anode} = -0.76 V$

Copper Half-Cell Reaction

• Copper electrode acts as the cathode.
• Half-reaction: $Cu^{2+} + 2e^- \rightarrow Cu$
• Overall half-reactions:
  • $H_2 \rightarrow 2H^+ + 2e^-$ (anode)
  • $Cu^{2+} + 2e^- \rightarrow Cu$ (cathode)
• $E^\circ$ for the system: 0.34 V.

Standard EMF Calculation with Copper

• $E^\circ<em>{cell} = E^\circ</em>{cathode} - E^\circ_{anode}$
• $0.34 V = E^\circ_{copper} - 0$
• $E^\circ_{copper} = 0.34 V$

Combining Zinc and Copper Cells

• Zinc will be oxidized, and copper will be reduced based on the activity series.
• $E_{cell} = 0.34 V (copper) - (-0.76 V zinc) = 1.10 V$

Standard Reduction Potentials and Oxidizing/Reducing Agents

• Higher standard reduction potentials indicate easier reduction (better oxidizing agents).
• Example:
  • $F_2$ (2.87 V) easily reduces and is a good oxidizing agent.
  • $Li(s)$ (-3.05 V) prefers oxidation and is a good reducing agent.
• $Zn^{2+}$ (-0.76 V) can be:
  • Oxidized by electrodes with E^\circ > -0.76 V (e.g., $H^+(0 V)$, $Cu^{2+}(0.34 V)$, $F_2(2.87 V)$).
  • Reduced by electrodes with E^\circ < -0.76 V (e.g., $H_2(-2.23 V)$, $Na^+(-2.71 V)$, $Li^+(-3.05 V)$).

Gibbs Free Energy and Cell Potential

• In a galvanic cell (spontaneous redox reaction), Gibbs free energy ($\Delta G^\circ$) must be negative: $\Delta G^\circ<em>{cell} = -nFE^\circ</em>{cell}$
  • n is the number of moles of electrons per mole of products.
  • F is the Faraday constant (~96485 C/mol).
• Rules:
  • If E^\circ_{cell} > 0, the process is spontaneous (galvanic cell).
  • If E^\circ_{cell} < 0, the process is nonspontaneous (electrolytic cell).
• For a spontaneous reaction (\Delta G^\circ < 0), $E^\circ<em>{cell}$ must be positive: $E^\circ</em>{cell} = E^\circ<em>{cathode} - E^\circ</em>{anode}$

Activity Series

• Identifies which species will be oxidized and reduced.
• Table of standard reduction potentials in decreasing order.
• Species at the top are more likely to be reduced; those at the bottom are more likely to be oxidized.
• When coupling a species from the top with one from the bottom, the top species will be reduced, and the bottom species will be oxidized.

Activity Series Table Examples

• Examples of reduction half-reactions and their standard reduction potentials (V):
  • $F_2(g) + 2e^- \rightarrow 2F^-(aq)$, +2.87
  • $S<em>2O</em>8^{2-}(aq) + 2e^- \rightarrow 2SO_4^{2-}(aq)$, +2.01
  • $O<em>2(g) + 4H^+(aq) + 4e^- \rightarrow 2H</em>2O(l)$, +1.23
  • $Br_2(l) + 2e^- \rightarrow 2Br^+(aq)$, +1.09
  • $Ag^+(aq) + e^- \rightarrow Ag(s)$, +0.80
  • $Fe^{3+}(aq) + e^- \rightarrow Fe^{2+}(aq)$, +0.77
  • $I_2(l) + 2e^- \rightarrow 2I^+(aq)$, +0.54
  • $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$, +0.34
  • $Sn^{4+}(aq) + 2e^- \rightarrow Sn^{2+}(aq)$, +0.15
  • $S(s) + 2H^+(aq) + 2e^- \rightarrow H_2S(g)$, +0.14
  • $2H^+(aq) + 2e^- \rightarrow H_2(g)$, 0.00
  • $Sn^{2+}(aq) + 2e^- \rightarrow Sn(g)$, -0.14
  • $V^{3+}(aq) + e^- \rightarrow V^{2+}(aq)$, -0.26
  • $Fe^{2+}(aq) + 2e^- \rightarrow Fe(s)$, -0.44
  • $Cr^{3+}(aq) + 3e^- \rightarrow Cr(s)$, -0.74
  • $Zn^{2+}(aq) + 2e^- \rightarrow Zn(s)$, -0.76
  • $Mn^{2+}(aq) + 2e^- \rightarrow Mn(s)$, -1.18
  • $Na^+(aq) + e^- \rightarrow Na(s)$, -2.71
  • $Li^+(aq) + e^- \rightarrow Li(s)$, -3.04

Additional Standard Reduction Potentials

• Examples of standard reduction potentials (E° (V)):
  • $MnO<em>4^- + 8 H</em>3O^+ + 5 e^-→ Mn^{2+} + 12 H_2O$, +1.49
  • $Au^{3+} + 3 e^- → Au$, +1.42
  • $O<em>2 (g) + 4 H</em>3O^+ + 4 e^- → 6 H_2O$, +1.23
  • $Br_2 (l) + 2 e^- ⇌ 2 Br^-$, +1.06
  • $NO<em>3^- (g) + 4 H</em>3O^+ + 3 e^-→ NO(g) + 6 H_2O$, +0.96
  • $Ag^+ + 1 e^- ⇌ Ag$, +0.80
  • $O<em>2(g) + 2 H</em>2O + 4 e^- ⇌ 4OH^-$, +0.40
  • $Cu^{2+} + 2 e^- ⇌ Cu$, +0.34