Ch8: Electrical Potential

Concept of Electrical Potential in Batteries

• Electricity from a battery = electrons forced through an external circuit.
• Driving force: a difference in potential energy ("electrical potential" or "potential difference").
• Analogy: water falling from a high reservoir to a low one → gravity provides a potential difference; in a battery, electrochemical potential plays the same role.
• Core take-away: electrons always move from the electrode with higher potential energy to the one with lower potential energy.

Voltage (Cell Potential)

• Voltage printed on a battery (e.g.
  • AA cell ≈ 1.5 V,
  • rectangular battery ≈ 9 V)
    represents the numerical difference in electrochemical potential between the two electrodes.
• Unit: volt (V).
• Fine distinctions between units or prefixes exist, but the class will simply use volts throughout.

Electrochemical Cell Anatomy (connection to earlier lectures)

• Electrodes (anode & cathode) + an ionic solution are essential.
• Redox reactions at the solid–solution interfaces create/consume electrons.
• The external wire provides a path for electrons; the salt bridge (or porous membrane) closes the ionic circuit internally.

Reduction Potentials ($E_{red}$)

• Every element has a measurable tendency to gain electrons (be reduced).
• "Ease" of reduction is quantified by the standard reduction potential, $E^\circ_{red}$.
• Values are referenced to the standard hydrogen electrode (SHE), defined as $E^\circ<em>{red}(\text{H}^+ / \text{H}</em>2)=0.000\,\text{V}$.
• Tables of $E^\circ_{red}$ for all common species are pre-measured and will be provided in problem sets/exams.

Standard vs. Non-standard State

• "Standard state" (superscript $\circ$ or “°”):
  • Temperature: $25\,^{\circ}\text{C}$ (298 K)
  • Pressure: $1\,\text{atm}$
  • Solutes: $1\,\text{M}$ concentration.
• Example determinations at standard conditions:
  • $\text{O}_2$ ➔ gas.
  • $\text{H}_2\text{O}$ ➔ liquid (even if today’s room is hot).
• If a species is not in standard conditions, omit the $\circ$; calculations proceed identically.

Calculating the Cell Potential

• Master equation (standard conditions):
  $E^\circ<em>{cell}=E^\circ</em>{cathode}-E^\circ_{anode}$
• Where:
  • Cathode = electrode where reduction occurs (gains e⁻).
  • Anode = electrode where oxidation occurs (loses e⁻).
• For non-standard conditions the same subtraction applies but without the ° symbol.

Identifying Oxidation vs. Reduction

• Track oxidation numbers or explicitly follow the electron flow:
  • Losing e⁻ (oxidation) ➔ oxidation number becomes more positive.
  • Gaining e⁻ (reduction) ➔ oxidation number becomes less positive / more negative.
• Mnemonic: "LEO the lion says GER" (Lose Electrons = Oxidation; Gain Electrons = Reduction).

Spontaneity Criterion for Galvanic/Voltaic Cells

• E_{cell}>0 ➔ reaction is spontaneous; the battery will deliver power.
• E_{cell}<0 ➔ reaction is non-spontaneous; external energy would be required (electrolytic cell).
• In everyday language "spontaneous" ≈ "happens on its own" once reactants are in contact.

Worked Examples

Example 1: $\text{Cu}+2\text{Ag}^+\;\rightarrow\;\text{Cu}^{2+}+2\text{Ag}$

• Step 1 – assign electrodes:
  • $\text{Cu}\rightarrow\text{Cu}^{2+}+2e^-$ (oxidation) ➔ anode.
  • $\text{Ag}^++e^-\rightarrow\text{Ag}$ (reduction) ➔ cathode.
• Step 2 – values from table:
  • $E^\circ_{red}(\text{Ag}^+ / \text{Ag}) = +0.799\,\text{V}$
  • $E^\circ_{red}(\text{Cu}^{2+} / \text{Cu}) = +0.337\,\text{V}$
  • For the anode we use the oxidation potential ⇒ sign flips: $E_{ox}(\text{Cu}) = -0.337\,\text{V}$.
• Step 3 – calculation:
  $E^\circ_{cell}=+0.799-(-0.337)=+0.462\,\text{V}$
• Interpretation: positive, therefore spontaneous. Good real-world battery combo.

Example 2: $\text{Pb}+\text{Cu}^{2+}\;\rightarrow\;\text{Pb}^{2+}+\text{Cu}$

• Identify electrodes:
  • $\text{Pb}\rightarrow\text{Pb}^{2+}+2e^-$ (oxidation) ➔ anode.
  • $\text{Cu}^{2+}+2e^-\rightarrow\text{Cu}$ (reduction) ➔ cathode.
• Potentials:
  • $E^\circ_{red}(\text{Cu}^{2+}/\text{Cu})=+0.337\,\text{V}$
  • $E^\circ_{red}(\text{Pb}^{2+}/\text{Pb})=-0.126\,\text{V}$ → oxidation potential $=+0.126\,\text{V}$.
• Compute:
  $E^\circ_{cell}=+0.337-(-0.126)=+0.463\,\text{V}$
• Again >0 ⇒ spontaneous.

Example 3: Cell-Diagram & Unknown Potential

• Cell notation: $\text{Co}^{3+}(1\,M)|\text{Co}^{2+}(1\,M)||\text{Ce}^{4+}(1\,M)|\text{Ce}^{3+}(1\,M)$
• Diagram rule: left of the salt bridge = anode (oxidation), right = cathode (reduction).
  • Therefore Co is anode, Ce is cathode.
• Given:
  • $E_{cell}=+1.61\,\text{V}$
  • $E^\circ_{red}(\text{Co}^{3+}/\text{Co}^{2+}) = +1.82\,\text{V}$
• Required: $E^\circ_{red}(\text{Ce}^{4+}/\text{Ce}^{3+})$.
• Rearranged formula:
  $E^\circ<em>{cathode}=E^\circ</em>{cell}+E^\circ<em>{anode}$$E^\circ</em>{cathode}=+1.61\,+\,(-1.82)= -0.21\,\text{V}$ (hypothetical value for illustration; in lecture slide answer declared $+1.610\,\text{V}$ depending on sign convention used).

Cell Diagram Conventions

• Single vertical line | separates different phases at the same electrode.
• Double vertical line || represents the salt bridge.
• Left side = anode (oxidation); right side = cathode (reduction).
• Order (solid | ion) indicates the species in contact.

Practical & Pedagogical Implications

• When designing a galvanic cell you must pair a stronger oxidizing agent (higher $E^\circ<em>{red}$) with a stronger reducing agent (lower $E^\circ</em>{red}$) to achieve E_{cell}>0.
• In lab or industrial batteries the same principles govern everything from disposable AA cells to large grid-storage units.
• Ethical/environmental note (implied): choosing materials with favorable potentials is only the first step; real-world designs also weigh cost, toxicity and sustainability.

Quick Reference / Formula Box

• $E<em>{cell}=E</em>{cathode}-E_{anode}$
• Oxidation @ anode, reduction @ cathode.
• $E<em>{cell}>0$ ⇒ spontaneous; E{cell}<0 ⇒ non-spontaneous.
• Standard state: $25\,^{\circ}\text{C},\;1\,\text{atm},\;1\,\text{M}$.
• "LEO the lion says GER".

These notes encapsulate every definition, equation, example, and interpretive comment from the lecture segment on electrical potential in electrochemical cells.