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5.3 Electrochemical Cells, Reduction Potentials & the Nernst Equation
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6 Organic Chemistry: Structure, Stereochemistry & Mechanisms
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7 Bio-Organic Reactions, Laboratory Separations & Spectroscopy
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8 Biochemistry: Amino Acids, Peptides & Enzymes
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9 Biochemistry: Cellular Metabolism & Bioenergetics
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10 Molecular Biology: Nucleic Acids & Genetic Technologies
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13 Human Physiology: Control & Transport Systems
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5.3 Electrochemical Cells, Reduction Potentials & the Nernst Equation
Key Takeaways Explain This Topic AI
In all electrochemical cells, oxidation occurs exclusively at the anode ('AN OX') and reduction occurs exclusively at the cathode ('RED CAT'), with electron flow traveling through the external wire from anode to cathode (e⁻: Anode → Cathode).
Galvanic (voltaic) cells are thermodynamically spontaneous (E°_cell > 0, ΔG° < 0) with a negative anode and positive cathode, whereas electrolytic cells are non-spontaneous (E°_cell < 0, ΔG° > 0), requiring an external power source that renders the anode positive and cathode negative.
Standard reduction potentials (E°) are intensive properties that reflect electron affinity relative to the Standard Hydrogen Electrode (SHE, 0.00 V); cell potential is calculated as E°_cell = E°_cathode - E°_anode and is never multiplied by stoichiometric coefficients.
The Nernst equation (E_cell = E°_cell - (0.0592 / n) log Q at 25°C) dictates cell voltage under non-standard conditions; concentration cells operate with identical electrodes (E°_cell = 0.00 V) driven entirely by the entropy of dilution between concentration gradients.
Faraday's law of electrolysis governs quantitative electrodeposition: the moles of chemical substance plated or gas liberated equal (I × t) / (n × F), where F is Faraday's constant (approximately 96,500 C/mol e⁻).
Last updated: September 2026
5.3 Electrochemical Cells, Reduction Potentials & the Nernst Equation
Note
Foundational Standard : Electrochemical principles govern mitochondrial oxidative phosphorylation, neuronal membrane potentials, action potentials, biosensors, and redox homeostasis. The MCAT heavily tests half-reaction balancing, cell notation, reduction potentials, the Nernst equation, and electrolytic calculations.
Electrochemistry analyzes chemical-electrical energy interconversion in redox reactions.
Oxidation-Reduction Fundamentals and Half-Reaction Balancing
Redox reactions involve electron transfer:
Oxidation : Loss of electrons ( e − e^- e − ); oxidation state increases.
Reduction : Gain of electrons ( e − e^- e − ); oxidation state decreases.
Mnemonics : OIL RIG (Oxidation Is Loss, Reduction Is Gain) and LEO says GER (Lose Electrons Oxidation, Gain Electrons Reduction).
Oxidizing Agent (Oxidant) : Accepts electrons; becomes reduced.
Reducing Agent (Reductant) : Donates electrons; becomes oxidized.
Oxidation State Assignment Rules
Free elements = 0 ( Na , O 2 , Fe \text{Na}, \text{O}_2, \text{Fe} Na , O 2 , Fe ).
Monatomic ions = ionic charge ( Fe 3 + = + 3 , Cl − = − 1 \text{Fe}^{3+} = +3, \text{Cl}^- = -1 Fe 3 + = + 3 , Cl − = − 1 ).
Group 1 = +1 ; Group 2 = +2 ; Fluorine = -1 .
Hydrogen = +1 with nonmetals, -1 with metal hydrides ( NaH \text{NaH} NaH ).
Oxygen = -2 in oxides, -1 in peroxides ( H 2 O 2 \text{H}_2\text{O}_2 H 2 O 2 ), +2 in OF 2 \text{OF}_2 OF 2 .
Sum of oxidation numbers equals net species charge.
Half-Reaction Balancing Method
Separate oxidation and reduction half-reactions.
Balance elements other than H and O.
Balance O using H 2 O \text{H}_2\text{O} H 2 O ; balance H using H + \text{H}^+ H + .
Balance charge adding e − e^- e − to the more positive side.
Multiply half-reactions by integers to equalize electrons ( n n n ).
Sum half-reactions and cancel identical species.
In base, neutralize H + \text{H}^+ H + with OH − \text{OH}^- OH − to form H 2 O \text{H}_2\text{O} H 2 O , then simplify waters.
Electrochemical Cell Architectures: Galvanic vs. Electrolytic
All electrochemical cells follow two universal rules:
"AN OX" : Oxidation occurs at the ANODE .
"RED CAT" : Reduction occurs at the CATHODE .
Electron Flow : Electrons travel from ANODE to CATHODE through the external circuit.
Current Flow : Conventional electrical current flows oppositely, from CATHODE to ANODE .
Galvanic (Voltaic) Cells
Galvanic cells exploit spontaneous redox reactions ( Δ G ∘ < 0 , E cell ∘ > 0 \Delta G^\circ < 0, E^\circ_{\text{cell}} > 0 Δ G ∘ < 0 , E cell ∘ > 0 ) to generate electrical work:
Anode Polarity : Negative ( − - − ) ; oxidation releases electrons, creating high negative charge density.
Cathode Polarity : Positive ( + + + ) ; consumes electrons during reduction.
Salt Bridge : Contains inert electrolyte (e.g., KNO 3 \text{KNO}_3 KNO 3 ). Anions migrate into the anode compartment to neutralize generated cations; cations migrate into the cathode compartment to replace consumed cations. Without a salt bridge, rapid charge buildup halts current.
Electrolytic Cells
Electrolytic cells use an external power supply to force a non-spontaneous reaction ( Δ G ∘ > 0 , E cell ∘ < 0 \Delta G^\circ > 0, E^\circ_{\text{cell}} < 0 Δ G ∘ > 0 , E cell ∘ < 0 ):
Anode Polarity : Positive ( + + + ) ; connected to the battery's positive terminal, which forcibly removes electrons.
Cathode Polarity : Negative ( − - − ) ; connected to the battery's negative terminal, which pumps electrons into the electrode.
Characteristic Galvanic (Voltaic) Cell Electrolytic Cell
Thermodynamic Spontaneity Spontaneous ( Δ G ∘ < 0 \Delta G^\circ < 0 Δ G ∘ < 0 ) Non-spontaneous ( Δ G ∘ > 0 \Delta G^\circ > 0 Δ G ∘ > 0 )
Standard Cell Potential ( E cell ∘ E^\circ_{\text{cell}} E cell ∘ ) Positive ( > 0 > 0 > 0 ) Negative ( < 0 < 0 < 0 )
- Anode (Oxidation) Negative ( − - − ) Positive ( + + + )
- Cathode (Reduction) Positive ( + + + ) Negative ( − - − )
- Electron Flow Anode to Cathode through wire Anode to Cathode through wire
- Internal Charge Balance Salt bridge ion migration Electrolyte ion migration driven by external field
- Typical Applications Batteries, pacemakers, fuel cells Electroplating, rechargeable battery recharging
- Standard Reduction Potentials ( E ∘ E^\circ E ∘ ) and Cell Voltage
Potentials are measured relative to the Standard Hydrogen Electrode (SHE) , defined as 0.00 V 0.00\text{ V} 0.00 V ( 2 H + ( a q , 1.0 M ) + 2 e − ⇌ H 2 ( g , 1.0 atm ) 2\text{H}^+(aq, 1.0\text{ M}) + 2e^- \rightleftharpoons \text{H}_2(g, 1.0\text{ atm}) 2 H + ( a q , 1.0 M ) + 2 e − ⇌ H 2 ( g , 1.0 atm ) ):
More positive E ∘ E^\circ E ∘ : Greater electron affinity; stronger oxidizing agent, readily reduced ( F 2 + 2 e − → 2 F − \text{F}_2 + 2e^- \to 2\text{F}^- F 2 + 2 e − → 2 F − , E ∘ = + 2.87 V E^\circ = +2.87\text{ V} E ∘ = + 2.87 V ).
More negative E ∘ E^\circ E ∘ : Lower electron affinity; oxidized form difficult to reduce, reduced form is a strong reducing agent ( Li + + e − → Li \text{Li}^+ + e^- \to \text{Li} Li + + e − → Li , E ∘ = − 3.04 V E^\circ = -3.04\text{ V} E ∘ = − 3.04 V ).
The standard cell potential is: E cell ∘ = E cathode ∘ − E anode ∘ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} E cell ∘ = E cathode ∘ − E anode ∘
where both values are standard reduction potentials.
INTENSIVE PROPERTY RULE : Reduction potential is an intensive property ( V = J/C \text{V} = \text{J/C} V = J/C ). NEVER multiply E ∘ E^\circ E ∘ by stoichiometric coefficients when balancing electrons!
Thermodynamics of Electrochemical Cells: Δ G ∘ \Delta G^\circ Δ G ∘ , E cell ∘ E^\circ_{\text{cell}} E cell ∘ & K eq K_{\text{eq}} K eq
Electrical work connects free energy to cell potential: Δ G ∘ = − n F E cell ∘ \Delta G^\circ = -n F E^\circ_{\text{cell}} Δ G ∘ = − n F E cell ∘
where n n n is moles of electrons transferred and F F F is Faraday's constant ( 96 , 485 C/mol e − ≈ 96 , 500 C/mol e − 96,485\text{ C/mol }e^- \approx \mathbf{96,500\text{ C/mol }e^-} 96 , 485 C/mol e − ≈ 96 , 500 C/mol e − ).
E cell ∘ > 0 ⟹ Δ G ∘ < 0 E^\circ_{\text{cell}} > 0 \implies \Delta G^\circ < 0 E cell ∘ > 0 ⟹ Δ G ∘ < 0 ( Spontaneous, Galvanic ).
E cell ∘ < 0 ⟹ Δ G ∘ > 0 E^\circ_{\text{cell}} < 0 \implies \Delta G^\circ > 0 E cell ∘ < 0 ⟹ Δ G ∘ > 0 ( Non-spontaneous, Electrolytic ).
E cell ∘ = 0 ⟹ Δ G ∘ = 0 E^\circ_{\text{cell}} = 0 \implies \Delta G^\circ = 0 E cell ∘ = 0 ⟹ Δ G ∘ = 0 ( Dynamic Equilibrium ).
Linking Δ G ∘ = − R T ln K eq \Delta G^\circ = -RT\ln K_{\text{eq}} Δ G ∘ = − RT ln K eq and Δ G ∘ = − n F E cell ∘ \Delta G^\circ = -nFE^\circ_{\text{cell}} Δ G ∘ = − n F E cell ∘ at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C gives: E cell ∘ = 0.0592 n log 10 K eq E^\circ_{\text{cell}} = \frac{0.0592}{n}\log_{10} K_{\text{eq}} E cell ∘ = n 0.0592 lo g 10 K eq
A cell with K eq > 1 K_{\text{eq}} > 1 K eq > 1 yields a positive standard voltage.
The Nernst Equation and Non-Standard Conditions
Dynamic concentrations alter cell voltage via the Nernst equation : E cell = E cell ∘ − R T n F ln Q = E cell ∘ − 0.0592 n log 10 Q ≈ E cell ∘ − 0.06 n log 10 Q E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF}\ln Q = E^\circ_{\text{cell}} - \frac{0.0592}{n}\log_{10} Q \approx E^\circ_{\text{cell}} - \frac{0.06}{n}\log_{10} Q E cell = E cell ∘ − n F RT ln Q = E cell ∘ − n 0.0592 lo g 10 Q ≈ E cell ∘ − n 0.06 lo g 10 Q
Q < 1 Q < 1 Q < 1 (reactants high, products low): log 10 Q < 0 ⟹ E cell > E cell ∘ \log_{10} Q < 0 \implies E_{\text{cell}} > E^\circ_{\text{cell}} lo g 10 Q < 0 ⟹ E cell > E cell ∘ (voltage rises).
Q > 1 Q > 1 Q > 1 (products accumulated): log 10 Q > 0 ⟹ E cell < E cell ∘ \log_{10} Q > 0 \implies E_{\text{cell}} < E^\circ_{\text{cell}} lo g 10 Q > 0 ⟹ E cell < E cell ∘ (voltage falls).
At Equilibrium ( Q = K eq Q = K_{\text{eq}} Q = K eq ) : E cell = 0.00 V E_{\text{cell}} = 0.00\text{ V} E cell = 0.00 V and Δ G = 0 \Delta G = 0 Δ G = 0 (battery discharges completely).
Concentration Cells and Membrane Potentials
A concentration cell contains identical half-cells differing solely in solute concentrations. Because electrodes are chemically identical, E cell ∘ = 0.00 V \mathbf{E^\circ_{\text{cell}} = 0.00\text{ V}} E cell ∘ = 0.00 V , driven purely by the entropy of dilution:
Anode : Dilute compartment ( [ M n + ] dilute [M^{n+}]_{\text{dilute}} [ M n + ] dilute ); oxidation increases ion concentration.
Cathode : Concentrated compartment ( [ M n + ] conc [M^{n+}]_{\text{conc}} [ M n + ] conc ); reduction consumes ions.
Voltage: E cell = 0.0592 n log 10 ( [ M n + ] conc [ M n + ] dilute ) E_{\text{cell}} = \frac{0.0592}{n}\log_{10}\left(\frac{[M^{n+}]_{\text{conc}}}{[M^{n+}]_{\text{dilute}}}\right) E cell = n 0.0592 lo g 10 ( [ M n + ] dilute [ M n + ] conc ) .
Biological membranes function as concentration cells. The biological Nernst potential at 37 ∘ C 37^\circ\text{C} 3 7 ∘ C calculates single-ion equilibrium voltages: V eq = 61.5 mV z log 10 ( [ ion ] out [ ion ] in ) V_{\text{eq}} = \frac{61.5\text{ mV}}{z}\log_{10}\left(\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}\right) V eq = z 61.5 mV lo g 10 ( [ ion ] in [ ion ] out )
For potassium ( [ K + ] in = 140 mM , [ K + ] out = 4 mM [\text{K}^+]_{\text{in}} = 140\text{ mM}, [\text{K}^+]_{\text{out}} = 4\text{ mM} [ K + ] in = 140 mM , [ K + ] out = 4 mM ), V K ≈ − 95 mV V_K \approx -95\text{ mV} V K ≈ − 95 mV , driving the resting membrane potential ( V m ≈ − 70 mV V_m \approx -70\text{ mV} V m ≈ − 70 mV ).
Faraday's Law of Electrolysis
Faraday's Law relates electric charge to electrodeposition: q = I × t ⟹ n e − = I × t F q = I \times t \implies n_{e^-} = \frac{I \times t}{F} q = I × t ⟹ n e − = F I × t Moles of Metal Plated ( n metal ) = I × t n × F \text{Moles of Metal Plated } (n_{\text{metal}}) = \frac{I \times t}{n \times F} Moles of Metal Plated ( n metal ) = n × F I × t Mass Plated ( m ) = I × t × Molar Mass n × F \text{Mass Plated } (m) = \frac{I \times t \times \text{Molar Mass}}{n \times F} Mass Plated ( m ) = n × F I × t × Molar Mass
Worked Example : Plating copper metal ( Cu \text{Cu} Cu , 63.55 g/mol 63.55\text{ g/mol} 63.55 g/mol ) from CuSO 4 \text{CuSO}_4 CuSO 4 ( Cu 2 + + 2 e − → Cu \text{Cu}^{2+} + 2e^- \to \text{Cu} Cu 2 + + 2 e − → Cu , n = 2 n = 2 n = 2 ) using 5.0 A 5.0\text{ A} 5.0 A for 1930 seconds 1930\text{ seconds} 1930 seconds :
Charge: q = 5.0 A × 1930 s = 9650 C q = 5.0\text{ A} \times 1930\text{ s} = 9650\text{ C} q = 5.0 A × 1930 s = 9650 C .
Moles of electrons: n e − = 9650 C / 96 , 500 C/mol e − = 0.100 mol e − n_{e^-} = 9650\text{ C} / 96,500\text{ C/mol }e^- = 0.100\text{ mol }e^- n e − = 9650 C /96 , 500 C/mol e − = 0.100 mol e − .
Moles of Cu \text{Cu} Cu : n Cu = 0.100 / 2 = 0.0500 mol Cu n_{\text{Cu}} = 0.100 / 2 = 0.0500\text{ mol }\text{Cu} n Cu = 0.100/2 = 0.0500 mol Cu .
Mass plated: m = 0.0500 mol × 63.55 g/mol = 3.18 g m = 0.0500\text{ mol} \times 63.55\text{ g/mol} = 3.18\text{ g} m = 0.0500 mol × 63.55 g/mol = 3.18 g .