SCIENCE · INVESTIGATE AND EXPLAIN

Preserve reaction direction and electron equivalents in a cell potential

A cell potential belongs to a specified redox direction and activity state.

Learning outcome: Vary Q at fixed E° and then E° at fixed Q. Track signed potential, ΔrG and the equilibrium quotient rather than treating voltage as an amount of energy.

Starting recap

Refresh state-function boundaries, absolute temperature, dimensionless logarithms, written reaction/electron equivalents, conserved charge and formal orbital/identity bookkeeping.

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Try

For a one-electron fictional reaction at298.15 K, each tenfold Q increase lowers E by about.05916 V; ΔrG=−FE.

Open the experiment

Predict

Can the actual cell direction reverse while its standard potential remains positive?

Your prediction and reason

Experiment

Vary Q at fixed E° and then E° at fixed Q. Track signed potential, ΔrG and the equilibrium quotient rather than treating voltage as an amount of energy.

Track cell direction and free energy with a defined reaction

Worked teaching model · synthetic values · Fictional one-electron cell reaction M(s)+N+⇌M++N(s), pure-metal activities1 and ideal controlled ionic activity ratio Q=a(M+)/a(N+), T298.15 K. E=E°−RT/F ln Q; ΔrG=−FE. Potentials are for the fixed written direction; negative E favors the reverse, not negative absolute energy or an automatically functioning device.

Standard potential of the written one-electron reaction: 0.06 V Log10 dimensionless reaction quotient: 1 log10 Q

Reset keeps your prediction, captures and practice history.

Signed cell potential: solid

Axes rescale. A multiplicity distribution, inverse-temperature relation and charge-budget graph have different meanings. Read each axis and do not treat a computed curve as additional measured evidence.

All calculated plot coordinates

Signed cell potential
log10 dimensionless activity quotient	potential for fixed written reaction (V)
-3	0.237478
-2.9	0.2315621
-2.8	0.2256462
-2.7	0.2197302
-2.6	0.2138143
-2.5	0.2078984
-2.4	0.2019824
-2.3	0.1960665
-2.2	0.1901506
-2.1	0.1842346
-2	0.1783187
-1.9	0.1724028
-1.8	0.1664868
-1.7	0.1605709
-1.6	0.154655
-1.5	0.148739
-1.4	0.1428231
-1.3	0.1369072
-1.2	0.1309912
-1.1	0.1250753
-1	0.1191593
-0.9	0.1132434
-0.8	0.1073275
-0.7	0.1014115
-0.6	0.09549561
-0.5	0.08957967
-0.4	0.08366374
-0.3	0.0777478
-0.2	0.07183187
-0.1	0.06591593
0	0.06
0.1	0.05408407
0.2	0.04816813
0.3	0.0422522
0.4	0.03633626
0.5	0.03042033
0.6	0.02450439
0.7	0.01858846
0.8	0.01267252
0.9	0.006756585
1	0.0008406503
1.1	-0.005075285
1.2	-0.01099122
1.3	-0.01690715
1.4	-0.02282309
1.5	-0.02873902
1.6	-0.03465496
1.7	-0.04057089
1.8	-0.04648683
1.9	-0.05240276
2	-0.0583187
2.1	-0.06423463
2.2	-0.07015057
2.3	-0.0760665
2.4	-0.08198244
2.5	-0.08789837
2.6	-0.09381431
2.7	-0.09973024
2.8	-0.1056462
2.9	-0.1115621
3	-0.117478

Calculated under the declared model
Quantity	Value	Unit
Signed potential for written reaction	0.0008406503	V
Current reaction free energy	-0.08111042	kJ/mol reaction
Standard reaction free energy	-5.78912	kJ/mol reaction
Log10 equilibrium constant	1.01421	log10 K
Transferred electrons per written reaction	1	mol electrons/mol reaction

The written reaction can deliver reversible electrical work in the ideal galvanic direction.

Subtract anode reduction potential from cathode reduction potential for a chosen galvanic direction, but never multiply electrode potentials by balancing coefficients: free energy and electron amount scale instead. Oxidation remains at anode and reduction at cathode in both galvanic and electrolytic operation; external forcing reverses the spontaneous direction, not those definitions. Real overpotential and resistance are omitted.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

The written reaction can deliver reversible electrical work in the ideal galvanic direction.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Balance the electron ledger before the energy ledger

The fictional written reaction is M(s)+N+⇌M++N(s), transferring one electron. Pure-metal activities are one and Q=a(M+)/a(N+). At298.15 K, E=E°−RT/F lnQ and ΔrG=−FE. A negative E for this fixed written direction means the reverse reaction is favored under the stated conditions.

A galvanic cathode is where reduction occurs and anode where oxidation occurs. Those reaction definitions also apply in an electrolytic cell, although external electrical work drives a nonspontaneous direction. Electrode sign and direction should be inferred for the specified operation rather than memorized without a boundary.

Distinguish intensive potential from extensive reaction energy

When half-reactions are scaled to cancel electrons, their potentials are not multiplied by the coefficients. Free energy and electron amount scale together, leaving E unchanged. For a chosen galvanic direction, subtract the anode reduction potential from the cathode reduction potential using the same reference convention.

Real working cells add ohmic losses, electrode overpotentials, junction effects and changing composition. The ideal Nernst relation predicts a reversible potential, not a guaranteed current or a physical operating protocol.

Transfer and check

For a separate two-electron written reaction with E=.0800 V, ΔrG=−2F(.0800)≈−15.438 kJ/mol reaction. Doubling the written reaction gives four electrons and twice that molar-per-written-reaction free energy, but still .0800 V. Explain why multiplying voltage itself by two would count the scaling twice.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All prose, cases, graphs and questions are original. These supplied thermodynamic, electrical, nuclear or orbital models are not actual measurements, apparatus instructions, synthesis protocols or practical certification. Retain conventions, independent constraints, changed-case reasoning and limits. No heating, wiring, electrolysis, source handling or chemical manipulation is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why are reduction potentials not multiplied by coefficients when balancing electrons?

Your explanation and limitations

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