Connect voltage, charge and reaction free energy

Keep the reaction unit visible

Compare the two written reactions Zn + Cu²⁺ → Zn²⁺ + Cu and 3 Zn + 3 Cu²⁺ → 3 Zn²⁺ + 3 Cu. They describe the same proportions. However, one mole of the first written reaction consumes one mole of zinc, while one mole of the second consumes three. “Per mole of reaction” is meaningful only with its equation specified.

The widget uses a whole-equation multiplier, not a slider for physically measured reaction progress. Multiplying all coefficients by three changes the definition of a reaction unit. It does not add a third electrode or place three cells in series.

First set zinc oxidation/copper reduction to multiplier 1. Record the voltage, electron stoichiometry and charge per mole of reaction. Predict which will change before choosing multiplier 3. Your evidence should include both captures and an explanation of the normalization.

Convert the units before interpreting the sign

For the first equation, n = 2 mol electrons per mol reaction. Here n is a positive stoichiometric factor. With the rounded Faraday constant F = 96485 C/mol electrons, the corresponding charge magnitude is nF = 192970 C/mol reaction. At standard potential +1.10 V, or +1.10 J/C, the energy magnitude is 192970 × 1.10 = 212267 J/mol reaction.

The standard molar reaction Gibbs free-energy change is ΔrG° = −nFE°cell. ΔrG° means the standard free-energy change per mole of the displayed reaction; the subscript r identifies reaction, and the degree symbol identifies reference states. Divide joules by 1000 to obtain kilojoules. Thus the modeled value is −212.267 kJ/mol reaction.

The negative sign means that forward reaction lowers Gibbs free energy at the stated standard conditions. Under reversible, constant-temperature and constant-pressure conditions, its magnitude gives the maximum non-expansion work available per mole of reaction. For the ideal electrochemical case considered here, that work can be electrical. It is not a promise that a practical device delivers that amount to a load.

OpenStax: potential and free energy gives the thermodynamic relation. The numerical precision here follows rounded teaching inputs; the last displayed digits are not an experimental uncertainty claim.

Why the voltage stays the same

At multiplier 3, the displayed reaction transfers six moles of electrons per mole of the newly defined reaction. The charge is 578910 C/mol reaction, and ΔrG° is −636.801 kJ/mol reaction. The potential stays +1.10 V because both energy and charge have tripled.

Check this yourself: convert 636.801 kJ to 636801 J, then divide by 578910 C. The ratio is 1.10 J/C. Carrying the energy sign in the thermodynamic equation gives E°cell = −ΔrG°/(nF). Dividing a kilojoule value directly by coulombs without converting would introduce a factor-of-1000 error.

For the same physical amount of conversion, the two equation normalizations must agree. Consuming one mole of zinc is one mole of the unscaled reaction but only one third of a mole of the tripled reaction. One third of −636.801 kJ is −212.267 kJ. The algebra has not created additional energy.

Distinguish reversal from scaling

At multiplier 3, select copper oxidation/zinc reduction. E°cell becomes −1.10 V, and ΔrG° becomes +636.801 kJ/mol reaction. Electron stoichiometry remains positive at six. Reversal changes direction and swaps the electrode roles; it does not create a negative number of electrons.

The positive standard free-energy change means the forward written direction is unfavorable under the specified reference conditions. It does not mean the reverse reaction is impossible to drive with external work. Nor does a negative ΔrG° prove a reaction is fast: the model has no activation barrier, surface kinetics or transport calculation.

The general thermodynamic criterion uses the actual reaction free energy at the actual composition. ΔrG° alone is a reference quantity. As a closed cell changes composition, its potential and reaction free energy can change; multiplying a fixed standard-state value by an arbitrary complete discharge amount is not a substitute for tracking that change. This investigation intentionally holds reference states fixed.

Diagnose what a power claim is missing

A report says, “The standard reaction free energy is −212.267 kJ/mol, so this cell delivers 212267 watts.” Explain the error. A watt is a joule per second. The report supplies neither a reaction rate nor an electrical current or duration. It also omits practical losses and changing composition. Free energy per mole cannot by itself establish delivered power.

Transfer: A fictional reaction transfers three moles of electrons per mole of reaction and has E°cell = +0.40 V. Use F = 96485 C/mol electrons. Calculate ΔrG°, then give the result for the reverse reaction written with every coefficient doubled.

Check the free-energy transfer

Forward: −3 × 96485 × 0.40 / 1000 = −115.782 kJ/mol reaction. The doubled reverse has n = 6, E°cell = −0.40 V and ΔrG° = +231.564 kJ/mol of that new equation. Reversal changes the signs; doubling changes the reaction normalization. Neither operation provides a current or a time.