Why are formal potentials used instead of standard electrode potentials? Understand real-world battery testing accuracy

Formal potentials are used because battery electrolytes rarely behave like ideal standard-state solutions. Standard electrode potentials, (E^\circ), assume every species has unit activity, an assumption that is difficult to satisfy or verify in concentrated, non-aqueous, or chemically complex battery electrolytes. The formal potential, (E^{\circ'}), is measured or defined under the actual electrolyte conditions and incorporates activity coefficients, complexation, ion pairing, and related equilibria.

The practical distinction is simple: (E^\circ) describes an idealized thermodynamic reference state, while (E^{\circ'}) describes the redox couple in a specified chemical medium. Battery testing systems use formal potentials because the latter provides a more realistic basis for interpreting measured cell voltages.

Why Standard Potentials Are Difficult to Apply

Standard potentials assume unit activity

For a reduction reaction,

[ \mathrm{O + ne^- \rightleftharpoons R} ]

the Nernst equation is formally written as

[ E = E^\circ + \frac{RT}{nF}\ln\left(\frac{a_{\mathrm O}}{a_{\mathrm R}}\right) ]

where (a_{\mathrm O}) and (a_{\mathrm R}) are activities, not simply concentrations.

Activity is related to concentration through the activity coefficient:

[ a_i=\gamma_i[i] ]

The standard potential assumes the relevant species are at unit activity. In practical battery electrolytes, that condition is usually neither established experimentally nor representative of the cell under test.

Battery electrolytes are chemically non-ideal

Battery systems often contain high salt concentrations, multiple solvents, additives, supporting electrolytes, and reactive electrode products. These components can significantly change the effective chemical environment experienced by the redox species.

As a result, the measured potential depends not only on the nominal concentration of the oxidized and reduced forms, but also on:

• Activity coefficients
• Ionic strength
• Solvation
• Ion pairing
• Complex formation
• Acid–base equilibria
• Side reactions and coupled equilibria

Using (E^\circ) without accounting for these effects can produce a voltage prediction that is thermodynamically inappropriate for the actual cell.

What a Formal Potential Represents

It is a medium-specific redox reference

The formal potential, (E^{\circ'}), is the effective potential of a redox couple under specified experimental conditions. Those conditions include the solvent, supporting electrolyte, ionic strength, temperature, and often the composition or acidity of the medium.

For a generalized couple, the practical expression is:

[ E = E^{\circ'}+ \frac{RT}{nF} \ln\left( \frac{[\mathrm O]^{\nu_{\mathrm O}}} {[\mathrm R]^{\nu_{\mathrm R}}} \right) ]

Here, the concentrations are typically analytical or total concentrations, and the formal potential absorbs the activity-related corrections associated with the defined medium.

It incorporates otherwise difficult corrections

Rather than separately measuring every activity coefficient and equilibrium constant, researchers determine or use a formal potential valid for the electrolyte being studied. This consolidates several medium-dependent effects into one experimentally useful parameter.

That is particularly valuable when the redox species exists in several forms, such as a free ion plus solvent-bound, ion-paired, or complexed forms.

It is conditional, not universal

A formal potential is not an intrinsic constant that applies in every solvent or electrolyte. It is conditional on the environment in which it was measured.

For example, the oxygen/superoxide couple has different reported formal potentials in different aprotic solvents:

• Approximately (-0.87\ \mathrm{V}) versus aqueous SCE in DMF
• Approximately (-0.82\ \mathrm{V}) in acetonitrile
• Approximately (-0.73\ \mathrm{V}) in DMSO

These differences arise from changes in solvation, ion pairing, and other solvent-dependent interactions.

Why This Matters in Battery Cell Testing

It improves interpretation of measured cell voltage

Battery testing systems measure potentials under real electrolyte conditions, not ideal unit-activity conditions. A formal potential therefore provides a more appropriate baseline for comparing the measured voltage with thermodynamic expectations.

This helps researchers distinguish among:

• Changes caused by concentration
• Changes caused by electrolyte composition
• Electrode polarization
• Reference-electrode offsets
• Genuine changes in redox chemistry

It supports more accurate open-circuit voltage analysis

The equilibrium voltage of a cell depends on the difference between the effective electrode potentials in the actual electrolyte. If those potentials are based on aqueous or idealized standard values, predicted open-circuit voltages can be substantially wrong.

Formal potentials tailored to the electrolyte provide a more realistic estimate of the redox driving force and the voltage window available to the cell.

It helps identify parasitic reactions

A redox couple’s formal potential can shift when the electrolyte changes. That shift affects whether the electrolyte, electrode additive, dissolved gas, or reaction intermediate is thermodynamically accessible at a given electrode potential.

This is important in systems such as:

• Non-aqueous lithium batteries
• Metal–air batteries
• Redox-flow batteries
• Electrolytes containing transition-metal complexes
• Cells with reactive dissolved intermediates

Formal potentials therefore help define practical electrochemical stability limits and flag possible side reactions.

Why Non-Aqueous Systems Require Special Care

Solvent effects can be large

In aprotic solvents such as DMF, acetonitrile, and DMSO, the solvation energies of ions and radicals differ substantially. These differences alter the relative stability of oxidized and reduced forms and consequently shift the formal potential.

A potential measured in water should not automatically be transferred to a non-aqueous battery electrolyte.

Reference couples also shift

Even commonly used reference couples are medium-dependent. The ferrocene/ferrocenium couple, for example, has been reported at approximately:

• (+0.460\ \mathrm{V}) versus aqueous SCE in one acetonitrile electrolyte
• (+0.382\ \mathrm{V}) under another acetonitrile supporting-electrolyte condition

The exact value depends on the solvent and supporting electrolyte. This is why a reference value must always specify its solvent, electrolyte, concentration, temperature, and reference-electrode scale.

Pseudo-reference calibration becomes important

Battery testing systems frequently use internal or pseudo-reference electrodes, especially in sealed or non-aqueous cells. Their potential may drift or may not have a fixed aqueous reference scale.

A known formal redox couple can be used to calibrate that internal reference under the same electrolyte conditions. This reduces errors from:

• Liquid-junction potentials
• Solvent incompatibility
• Reference-electrode leakage
• Unstable reference potentials
• Incorrect conversion between potential scales

How Complexation Changes the Effective Potential

The measured couple may not be a free-ion couple

Consider a metal redox pair such as (\mathrm{Fe^{3+}/Fe^{2+}}). If either oxidation state binds strongly to chloride, phosphate, or another ligand, the concentrations of the free ions differ from their total analytical concentrations.

The equilibrium potential responds to the chemically active species, while the experiment may measure and report total concentrations. The formal potential accounts for that difference under the selected medium.

Acid and ligand composition can shift the potential

Reported formal potentials for the (\mathrm{Fe(III)/Fe(II)}) couple vary with the acid medium, including approximate values of:

• (+0.735\ \mathrm{V}) versus NHE in (1\ \mathrm{M}) perchloric acid
• (+0.70\ \mathrm{V}) in (1\ \mathrm{M}) hydrochloric acid
• (+0.53\ \mathrm{V}) in (10\ \mathrm{M}) hydrochloric acid
• (+0.46\ \mathrm{V}) in (2\ \mathrm{M}) phosphoric acid

The shifts reflect differences in complexation and chemical interactions with the medium. A single aqueous standard potential would not capture these conditions.

Understanding the Trade-offs

Formal potentials are more useful but less transferable

The main advantage of (E^{\circ'}) is practical accuracy in a defined medium. The corresponding limitation is that the value may not transfer reliably to another solvent, salt concentration, supporting electrolyte, or temperature.

A formal potential should therefore always be reported with its measurement conditions.

Concentration-based equations remain approximations

Using concentrations with (E^{\circ'}) is often the most practical approach, but it does not eliminate non-ideal behavior. If the electrolyte composition changes substantially during cycling, the activity coefficients and speciation may also change.

For high-precision modeling, researchers may still need activity-based thermodynamic models or direct measurements under multiple compositions.

Formal potential does not describe kinetics

A formal potential primarily describes the thermodynamic position of a redox couple under defined conditions. It does not by itself determine:

• Charge-transfer rate
• Exchange-current density
• Diffusion limitations
• Nucleation barriers
• Overpotential
• Electrode resistance

These kinetic and transport properties must be characterized separately through appropriate electrochemical measurements.

Mixing potential scales creates errors

Comparing a formal potential measured against aqueous SCE or NHE with a value measured against a non-aqueous pseudo-reference can lead to misleading conclusions. The reference electrode, solvent, supporting electrolyte, and calibration procedure must be stated clearly.

Making the Right Choice for Your Goal

The correct choice depends on whether you are describing an ideal thermodynamic reference or interpreting a real battery experiment.

• If your primary focus is fundamental thermodynamic comparison: Use (E^\circ), but state that the comparison assumes standard-state activities and recognize that real electrolyte effects may be excluded.
• If your primary focus is battery-cell voltage prediction: Use (E^{\circ'}) measured or validated in the actual electrolyte medium.
• If your primary focus is non-aqueous or concentrated-electrolyte testing: Use medium-specific formal potentials and calibrate the internal or pseudo-reference electrode under matching conditions.
• If your primary focus is electrolyte stability and side reactions: Compare the relevant formal potentials with the operating voltage range, while separately accounting for kinetic barriers and polarization.
• If your primary focus is quantitative modeling across changing compositions: Treat (E^{\circ'}) as conditional and consider activity coefficients, speciation, and composition-dependent potential shifts.

Formal potentials are used in battery testing because they connect electrochemical theory to the chemical reality of the electrolyte being measured.

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