ΔG and Cell Potential: A-Level Chemistry Guide

In A-Level Chemistry, electrochemical cells represent one of the most elegant intersections of thermodynamics and redox chemistry. The electrode potential of a half-cell — a measurable physical quantity in volts — is directly and quantitatively linked to the Gibbs free energy change of the corresponding redox reaction. Understanding this relationship is essential for tackling the full range of electrochemistry questions, from simple identification of cathode and anode materials through to quantitative calculations involving the Nernst equation. This guide systematically builds the conceptual framework, clarifies the key relationships, and addresses the procedural errors that most frequently cost marks in this topic area.

What standard electrode potentials measure

The standard electrode potential, E°, of a half-cell is defined as the potential difference developed between a metal electrode immersed in a solution containing its ions at a concentration of 1 mol dm⁻³ and a standard hydrogen electrode, measured under standard conditions (298 K, 1 atm pressure). The standard hydrogen electrode is assigned a potential of exactly zero volts by convention, and all other E° values are measured relative to it.

For a given reduction–oxidation (redox) couple, the sign and magnitude of E° encode critical thermodynamic information. A more positive E° value indicates a stronger tendency for the species to accept electrons — to undergo reduction. Conversely, a negative E° value indicates that the species is more likely to lose electrons — to undergo oxidation — under standard conditions. This hierarchy of E° values enables prediction of whether a given redox reaction will proceed spontaneously when two half-cells are combined.

Standard electrode potentials are listed in data tables, and candidates are expected to extract and interpret these values accurately. The key convention is that E° values are always quoted for reduction half-reactions, even when the species in question functions as an oxidising agent in a galvanic cell. This consistency is what allows the E° value of a half-cell to be used regardless of the direction in which it operates within a particular electrochemical cell.

The Gibbs free energy–electrode potential relationship

The central conceptual link in electrochemistry is the equation that relates Gibbs free energy change to the electrical work a cell can perform:

ΔG = −nFE

In this expression, n represents the number of electrons transferred in the balanced cell reaction, F is the Faraday constant (96,500 C mol⁻¹), and E is the cell potential in volts. The product nFE has the units of joules — the electrical work obtainable from one mole of the cell reaction. This is not a definition but a derived thermodynamic result, and it connects two fundamental domains of physical chemistry: the thermodynamics of spontaneity and the measurable electrical properties of electrochemical cells.

The sign convention follows directly from this relationship. When E is positive, ΔG is negative, and the cell reaction is thermodynamically spontaneous in the forward direction — this is a galvanic cell. When E is negative, ΔG is positive, and the reaction is non-spontaneous in the forward direction — it would proceed in the reverse direction if the electrodes were connected without an external voltage source. When E equals zero, ΔG equals zero, and the system is at equilibrium.

From this foundation, the relationship between the standard equilibrium constant K and the standard cell potential E° emerges through substitution into the Gibbs free energy equation:

log₁₀K = nE° / 0.0592

This expression, valid at 298 K, provides a direct route to the equilibrium constant without the intermediate step of calculating ΔG°. The magnitude of nE° determines how far to the right the equilibrium lies: a large positive nE° value produces a very large K, indicating an essentially complete reaction in the forward direction, while a negative nE° value produces a K much less than 1, indicating that the reverse reaction is favoured at equilibrium.

Calculating standard cell potentials from half-cell data

When two half-cells are combined to form a galvanic cell, the standard cell potential is calculated as the difference between the two standard electrode potentials, taken with their appropriate signs:

E°cell = E°cathode − E°anode

The cathode is the half-cell where reduction occurs; the anode is where oxidation occurs. In any galvanic cell, the half-reaction with the more positive E° value proceeds as reduction (and therefore functions as the cathode), while the half-reaction with the less positive E° value reverses and proceeds as oxidation (functioning as the anode). This systematic approach — comparing E° values rather than attempting to recall which metal is which — ensures that candidates consistently identify the correct electrodes.

For the Daniell cell (zinc–copper system), E° for the Cu²⁺/Cu half-cell is +0.34 V, and E° for the Zn²⁺/Zn half-cell is −0.76 V. Since +0.34 V is the more positive value, Cu²⁺ is reduced at the copper electrode (cathode), and Zn is oxidised at the zinc electrode (anode). The standard cell potential is therefore:

E°cell = (+0.34 V) − (−0.76 V) = +1.10 V

The cell notation for this arrangement is Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s), where the single vertical bars denote phase boundaries and the double vertical bar denotes the salt bridge. The more negative electrode (the anode) is conventionally placed on the left-hand side of the cell notation.

E°cell > 0: forward reaction is spontaneous (galvanic cell)
E°cell = 0: system at equilibrium
E°cell < 0: forward reaction is non-spontaneous; reverse reaction is spontaneous

Applying the Nernst equation to non-standard conditions

The standard cell potential E° applies only when all species are at their standard concentrations (typically 1 mol dm⁻³ for solutes, 1 atm for gases). When concentrations deviate from standard conditions, the actual cell potential E differs from E°, and the Nernst equation provides the quantitative correction:

E = E° − (RT / nF) ln Q

At 298 K, this can be expressed in base-10 logarithm form for computational convenience:

E = E° − (0.0592 / n) log₁₀ Q

In this expression, Q is the reaction quotient for the overall cell reaction, expressed in terms of concentrations and partial pressures at the moment of interest. The reaction quotient Q takes the same algebraic form as the equilibrium expression K for the overall cell reaction, but it describes the current state of the system rather than the equilibrium state.

Consider the Daniell cell again, with the cell reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s). The reaction quotient is:

Q = [Zn²⁺] / [Cu²⁺]

If [Cu²⁺] is reduced to 0.001 mol dm⁻³ while [Zn²⁺] remains at 1 mol dm⁻³, then Q = 1 / 0.001 = 1000. With n = 2, the Nernst equation gives:

E = 1.10 − (0.0592 / 2) × log₁₀(1000) = 1.10 − (0.0296) × 3 = 1.10 − 0.0888 ≈ 1.01 V

The cell potential has decreased from the standard value because the reaction has shifted in the forward direction (Le Chatelier's principle: reducing Cu²⁺ concentration favours the forward reaction, which consumes Cu²⁺), decreasing the thermodynamic driving force of the overall cell reaction.

The sign of the correction term has a direct physical interpretation: when Q < K (reactant-favoured conditions), the correction term is negative, E is greater than E°, and the cell potential is larger — the forward reaction is more strongly favoured than under standard conditions. When Q > K (product-favoured conditions), the correction term is positive, E is less than E°, and the cell potential is reduced. These relationships must be understood conceptually, not merely applied as formula-filling exercises.

Galvanic cells, electrolytic cells, and the question of spontaneity

One recurring conceptual confusion in A-Level Chemistry electrochemistry concerns the relationship between cell type and thermodynamic spontaneity. Galvanic cells are often described as spontaneous and electrolytic cells as non-spontaneous, but this shorthand can mislead if not understood precisely.

A galvanic cell converts chemical energy into electrical energy; the cell reaction proceeds spontaneously (ΔG < 0, E > 0). An electrolytic cell consumes electrical energy from an external power supply to drive a non-spontaneous reaction (ΔG > 0, E < 0). The distinction is not about whether the reaction itself is thermodynamically spontaneous in isolation, but about the direction of energy conversion and the sign convention of the applied or measured potential.

The same redox couple can appear in both contexts. For example, the electrolysis of molten sodium chloride involves the Na⁺/Na half-reaction at the cathode and the Cl₂/Cl⁻ half-reaction at the anode. The reaction as written is non-spontaneous (E°cell = −4.07 V), and electrical energy must be supplied. During the discharge of a sodium-ion battery, the reverse process occurs spontaneously, generating electrical energy. The spontaneity is determined entirely by the signs of ΔG and E, not by whether the process is categorised as galvanic or electrolytic.

The practical implication for examination questions is that candidates must determine spontaneity from the quantitative relationship ΔG = −nFE, from the sign of Ecell, or from the comparison of Q with K, rather than from a categorical label assigned to the cell type.

Common procedural errors in electrochemistry calculations

Electrode potential and Nernst equation questions reward careful procedure and punish several recurring categories of error. Awareness of these pitfalls — and systematic strategies to avoid them — directly improves examination performance.

The most prevalent error involves the electron count n. The value of n in the Nernst equation is the number of electrons transferred per mole of the overall cell reaction as balanced, not the number of electrons appearing in a half-reaction. For the Daniell cell, each half-reaction involves two electrons, but the overall cell reaction also involves two electrons per mole of cell reaction. The value of n is the same whether derived from the half-reactions or the overall reaction; it is simply the total electrons transferred. Candidates who incorrectly use n = 1 for the Daniell cell will obtain an incorrect numerical answer by a factor of two.

A second systematic error involves the reaction quotient Q. The expression for Q must correspond to the stoichiometry of the overall balanced cell reaction, not to the ratio of concentrations within a single half-cell. For the cell reaction Cu²⁺(aq) + Zn(s) → Cu(s) + Zn²⁺(aq), Q = [Zn²⁺] / [Cu²⁺] is correct. A common incorrect formulation would use Q = [Cu²⁺] / [Zn²⁺], reversing the numerator and denominator, or would treat the solid species as if they appeared in the expression.

A third category of error concerns the sign of the Nernst correction. When Q > K, the log term is positive, the correction E° − (0.0592/n) log Q is negative, and E < E°. This reduction in cell potential reflects that the reaction is less spontaneous when product concentrations are elevated relative to the equilibrium position. Candidates who apply the correction with an incorrect sign invert the physical meaning of their result.

A fourth and subtler error involves neglecting the effect of ion concentrations on both half-cells simultaneously. In a general galvanic cell, both half-cell potentials may shift when concentrations change, and the overall cell potential is the difference of the two shifted potentials. Candidates who apply the Nernst correction only to the cell overall, without verifying that both half-reactions are correctly represented in the expression for Q, risk missing contributions from both sides of the cell.

Concentration cells and ion-selective electrodes

Concentration cells represent a particularly instructive application of the Nernst equation because E° for both half-reactions is identical, yet a measurable cell potential arises from differences in concentration. When the two half-cells contain the same redox couple at different concentrations, the standard potentials cancel, and the cell potential depends solely on the concentration ratio.

Consider a cell in which silver electrodes are immersed in AgNO₃ solutions of different concentrations: left half-cell [Ag⁺] = 1.00 mol dm⁻³, right half-cell [Ag⁺] = 0.001 mol dm⁻³. Since the half-reaction is Ag⁺(aq) + e⁻ → Ag(s) with E° = +0.80 V, and since both half-cells share this same E° value, the standard cell potential is zero. Applying the Nernst equation to each half-cell and then finding the difference yields:

Ecell = (0.0592 / 1) log₁₀([Ag⁺]dilute / [Ag⁺]concentrated) = 0.0592 × log₁₀(0.001) = 0.0592 × (−3) = −0.18 V

The negative sign indicates that the left half-cell (concentrated Ag⁺) is the cathode and the right half-cell (dilute Ag⁺) is the anode. This is consistent with the physical intuition that the more concentrated solution has the higher reduction potential and therefore accepts electrons from the less concentrated solution, in which Ag⁺ is less readily reduced.

Ion-selective electrodes, including the widely used pH glass electrode, operate on this same principle. A thin glass membrane separates the sample solution from an internal reference solution of fixed concentration; the potential difference across the membrane varies with the logarithm of the ion concentration in the sample. This quantitative relationship between potential and concentration is precisely what the Nernst equation predicts, and it underlies the analytical utility of potentiometric methods in both laboratory and industrial contexts.

Strategic approach to electrochemistry questions in examinations

A reliable procedural framework reduces errors and builds confidence when tackling electrochemistry questions under time pressure. The following sequence provides a systematic foundation applicable to the full range of A-Level Chemistry electrochemistry questions:

Write the two relevant half-equations from the data provided, with states of matter specified.
Identify which half-reaction has the more positive E° value — this is the reduction half-reaction and the cathode.
Calculate E°cell = E°cathode − E°anode; confirm the sign is consistent with the expected cell type.
Determine n by balancing the two half-reactions so that electrons cancel; verify n is the total electrons per mole of overall cell reaction.
Write the overall balanced cell reaction by combining the half-reactions.
Formulate Q for the overall cell reaction, checking that all coefficients are correctly reflected and that solids and liquids are excluded.
Substitute into the Nernst equation (or the simplified E°cell − (0.0592/n) log Q form) to find E under the specified conditions.
Interpret the sign of E: if positive, the forward reaction is spontaneous; if negative, the reverse reaction is spontaneous.

This sequence should be practised repeatedly until it becomes automatic. Examination questions may omit or combine some steps, but the underlying logic is consistent across all variants. Candidates who understand why each step is necessary — not merely which formula to apply — are better equipped to handle unfamiliar question formats or partial information.

Connecting electrochemistry to broader physical chemistry

Electrode potentials do not exist in isolation within the A-Level Chemistry syllabus; they connect directly to the thermodynamic and kinetic topics that constitute the physical chemistry core. The relationship ΔG = −nFE links electrochemistry to the Gibbs free energy framework that also governs equilibrium position and temperature effects on spontaneity. The relationship log₁₀K = nE°/0.0592 connects equilibrium constants directly to measurable electrical quantities, providing an alternative experimental route to thermodynamic data.

Understanding these connections deepens conceptual clarity and improves performance across the physical chemistry component as a whole. Candidates who can move fluently between ΔG, E, K, and reaction quotient Q — understanding what each quantity measures and how they interrelate — demonstrate a level of mastery that enables them to tackle novel question formats with confidence rather than relying on recognition of familiar problem types.

Relationship	Equation	Conditions / Significance
Gibbs free energy to cell potential	ΔG = −nFE	Universal; E > 0 implies ΔG < 0 (spontaneous forward reaction)
Standard cell potential from half-cells	E°cell = E°cathode − E°anode	E°cathode is the more positive of the two E° values
Standard potential and equilibrium constant	log₁₀K = nE° / 0.0592	Valid at 298 K; large K when nE° is positive and large
Nernst equation (simplified, 298 K)	E = E° − (0.0592 / n) log₁₀ Q	Q is the reaction quotient for the overall balanced cell reaction
Concentration cell potential	Ecell = ±(0.0592 / n) log₁₀(ratio of concentrations)	E° cancels; direction determined by which concentration is higher

The conceptual thread running through all of physical chemistry — from energy changes in Hess's Law calculations through to rate expressions and equilibrium constants — is the quantitative description of chemical change. Electrochemistry provides a particularly rich context for applying this quantitative thinking because it connects thermodynamic quantities directly to experimentally accessible electrical measurements. Candidates who develop fluency with these relationships position themselves strongly not only in the electrochemistry section of the examination but across the physical chemistry syllabus more broadly.

Frequently asked questions

How do I determine which half-cell is the cathode and which is the anode using E° values?

The half-cell with the more positive standard electrode potential undergoes reduction and is therefore the cathode. The half-cell with the less positive (or more negative) E° value undergoes oxidation and is the anode. Calculate E°cell as E°cathode minus E°anode. This approach eliminates reliance on memorising which metals are noble or active and works reliably for any combination of half-cells listed in the data table.

What is the correct value of n to use in the Nernst equation for a galvanic cell?

The value of n is the number of electrons transferred per mole of the overall balanced cell reaction. It is not simply the number of electrons in a single half-reaction, though in many cells these two numbers happen to be the same. When combining half-reactions, balance the electrons first to find the overall cell reaction, then extract n from that balanced equation. For the Daniell cell, n = 2. Using n = 1 would halve the numerical value of the Nernst correction, producing an incorrect answer.

Why does a concentration cell produce a potential difference when both half-cells have the same E° value?

Standard electrode potentials are identical for both half-cells only under standard conditions. When the concentrations differ, each half-cell potential shifts according to the Nernst equation, but by different amounts. The difference in these shifted potentials produces a measurable cell potential. In the simplified expression for a concentration cell, E° cancels entirely, leaving Ecell proportional to log₁₀ of the concentration ratio. This is the principle underlying ion-selective electrodes and pH meters.

Can a galvanic cell ever have a negative E°cell value?

Technically, a galvanic cell is defined by the convention E°cell > 0, indicating a spontaneous reaction producing electrical energy. If the calculation E°cathode minus E°anode yields a negative result, the cell as written is not galvanic; the reverse combination of half-cells would be galvanic. However, the half-cell potentials themselves remain as given in the data table — only the assignment of cathode and anode changes when the cell is reoriented. Understanding this distinction is important when a question asks for the maximum potential achievable or requires identification of the spontaneous cell configuration.

How does the Nernst equation apply to temperature changes in electrochemical cells?

The full Nernst equation E = E° minus (RT divided by nF) times ln Q contains explicit temperature dependence through the RT term. At temperatures other than 298 K, the value of RT/F changes, affecting the magnitude of the concentration correction to the cell potential. In many A-Level contexts, questions specify 298 K to enable use of the simplified 0.0592/n form, but candidates should recognise that temperature is a variable that influences cell potential and should not be ignored when non-standard temperatures are specified.

From ΔG to Cell Potential in A-Level Chemistry Electrochemistry