A-Level Chemistry: Electrode Potentials and Fuel Cells

Electrode potentials are the quantitative language of redox chemistry, translating chemical reactivity into measurable voltages. Understanding this language allows you to predict which reactions are spontaneous, design batteries that power our world, and innovate sustainable energy solutions like fuel cells. This knowledge bridges fundamental theory and the advanced technology that defines modern energy storage and conversion.

Standard Electrode Potentials and the Hydrogen Reference

At the heart of quantitative electrochemistry is the concept of the standard electrode potential, denoted $E^{\theta }$. This is the voltage produced when a half-cell, under standard conditions (298 K, 100 kPa, and 1.00 mol dm${}^{-3}$ solution), is connected to a standard hydrogen electrode (SHE).

The SHE acts as the universal zero point. It consists of hydrogen gas at 100 kPa bubbled over a platinum electrode immersed in a solution of 1.00 mol dm${}^{-3}$ H${}^{+}$(aq) ions. By definition, its standard electrode potential is assigned a value of 0.00 V. To measure a standard electrode potential, you construct a cell where the SHE is the left-hand electrode. For example, to find $E^{\theta }$ for the Zn${}^{2+}$/Zn couple, you would connect a zinc electrode in 1.00 mol dm${}^{-3}$ Zn${}^{2+}$(aq) to the SHE. If electrons flow from the zinc to the hydrogen electrode, zinc is the more negative half-cell, and its $E^{\theta }$ is recorded as a negative value (e.g., –0.76 V).

The sign of $E^{\theta }$ is crucial. A more negative (or less positive) $E^{\theta }$ indicates a greater tendency for the reduced form (e.g., Zn) to lose electrons and be oxidised. A more positive $E^{\theta }$ indicates a greater tendency for the oxidised form (e.g., Cu${}^{2+}$) to gain electrons and be reduced.

Cell Diagrams, EMF, and the Electrochemical Series

$$\text{Zn(s)}|{\text{Zn}}^{2+}\text{(aq)}||{\text{Cu}}^{2+}\text{(aq)}|\text{Cu(s)}$$

The standard cell EMF (electromotive force), $E_{cell}^{\theta }$, is the potential difference between the two half-cells. It is calculated using the formula: $$E_{cell}^{\theta }=E_{\text{(right-hand electrode)}}^{\theta }-E_{\text{(left-hand electrode)}}^{\theta }$$ This formula inherently accounts for the direction of electron flow. A positive $E_{cell}^{\theta }$ indicates a spontaneous reaction under standard conditions.

A list of standard electrode potentials arranged in order forms the electrochemical series. This powerful tool allows you to predict reaction feasibility. The fundamental rule is: the species with the more positive (less negative) $E^{\theta }$ will undergo reduction, and the species with the more negative (less positive) $E^{\theta }$ will undergo oxidation. Therefore, for a redox reaction to be feasible, $E_{cell}^{\theta }$ for the reaction, calculated as (E${}^{\theta }$ of oxidising agent) – (E${}^{\theta }$ of reducing agent), must be positive.

Predicting Feasibility and Non-Standard Conditions

While the electrochemical series predicts thermodynamic feasibility, it does not indicate reaction rate. A reaction with a positive $E_{cell}^{\theta }$ may be kinetically slow. Furthermore, predictions assume standard conditions. The Nernst equation (which is beyond the core A-Level requirement but conceptually important) describes how electrode potential, $E$, changes with concentration: $$E=E^{\theta }-\frac{0.0591}{n}\log Q\text{(at 298 K)}$$ where $n$ is the number of electrons transferred and $Q$ is the reaction quotient. This explains why a cell's voltage decreases as it discharges (reactant concentrations fall) and is critical for understanding sensors and biological potentials.

A key application of feasibility predictions is in displacement reactions. For instance, can zinc displace copper from solution? The half-equations are: Zn${}^{2+}$(aq) + 2e${}^{-}$ ⇌ Zn(s) | $E^{\theta }$ = –0.76 V Cu${}^{2+}$(aq) + 2e${}^{-}$ ⇌ Cu(s) | $E^{\theta }$ = +0.34 V

Copper has the more positive $E^{\theta }$, so Cu${}^{2+}$ is the better oxidising agent and will be reduced. Zinc has the more negative $E^{\theta }$, so Zn is the better reducing agent and will be oxidised. The cell potential is $E_{cell}^{\theta }$ = +0.34 – (–0.76) = +1.10 V. The positive value confirms the reaction Zn(s) + Cu${}^{2+}$(aq) → Zn${}^{2+}$(aq) + Cu(s) is feasible.

Commercial Applications: Batteries, Fuel Cells, and Electroplating

The principles of electrode potentials directly enable vital technologies. Rechargeable batteries, like lithium-ion cells, involve redox reactions that are reversible. During discharge, spontaneous redox reactions generate a current. During charging, an external voltage greater than the cell's EMF is applied to force the non-spontaneous reverse reaction, regenerating the reactants. The cell potential dictates the maximum voltage the battery can provide.

Fuel cells are devices that convert the chemical energy of a fuel directly into electricity via controlled redox reactions, with oxygen as the common oxidant. A hydrogen-oxygen fuel cell in an alkaline electrolyte operates with these half-equations:

• Negative electrode (oxidation): H${}_2$(g) + 2OH${}^{-}$(aq) → 2H${}_2$O(l) + 2e${}^{-}$
• Positive electrode (reduction): O${}_2$(g) + 2H${}_2$O(l) + 4e${}^{-}$ → 4OH${}^{-}$(aq)

The overall reaction is 2H${}_2$(g) + O${}_2$(g) → 2H${}_2$O(l). The key advantage over combustion is higher efficiency, as energy is converted directly to electricity without the intermediate step of heat. The theoretical cell voltage is determined by the $E^{\theta }$ values of the involved couples.

Electroplating is an application of electrolysis, where a non-spontaneous redox reaction is driven by an external power supply. To electroplate an object with silver, you make it the cathode (negative electrode) and immerse it in a solution containing [Ag(CN)${}_2$]${}^{-}$ ions. The applied voltage provides the energy to reduce Ag${}^{+}$ to Ag(s) onto the object's surface: [Ag(CN)${}_2$]${}^{-}$(aq) + e${}^{-}$ → Ag(s) + 2CN${}^{-}$(aq). The electrode potential of the Ag${}^{+}$/Ag couple influences the minimum voltage required for the process.

Common Pitfalls

1. Incorrect Sign in E${}_{cell}^{\theta }$ Calculations: The most frequent error is subtracting potentials in the wrong order. Always use: $E_{cell}^{\theta }=E_{\text{(reduction half-cell)}}^{\theta }-E_{\text{(oxidation half-cell)}}^{\theta }$. Since the reduction half-cell is on the right in a cell diagram, the formula is reliably $E_{\text{(right)}}^{\theta }-E_{\text{(left)}}^{\theta }$. A negative result means your assumed spontaneous direction is wrong.

1. Confusing Feasibility with Speed: A positive $E_{cell}^{\theta }$ means a reaction is thermodynamically feasible (spontaneous), not that it will happen at an observable rate. The reaction between hydrogen and oxygen has a large positive $E_{cell}^{\theta }$, but without a catalyst or spark, it is imperceptibly slow at room temperature—this is a kinetic barrier, not a thermodynamic one.

1. Misinterpreting the Electrochemical Series for Complex Ions: Predictions assume aqueous conditions and the species listed. For example, the series shows that sodium metal ($E^{\theta }$ = –2.71 V) is a powerful reducing agent. However, you cannot use it to displace metals from their aqueous solutions because sodium would react violently with water first. The feasibility prediction only holds for the direct redox couples being considered.

1. Drawing Cell Diagrams with Incorrect Order: Remember the sequence: oxidized species | reduced species. For a metal/metal ion half-cell, it is always M${}^{n+}$(aq) | M(s). Placing the solid metal on the wrong side (e.g., M(s) | M${}^{n+}$(aq)) is a common diagrammatic error that misrepresents the phase boundary.

Summary

• Standard electrode potentials ($E^{\theta }$) are measured relative to the standard hydrogen electrode (SHE), which is defined as 0.00 V. The sign of $E^{\theta }$ indicates the relative tendency of a species to be reduced.
• Cell diagrams follow IUPAC conventions (oxidation on left, reduction on right, salt bridge as ||). The standard cell EMF is calculated as $E_{cell}^{\theta }=E_{\text{(right)}}^{\theta }-E_{\text{(left)}}^{\theta }$, and a positive value indicates a spontaneous reaction.
• The electrochemical series allows prediction of redox feasibility: the species with the more positive $E^{\theta }$ undergoes reduction. This underpins displacement reaction predictions.
• Key applications include rechargeable batteries (spontaneous discharge, non-spontaneous recharge), fuel cells (direct efficient energy conversion), and electroplating (non-spontaneous redox driven by an external supply).
• Always distinguish thermodynamic feasibility (from $E^{\theta }$) from kinetic rate, and be meticulous with signs and conventions in calculations and diagrams.