Electrochemical Cells and Electrode Potentials

Electrochemical cells are the fundamental technology behind batteries that power everything from your phone to electric vehicles. Understanding how they convert chemical energy into electrical energy—and vice versa—is crucial for grasping modern energy solutions, materials corrosion, and even biological processes like nerve signaling. For your IB Chemistry studies, mastering electrochemical cells and electrode potentials provides a predictive framework for determining which chemical reactions can spontaneously produce electricity and exactly how much voltage they will generate.

The Basic Principle of an Electrochemical Cell

At its core, an electrochemical cell is a device that generates an electrical current from a spontaneous redox reaction or uses an electrical current to drive a non-spontaneous redox reaction. A redox reaction is one where oxidation (loss of electrons) and reduction (gain of electrons) occur simultaneously. In a cell, these two half-reactions are physically separated. This separation forces the electrons to travel through an external wire, creating an electric current, instead of being transferred directly between reactants.

Cells are categorized into two main types. A voltaic cell (or galvanic cell) converts chemical energy from a spontaneous redox reaction into electrical energy; this is what a battery is. An electrolytic cell uses electrical energy from an external source to drive a non-spontaneous redox reaction, such as in the electroplating of metals or the electrolysis of water. Your IB focus is primarily on understanding and analyzing voltaic cells.

Components of a Voltaic Cell

A functional voltaic cell requires several key components, each with a specific role in maintaining the flow of electricity.

1. Two Half-Cells: Each half-cell contains an electrode immersed in an electrolyte. One half-cell is the site of oxidation, and the other is the site of reduction. A half-cell typically consists of a metal electrode in a solution of its own ions (e.g., a Zn(s) strip in a Zn²⁺(aq) solution), but other combinations, like a platinum electrode with different oxidation states of an ion, are also common.
2. Electrodes: These are solid conductors where the half-reaction occurs. The anode is the electrode where oxidation happens; it loses mass in metal/metal-ion cells and donates electrons to the external circuit. The cathode is the electrode where reduction happens; it gains mass in metal/metal-ion cells and accepts electrons from the external circuit.
3. Electrolytes: These are ionic solutions (or molten ionic compounds) that contain the ions involved in the redox reactions. They complete the internal circuit by allowing the movement of ions to balance charge.
4. Salt Bridge: This is a crucial component that connects the two half-cells. It is typically a tube filled with an inert, ionic salt like KNO₃(aq) in a gel. Its function is to maintain electrical neutrality in each half-cell. As electrons flow from the anode to the cathode, positive ions (cations) migrate from the salt bridge into the cathode compartment to balance the negative charge building up from the reduction of cations. Meanwhile, negative ions (anions) from the salt bridge migrate into the anode compartment to balance the positive charge building up from the formation of metal ions. Think of it as an "ion highway" that prevents the reaction from stopping due to charge buildup.

Standard Electrode Potentials and the SHE

It's impossible to measure the potential (voltage) of a single half-cell in isolation; we can only measure the difference in potential between two half-cells. To create a universal reference scale, chemists have defined the standard hydrogen electrode (SHE). The SHE is assigned a standard electrode potential of exactly 0.00 V under standard conditions (298 K, 1 atm pressure, 1.0 mol dm⁻³ solutions).

The SHE consists of a platinum electrode coated with platinum black (for high surface area) immersed in a 1.0 mol dm⁻³ H⁺(aq) solution, with hydrogen gas at 1 atm bubbled over it. The half-reaction is: $$2H^{+}(aq)+2e^{-}\rightleftharpoons H_2(g)E^{\circ }=0.00\text{ V}$$

The standard electrode potential ($E^{\circ }$) of any other half-cell is measured by connecting it to the SHE under standard conditions. The sign of the $E^{\circ }$ value is crucial. A negative $E^{\circ }$ indicates the half-cell undergoes oxidation more readily than the SHE. A positive $E^{\circ }$ indicates it undergoes reduction more readily than the SHE. For example, the Zn²⁺/Zn half-reaction has $E^{\circ }=-0.76$ V, meaning Zn loses electrons more easily than H₂. The Cu²⁺/Cu half-reaction has $E^{\circ }=+0.34$ V, meaning Cu²⁺ gains electrons more easily than H⁺.

Using Standard Electrode Potentials to Predict Spontaneity

Tables of standard electrode potentials are powerful tools. The key principle is: The half-reaction with the more positive (or less negative) $E^{\circ }$ value will proceed as a reduction. The half-reaction with the more negative (or less positive) $E^{\circ }$ value will proceed as oxidation. The overall cell reaction is spontaneous under standard conditions when the calculated standard cell electromotive force (EMF), denoted $E_{cell}^{\circ }$, is positive.

To calculate $E_{cell}^{\circ }$: $$E_{cell}^{\circ }=E_{(\text{cathode, reduction})}^{\circ }-E_{(\text{anode, oxidation})}^{\circ }$$ Since the cathode is the site of reduction and the anode is the site of oxidation, this formula can be remembered as $E_{cell}^{\circ }=E_{(\text{reduction})}^{\circ }-E_{(\text{oxidation})}^{\circ }$.

Worked Example: Will a voltaic cell formed from Zn²⁺/Zn and Cu²⁺/Cu half-cells be spontaneous, and what is its $E_{cell}^{\circ }$?

• Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) \quad $E^{\circ }=-0.76$ V
• Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) \quad $E^{\circ }=+0.34$ V

Cu²⁺/Cu has the more positive $E^{\circ }$, so it will be the reduction half-reaction (cathode). Zn²⁺/Zn will be the oxidation half-reaction (anode, which is written in reverse). $$E_{cell}^{\circ }=E_{({\text{Cu}}^{2+}/\text{Cu})}^{\circ }-E_{({\text{Zn}}^{2+}/\text{Zn})}^{\circ }=(+0.34)-(-0.76)=+1.10\text{ V}$$ The positive value (+1.10 V) confirms the cell reaction is spontaneous.

Drawing Conventional Cell Diagrams (Cell Notation)

Chemists use a shorthand notation to represent electrochemical cells unambiguously. The rules for conventional cell diagrams are:

1. The anode (oxidation) half-cell is written on the left.
2. The cathode (reduction) half-cell is written on the right.
3. A single vertical line (|) represents a phase boundary (e.g., between a solid electrode and a solution).
4. A double vertical line (||) represents the salt bridge.
5. The chemical state (s, l, g, aq) and concentration (if non-standard) are often noted.
6. Inert electrodes, like platinum, are included if no solid metal is present in the half-reaction.

Example: The Zn-Cu cell described above is written as:

Example with an inert electrode: For a cell with Fe³⁺/Fe²⁺ and Cl₂/Cl⁻ half-cells, the diagram would be:

Platinum is used in both halves as an inert conductor of electrons since all species are in solution or gaseous states.

Common Pitfalls

1. Confusing the Sign of $E_{cell}^{\circ }$: The most common error is reversing the subtraction order. Remember, it is always Cathode (Reduction) Potential minus Anode (Oxidation) Potential. If you get a negative $E_{cell}^{\circ }$ for a predicted spontaneous cell, you have likely reversed the roles of the electrodes. A negative $E_{cell}^{\circ }$ correctly indicates a non-spontaneous reaction under standard conditions.

1. Miswriting Cell Diagrams: Placing the anode on the right or omitting necessary inert electrodes are frequent mistakes. Always start by identifying the oxidation (anode) and reduction (cathode) half-reactions from the $E^{\circ }$ values. If a half-reaction lacks a solid conductive element, you must add an inert electrode like Pt(s) or C(graphite).

1. Changing $E^{\circ }$ Values When Reversing a Half-Reaction: Standard electrode potentials are intensive properties. The $E^{\circ }$ value for a half-reaction is fixed for the reaction as written in the reduction direction (oxidized form + ne⁻ → reduced form). If you reverse the reaction to write the oxidation, you reverse the sign of the $E^{\circ }$ for calculation purposes within the $E_{cell}^{\circ }$ formula, but the value in the data booklet remains unchanged. The formula $E_{cell}^{\circ }=E_{(\text{cathode})}^{\circ }-E_{(\text{anode})}^{\circ }$ automatically accounts for this if you use the tabled (reduction) potentials for both.

Summary

• Electrochemical cells separate oxidation and reduction into half-cells, forcing electron transfer through an external circuit to generate electricity. A salt bridge maintains charge balance by allowing ion migration.
• Standard electrode potentials ($E^{\circ }$) measure the tendency of a half-cell to undergo reduction compared to the Standard Hydrogen Electrode (SHE = 0.00 V). More positive $E^{\circ }$ means greater tendency for reduction.
• Spontaneity is predicted by identifying the half-cell with the more positive $E^{\circ }$ as the cathode (reduction) and the more negative as the anode (oxidation). The reaction is spontaneous if the calculated standard cell EMF is positive: $E_{cell}^{\circ }=E_{(\text{cathode})}^{\circ }-E_{(\text{anode})}^{\circ }$.
• Conventional cell diagrams place the anode on the left and the cathode on the right, using | for phase boundaries and || for the salt bridge. Inert electrodes like Pt(s) must be included if no solid metal is present in the half-reaction.
• The magnitude of $E_{cell}^{\circ }$ indicates the theoretical "push" or voltage of the cell under standard conditions and is directly related to the Gibbs free energy change of the reaction: $\Delta G^{\circ }=-nF{E}_{cell}^{\circ }$, where $n$ is moles of electrons and $F$ is the Faraday constant.