Electrochemistry: Unit Review

Introduction

The unit began with an ideal reversible cell and added three forms of realism. Ionic interactions alter activities and therefore equilibrium potentials. Electron-transfer barriers and interfacial charging shape measured current. Transport, resistance and active-material limits shape the voltage and energy of actual batteries. A complete solution identifies which layer of the problem each quantity belongs to.

Core explanation

Thermodynamics uses μi = μi° + RT ln ai and E = E° − (RT/nF)ln Q. Dissolved-ion activities are expressed through dimensionless concentration or molality ratios and activity coefficients. Ionic strength is I = ½Σci zi² on a concentration basis, with all ions included. The Debye–Hückel limiting law predicts a leading log γ proportional to −z²√I for sufficiently dilute solutions. Mean ionic coefficients describe electroneutral salts more directly than convention-dependent single-ion coefficients. Finite ion size, pairing and specific interactions limit simple extrapolation to concentrated electrolyte.

At an electrode, the electrical double layer stores charge while redox reactions transfer electrons to chemical species. Double-layer current is non-faradaic; oxidation or reduction current is faradaic. For a target n-electron reaction, product molar rate is the target faradaic current divided by nF. Net current is zero at equilibrium even when opposing partial reactions occur rapidly, with their magnitude characterized by exchange current density j0.

Overpotential drives net current. In a simple Butler–Volmer model, anodic and cathodic exponential terms differ and cancel at η = 0. Near equilibrium the relation is approximately linear and gives charge-transfer resistance RT/(nFj0) on an area-specific basis. At larger charge-transfer-controlled η, a Tafel relation can emerge. Neither model describes a reactant supply ceiling without transport. Diffusion, migration and convection deliver species; a simple steady diffusion layer gives jlim = nFDcb/δ when surface reactant is depleted.

Battery analysis combines these ideas. Capacity is ∫I dt, delivered energy is ∫V dQ, and power is VI. Theoretical active-material capacity follows electron stoichiometry nF/M, but full-cell energy includes both electrodes and supporting mass. Loaded discharge voltage is below reversible voltage because of activation, concentration and resistive losses. Charge voltage is higher, so energy efficiency can be lower than coulombic efficiency.

Specific chemistries demonstrate different constraints. Zinc–MnO2 primary cells oxidize zinc and reduce manganese dioxide. Lead–acid cells make PbSO4 on both plates while consuming acid. NiCd and NiMH share a nickel oxyhydroxide positive electrode but use different negative materials. Lithium-ion cells shuttle Li+ between hosts such as graphite and layered oxides, with interfaces and lithium plating affecting life and safety. Emerging systems trade energy, cost, power and complexity differently.

Step-by-step reasoning

For a new problem, first classify the requested quantity: equilibrium potential, current, reaction rate, capacity or energy. Balance the reaction and identify n. Compute activities and a Nernst potential only if equilibrium composition matters. For current, check j0, overpotential, transport and charging. For a device, account for resistance, voltage window, mass basis and efficiency. Carry units through each conversion and state the model assumptions.

Visual explanation

Draw a three-level map. The first level, “solution thermodynamics,” contains ionic strength, γ, activities and Nernst voltage. The second, “electrode interface,” contains double layer, j0, Butler–Volmer and transport. The third, “device,” contains loaded voltage, Ah, Wh, power and aging. Draw arrows from the first to reversible voltage and from the second to operating losses that affect the third.

Real-world analogy

A water-power system has stored pressure, a valve with finite opening speed, supply pipes and an output meter. Chemical activities establish the available driving force, electrode kinetics and transport determine flow, and the device reports delivered work. The analogy is useful only if one keeps pressure, flow and total energy as different quantities.

Real-world example

A cell at rest may show a composition-dependent open-circuit voltage. Under a high-current load, its terminal voltage falls immediately from iR and activation effects and may fall further as surface concentrations change. Its Ah delivered to cut-off and the area under its V–Ah curve quantify usable capacity and energy at that rate, not the full theoretical active-material charge.

Why?

Electrochemical systems connect Gibbs-energy differences to electrical work but operate through finite-rate interfaces and finite transport pathways. Thermodynamic activities determine what is reversibly possible; kinetics and resistance determine the extra driving force required; material inventories and voltage profiles determine how much work is actually delivered.

Common misconception

Do not use analytical concentration as exact activity, net zero current as proof of no microscopic reaction, or high theoretical capacity as a full-cell energy rating. Likewise, one voltage measurement cannot reveal whether a deficit arises from non-ideal solution thermodynamics, interfacial kinetics or resistance without additional measurements.

Worked example

Question: A one-electron reversible cell has Erev = 1.20 V at its actual activities. Under a 0.50 A discharge it loses 0.08 V to electrode polarization and 0.04 V to iR. It runs for two hours at approximately constant voltage. Estimate terminal voltage, capacity and energy.

Reasoning: Subtract the two operating loss magnitudes: V ≈ 1.20 − 0.08 − 0.04 = 1.08 V. Capacity is 0.50 A × 2 h = 1.0 Ah. With the stated approximately constant voltage, energy is 1.08 V × 1.0 Ah = 1.08 Wh. The supplied Erev already accounts for activity, so no additional γ correction should be subtracted.

Answer: About 1.08 V terminal voltage, 1.0 Ah delivered capacity and 1.08 Wh energy.

Quick check

1. What term connects moles of electrons to electrical charge? Answer: Faraday's constant F, about 96,485 C mol−1 of electrons.

Exam focus

Write activities into Q and name the standard state. For kinetics, state η and current sign; for transport, distinguish diffusion layer from double layer. For batteries, label open-circuit versus loaded voltage and active-material versus full-cell mass. Use equations only within their dilute, small-signal or steady-transport limits.

Advanced insight

Several measured “constants” are conditional. A formal potential depends on medium, an exchange current depends on surface and activities, and an impedance-derived resistance depends on operating point. Reporting conditions is therefore part of the scientific result, not an optional footnote.

Summary

University electrochemistry links non-ideal solution free energy to reversible voltage, finite interfacial kinetics and transport to current, and accumulated charge plus voltage to battery energy. Ionic strength, activity, double-layer charging, exchange current, limiting current and device losses each answer a distinct question.

Practice questions

1. What is ionic strength of a fully dissociated 0.010 M 1:1 salt alone? Answer: 0.010 M on the concentration scale. 2. Does a high j0 imply high net equilibrium current? Answer: No. Equal high partial currents still cancel at equilibrium. 3. What causes a simple diffusion limiting current? Answer: Surface reactant concentration approaches zero while supply remains finite. 4. Why is coulombic efficiency not energy efficiency? Answer: Charge recovery does not include the higher charging voltage and lower discharge voltage caused by losses.