{ "node": { "id": "term:nernst-equation", "type": "Term", "label": "Nernst equation", "properties": { "id": "nernst-equation", "name": "Nernst equation", "section": "topic-electrochemistry", "definition": "The relation between an electrode’s potential and the concentrations, or activities, of the species in its half-reaction. It explains why open-circuit voltage changes with state of charge and temperature.", "formula": "E = E° − (RT/nF)·ln Q", "related": [ "electrode-potential", "standard-potential", "open-circuit-voltage", "gibbs-free-energy" ], "example": { "title": "Change a reaction quotient by a decade", "text": "At 298.15 K with n = 1, increasing the dimensionless reaction quotient from 1 to 10 lowers E by about 59.2 mV. Use activities or a justified concentration approximation." }, "url": "https://lemonergy.com/learn/glossary/nernst-equation/", "mentions": [ "electrode", "state-of-charge", "half-reaction" ] } }, "edges": [ { "id": "edge:1869", "source": "term:nernst-equation", "target": "topic:topic-electrochemistry", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:1870", "source": "term:nernst-equation", "target": "term:electrode-potential", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1871", "source": "term:nernst-equation", "target": "term:standard-potential", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1872", "source": "term:nernst-equation", "target": "term:open-circuit-voltage", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1873", "source": "term:nernst-equation", "target": "term:gibbs-free-energy", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/nernst-equation/electrode", "source": "term:nernst-equation", "target": "term:electrode", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:mentions/nernst-equation/state-of-charge", "source": "term:nernst-equation", "target": "term:state-of-charge", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:mentions/nernst-equation/half-reaction", "source": "term:nernst-equation", "target": "term:half-reaction", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:1877", "source": "term:nernst-equation", "target": "visual:nernst", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:1878", "source": "term:nernst-equation", "target": "reference:iupac-nernst", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "topic:topic-electrochemistry", "type": "Topic", "label": "Electrochemistry fundamentals", "properties": { "id": "topic-electrochemistry", "name": "Electrochemistry fundamentals", "lede": "The reactions and potentials that make a cell a battery.", "context": "Connect reaction sites and transport paths.", "example": "A circuit can predict terminal voltage while leaving electrode potentials and reaction kinetics unresolved.", "lesson_url": "https://lemonergy.com/learn/fundamentals/cell-anatomy/", "lesson_label": "Open cell anatomy" } }, { "id": "term:electrode-potential", "type": "Term", "label": "Electrode potential", "properties": { "id": "electrode-potential", "name": "Electrode potential", "section": "topic-electrochemistry", "definition": "The potential of an electrode relative to a reference, which for lithium-ion work is lithium metal in the same electrolyte, written as V vs Li/Li⁺. Graphite sits near 0.1 V and layered oxides near 3.7–4.3 V on this scale.", "unit": "V vs Li/Li⁺", "related": [ "standard-potential", "cell-voltage", "reference-electrode", "half-reaction" ], "lesson": "labs/battery-materials-lab/#battery-materials-lab", "url": "https://lemonergy.com/learn/glossary/electrode-potential/", "mentions": [ "electrode", "graphite", "electrolyte" ] } }, { "id": "term:standard-potential", "type": "Term", "label": "Standard electrode potential", "properties": { "id": "standard-potential", "name": "Standard electrode potential", "abbr": "E°", "section": "topic-electrochemistry", "definition": "An electrode’s potential under standard conditions, tabulated against the standard hydrogen electrode. Lithium’s −3.04 V is the most negative of any metal, which is why lithium cells have the highest voltages.", "unit": "V", "related": [ "electrode-potential", "nernst-equation", "cell-voltage" ], "url": "https://lemonergy.com/learn/glossary/standard-potential/", "mentions": [ "electrode", "standard-hydrogen-electrode" ] } }, { "id": "term:open-circuit-voltage", "type": "Term", "label": "Open-circuit voltage", "properties": { "id": "open-circuit-voltage", "name": "Open-circuit voltage", "abbr": "OCV", "section": "topic-state", "definition": "The voltage across a cell’s terminals when no current flows and the cell has rested long enough for the voltage to settle. It depends on state of charge and temperature, and a cell whose open-circuit voltage falls unusually fast in storage may have an internal short.", "unit": "V", "related": [ "ocv-soc-curve", "relaxation", "voltage-hysteresis", "k-value", "internal-short-circuit" ], "lesson": "fundamentals/cell-production/#finishing", "url": "https://lemonergy.com/learn/glossary/open-circuit-voltage/", "mentions": [ "state-of-charge" ] } }, { "id": "term:gibbs-free-energy", "type": "Term", "label": "Gibbs free energy", "properties": { "id": "gibbs-free-energy", "name": "Gibbs free energy", "abbr": "ΔG", "section": "topic-electrochemistry", "definition": "The maximum useful work a reaction can deliver at constant temperature and pressure. For a cell it equals the charge transferred times the cell voltage, with a negative sign, which ties the thermodynamics of the materials to the voltage on the terminals.", "formula": "ΔG = −nFE", "unit": "kJ/mol", "related": [ "cell-voltage", "nernst-equation", "faradays-constant", "entropy-coefficient" ], "example": { "title": "Convert voltage to molar free energy", "text": "For a one-electron reaction with equilibrium voltage 3.0 V, ΔG = −nFE is approximately −289 kJ/mol. The sign refers to the reaction direction and the equilibrium electrical work." }, "url": "https://lemonergy.com/learn/glossary/gibbs-free-energy/", "mentions": [] } }, { "id": "term:electrode", "type": "Term", "label": "Electrode", "properties": { "id": "electrode", "name": "Electrode", "section": "topic-components", "definition": "A solid conductor where the cell’s reaction happens, in contact with the electrolyte. A lithium-ion cell has a negative electrode and a positive electrode, each a porous coating on a metal foil.", "related": [ "negative-electrode", "positive-electrode", "porous-electrode", "current-collector" ], "lesson": "fundamentals/cell-anatomy/#components", "example": { "title": "Two transport paths", "text": "Electrons need connected solid paths to the collector; ions need electrolyte paths to reaction sites. More of one constituent displaces others at fixed volume." }, "url": "https://lemonergy.com/learn/glossary/electrode/", "mentions": [ "electrolyte", "coating" ] } }, { "id": "term:state-of-charge", "type": "Term", "label": "State of charge", "properties": { "id": "state-of-charge", "name": "State of charge", "abbr": "SOC", "section": "topic-state", "definition": "How full a cell is, as a fraction of its available capacity. State of charge, like temperature, affects how fast a stored cell ages.", "unit": "%", "related": [ "depth-of-discharge", "ocv-soc-curve", "coulomb-counting", "state-of-health", "bms" ], "lesson": "fundamentals/battery-aging/#storage-soc", "example": { "title": "Interpret a charge inventory", "text": "If available capacity is 5 Ah and 3 Ah remains by the chosen estimator, SOC is 60%. A different estimate of available capacity changes this percentage, so compare SOC values only with the capacity convention recorded." }, "url": "https://lemonergy.com/learn/glossary/state-of-charge/", "mentions": [ "usable-capacity" ] } }, { "id": "term:half-reaction", "type": "Term", "label": "Half-reaction", "properties": { "id": "half-reaction", "name": "Half-reaction", "aka": [ "half-cell reaction" ], "section": "topic-electrochemistry", "definition": "The oxidation or reduction occurring at one electrode, written on its own with electrons shown explicitly. The cell reaction is the sum of its two half-reactions, and the cell voltage is the difference of their potentials.", "related": [ "redox-reaction", "electrode-potential", "half-cell", "cell-voltage" ], "lesson": "labs/battery-materials-lab/#bml-liion-mechanism", "url": "https://lemonergy.com/learn/glossary/half-reaction/", "mentions": [ "electrode", "oxidation", "reduction" ] } }, { "id": "visual:nernst", "type": "Visual", "label": "Activities shift equilibrium potential", "properties": { "title": "Activities shift equilibrium potential", "summary": "The logarithm of the reaction quotient changes equilibrium potential; reference electrodes set the voltage zero.", "readout": "A tenfold increase in Q shifts E by −59.16 mV at 25 °C for n = 1.", "formula": "E − E° = −(RT/nF) ln Q; E(vs SHE) ≈ E(vs Li/Li⁺) − 3.04 V", "note": "Q is dimensionless activity quotient, not electrical charge. The −3.04 V reference offset is an approximate conventional value; it is not recomputed with temperature.", "software": { "status": "reference", "label": "Reference concept", "body": "This is a reference thermodynamic calculation. battery-core does not construct an activity model or compute OCV from a half-reaction.", "href": "../chapter-1/" }, "html": "
Potential shift by activity quotient
Potential shift by activity quotientlog₁₀(reaction quotient Q) versus E − E° (mV). Nernst shift. Interpretation follows the graphs.-177-3-88.7-1.50088.71.51773log₁₀(reaction quotient Q)E − E° (mV)
Nernst shift
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Reference-scale conversion
Reference-scale conversionPotential vs Li/Li⁺ (V) versus Potential vs SHE (V). Approximate conversion. Interpretation follows the graphs.-3.040-1.791.25-0.542.50.713.751.965Potential vs Li/Li⁺ (V)Potential vs SHE (V)
Approximate conversion
" } }, { "id": "reference:iupac-nernst", "type": "Reference", "label": "Nernst equation", "properties": { "title": "Nernst equation", "publisher": "IUPAC Gold Book", "url": "https://goldbook.iupac.org/terms/view/09068", "type": "Terminology reference", "scope": "Equilibrium potential as a function of activities; distinguishes activities from concentration approximations.", "year": 2025, "accessed": "2026-10-27" } } ] }