{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"nernst-equation"},"result":{"entity_type":"calculator","id":"nernst-equation","calculator_id":"nernst-equation","canonical_url":"https://tttkmbb.com/chemistry/nernst-equation","name":"Nernst Equation Calculator","title":"Nernst Equation Calculator – Cell Potential from E°, Reaction Quotient, Electrons and Temperature","category":"chemistry","category_name":"Chemistry","tool_name":"calculate_nernst_potential","featured_mcp_tool":false,"description":"Computes the cell (or electrode) potential under non-standard conditions with the Nernst equation E = E° − (RT/nF)·ln Q, the textbook 0.0592/n·log Q form at 25 °C, the Gibbs energy ΔG = −nFE and the equilibrium constant from E°.","use_when":"You know a standard potential and the concentrations (reaction quotient) of an electrochemical cell or half-cell and need its actual potential, ΔG or K, including at temperatures other than 25 °C.","do_not_use_when":"You need the mass deposited or charge passed during electrolysis (use faraday-electrolysis), or the pH of a solution from concentrations (use ph).","inputs":[{"name":"standard_potential_v","label":"Standard potential E°","type":"number","unit":"V","required":true,"min":-10,"max":10,"description":"Standard cell potential E°cell (cathode − anode) or standard reduction potential of the half-reaction, in volts.","example":1.1},{"name":"electrons","label":"Electrons transferred n","type":"integer","required":true,"min":1,"max":20,"description":"Number of moles of electrons in the balanced cell reaction (2 for Zn + Cu²⁺ → Zn²⁺ + Cu).","example":2},{"name":"reaction_quotient","label":"Reaction quotient Q","type":"number","required":true,"exclusive_min":0,"description":"Q = product activities / reactant activities with stoichiometric exponents, e.g. [Zn²⁺]/[Cu²⁺]; pure solids and liquids are omitted. Use Q = 1 for standard conditions.","example":100},{"name":"temperature","label":"Temperature","type":"number","required":false,"default":25,"description":"Cell temperature in temperature_unit.","example":25},{"name":"temperature_unit","label":"Temperature unit","type":"enum","required":false,"default":"celsius","values":[{"value":"celsius","label":"°C","aliases":["c"]},{"value":"kelvin","label":"K","aliases":["k"]}],"description":"Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).","example":"celsius"}],"outputs":[{"name":"cell_potential_v","label":"Cell potential E","type":"number","unit":"V","decimals":5,"description":"E = E° − (RT/nF)·ln Q at the given temperature."},{"name":"nernst_correction_v","label":"Nernst term (RT/nF)·ln Q","type":"number","unit":"V","decimals":5,"description":"Amount subtracted from E°; negative when Q < 1."},{"name":"rt_over_nf_v","label":"RT/nF","type":"number","unit":"V","decimals":6,"description":"Thermal voltage divided by n (0.025693/n V at 25 °C)."},{"name":"cell_potential_25c_log_form_v","label":"E by 0.0592/n·log Q form","type":"number","unit":"V","decimals":5,"description":"E° − (0.0592/n)·log10 Q, the textbook approximation valid at 25 °C regardless of the temperature entered."},{"name":"gibbs_energy_kj_per_mol","label":"ΔG","type":"number","unit":"kJ/mol","decimals":3,"description":"−n·F·E: negative for a spontaneous reaction as written."},{"name":"standard_gibbs_energy_kj_per_mol","label":"ΔG°","type":"number","unit":"kJ/mol","decimals":3,"description":"−n·F·E°."},{"name":"log10_equilibrium_constant","label":"log10 K","type":"number","decimals":4,"description":"n·F·E° / (R·T·ln 10) at the given temperature."},{"name":"equilibrium_constant_scientific","label":"Equilibrium constant K","type":"string","decimals":4,"description":"K = exp(nFE°/RT) in scientific notation."},{"name":"spontaneous","label":"Spontaneity","type":"string","decimals":4,"description":"Whether the reaction as written is spontaneous at the given Q (E > 0), at equilibrium (E = 0) or non-spontaneous (E < 0)."},{"name":"temperature_k","label":"Temperature","type":"number","unit":"K","decimals":2,"description":"Absolute temperature used."}],"input_schema":{"type":"object","properties":{"standard_potential_v":{"description":"Standard cell potential E°cell (cathode − anode) or standard reduction potential of the half-reaction, in volts. Unit: V.","type":"number","minimum":-10,"maximum":10,"examples":[1.1],"x-unit":"V"},"electrons":{"description":"Number of moles of electrons in the balanced cell reaction (2 for Zn + Cu²⁺ → Zn²⁺ + Cu).","type":"integer","minimum":1,"maximum":20,"examples":[2]},"reaction_quotient":{"description":"Q = product activities / reactant activities with stoichiometric exponents, e.g. [Zn²⁺]/[Cu²⁺]; pure solids and liquids are omitted. Use Q = 1 for standard conditions.","type":"number","exclusiveMinimum":0,"examples":[100]},"temperature":{"description":"Cell temperature in temperature_unit.","type":"number","default":25,"examples":[25]},"temperature_unit":{"description":"Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).","type":"string","enum":["celsius","kelvin"],"default":"celsius","examples":["celsius"]}},"additionalProperties":false,"required":["standard_potential_v","electrons","reaction_quotient"]},"output_schema":{"type":"object","properties":{"cell_potential_v":{"description":"E = E° − (RT/nF)·ln Q at the given temperature. Unit: V.","type":"number","x-unit":"V"},"nernst_correction_v":{"description":"Amount subtracted from E°; negative when Q < 1. Unit: V.","type":"number","x-unit":"V"},"rt_over_nf_v":{"description":"Thermal voltage divided by n (0.025693/n V at 25 °C). Unit: V.","type":"number","x-unit":"V"},"cell_potential_25c_log_form_v":{"description":"E° − (0.0592/n)·log10 Q, the textbook approximation valid at 25 °C regardless of the temperature entered. Unit: V.","type":"number","x-unit":"V"},"gibbs_energy_kj_per_mol":{"description":"−n·F·E: negative for a spontaneous reaction as written. Unit: kJ/mol.","type":"number","x-unit":"kJ/mol"},"standard_gibbs_energy_kj_per_mol":{"description":"−n·F·E°. Unit: kJ/mol.","type":"number","x-unit":"kJ/mol"},"log10_equilibrium_constant":{"description":"n·F·E° / (R·T·ln 10) at the given temperature.","type":"number"},"equilibrium_constant_scientific":{"description":"K = exp(nFE°/RT) in scientific notation.","type":"string"},"spontaneous":{"description":"Whether the reaction as written is spontaneous at the given Q (E > 0), at equilibrium (E = 0) or non-spontaneous (E < 0).","type":"string"},"temperature_k":{"description":"Absolute temperature used. Unit: K.","type":"number","x-unit":"K"}}},"formula":"E = E° − (R × T / (n × F)) × ln Q with R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol; at 25 °C E ≈ E° − (0.0592 / n) × log10 Q; ΔG = −n × F × E; ΔG° = −n × F × E°; ln K = n × F × E° / (R × T)","method":"Concentrations are used in place of activities, which is accurate for dilute solutions; the constant 0.05916 V is RT·ln10/F at 298.15 K (0.0592 in most textbooks). E° is taken as temperature-independent, so the temperature only enters through RT/nF.","sources":[{"name":"OpenStax Chemistry 2e – 17.4 Potential, Free Energy, and Equilibrium","url":"https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium","type":"textbook","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Nernst equation","url":"https://en.wikipedia.org/wiki/Nernst_equation","type":"reference","retrieved_at":"2026-09-24"},{"name":"NIST – CODATA internationally recommended values of the fundamental physical constants (Faraday constant F = 96 485.33212 C/mol, exact)","url":"https://physics.nist.gov/cuu/Constants/index.html","type":"standard","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Zn/Cu cell, E° 1.10 V, [Zn²⁺]/[Cu²⁺] = 100, 25 °C","inputs":{"standard_potential_v":1.1,"electrons":2,"reaction_quotient":100,"temperature":25},"expected":{"cell_potential_v":1.04084,"nernst_correction_v":0.05916,"rt_over_nf_v":0.012846,"cell_potential_25c_log_form_v":1.0408,"gibbs_energy_kj_per_mol":-200.852,"standard_gibbs_energy_kj_per_mol":-212.268,"log10_equilibrium_constant":37.1877,"spontaneous":"Spontaneous as written (E > 0)"},"url":"https://tttkmbb.com/api/v1/calculate/nernst-equation?standard_potential_v=1.1&electrons=2&reaction_quotient=100&temperature=25"},{"name":"E° 0.34 V, n = 2, Q = 0.001 at 50 °C","inputs":{"standard_potential_v":0.34,"electrons":2,"reaction_quotient":0.001,"temperature":50},"expected":{"cell_potential_v":0.43618,"rt_over_nf_v":0.013923,"nernst_correction_v":-0.09618,"cell_potential_25c_log_form_v":0.4288,"temperature_k":323.15},"url":"https://tttkmbb.com/api/v1/calculate/nernst-equation?standard_potential_v=0.34&electrons=2&reaction_quotient=0.001&temperature=50"}],"faq":[{"q":"How do I build Q?","a":"Write the overall cell reaction, then Q = (products)/(reactants) with each concentration raised to its coefficient, omitting solids, pure liquids and the solvent; gases enter as partial pressure in bar (or atm)."},{"q":"Why do the exact and 0.0592 values differ?","a":"The 0.0592/n·log Q form is the Nernst equation evaluated at 25 °C. At other temperatures use cell_potential_v, which uses RT/nF at the temperature entered."},{"q":"Does this work for a single half-cell?","a":"Yes: enter the standard reduction potential, the electrons of the half-reaction and Q = [reduced]/[oxidized] to get the electrode potential versus SHE."}],"tags":["nernst equation","cell potential","electrochemistry","reaction quotient","gibbs free energy","equilibrium constant from e°"],"related":[{"calculator_id":"faraday-electrolysis","reason":"Charge, mass and time in electrolysis with the same Faraday constant."},{"calculator_id":"ph","reason":"Convert [H⁺] for hydrogen-electrode or pH-dependent potentials."},{"calculator_id":"logarithm","reason":"Natural and base-10 logarithm arithmetic."}],"links":{"html":"https://tttkmbb.com/chemistry/nernst-equation","markdown":"https://tttkmbb.com/chemistry/nernst-equation.md","json":"https://tttkmbb.com/chemistry/nernst-equation.json","api":"https://tttkmbb.com/api/v1/calculate/nernst-equation","schema":"https://tttkmbb.com/api/v1/calculators/nernst-equation","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:48:39Z","next_actions":[{"tool":"run_calculator","calculator_id":"nernst-equation","reason":"Run Nernst Equation Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/chemistry/nernst-equation.md"}}