Electrochemistry Calculators

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Electrochemistry studies the relationship between chemical energy and electrical energy — specifically, oxidation-reduction (redox) reactions that involve electron transfer. In a galvanic (voltaic) cell, spontaneous redox reactions generate electrical current. In an electrolytic cell, electrical current drives non-spontaneous chemical reactions (electrolysis). Key principles include: standard reduction potentials (E°) from which cell voltage is calculated; the Nernst equation relating actual cell voltage to ion concentrations; Faraday's laws of electrolysis; and applications from batteries to electroplating to biological energy transduction.

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Galvanic Cell and Cell Potential

E°_cell = E°_cathode − E°_anode (both from the standard reduction potential table). Spontaneous: E°_cell > 0. Example: Zn-Cu cell: E°_cathode (Cu²⁺/Cu) = +0.34 V; E°_anode (Zn²⁺/Zn) = −0.76 V. E°_cell = +0.34 − (−0.76) = +1.10 V.

Nernst Equation

E = E° − (RT/nF) × ln(Q). At 25°C: E = E° − (0.0592/n) × log(Q). Equilibrium: E = 0 → log Keq = nE°/0.0592. ΔG = −nFE; ΔG° = −nFE°.

Faraday's Laws of Electrolysis

1st law: mass deposited ∝ charge passed. 2nd law: mass deposited ∝ equivalent weight. m = (Q × M) / (n × F). Q = charge (C); M = molar mass; n = electrons; F = 96,485 C/mol.

Biological Electrochemistry

Electron transport chain: series of redox reactions generating proton motive force; ATP synthase uses proton gradient (ΔμH⁺) to synthesize ATP. Biological redox potentials: NAD⁺/NADH = −0.32 V; O₂/H₂O = +0.82 V. Total ETC: ΔE°' = 0.82 − (−0.32) = +1.14 V → ΔG°' = −nFΔE°' = −2 × 96,485 × 1.14/1000 = −220 kJ/mol per NADH.

Glossary

Galvanic Cell
An electrochemical cell in which a spontaneous redox reaction generates electrical energy; E°_cell > 0; oxidation at anode (−); reduction at cathode (+); examples: batteries, fuel cells.
Standard Reduction Potential (E°)
The voltage of a half-reaction under standard conditions (1 M, 25°C, 1 atm) relative to the standard hydrogen electrode (SHE = 0 V); E°_cell = E°_cathode − E°_anode; spontaneous when E°_cell > 0.
Faraday's Law
m = (Q × M)/(n × F); mass deposited at electrode proportional to charge passed; Q = A × s; F = 96,485 C/mol; n = electrons per formula unit; used for electroplating and electrolysis calculations.

Frequently Asked Questions

Electrochemistry studies redox reactions that produce or consume electrical energy. Galvanic (voltaic) cell: spontaneous redox reaction generates electrical energy; E°_cell > 0; ΔG < 0. Oxidation occurs at the anode (negative electrode); reduction at the cathode (positive electrode). The salt bridge maintains electrical neutrality by allowing ion flow between half-cells. Examples: Zn-Cu Daniell cell (1.10 V); lithium-ion batteries; fuel cells; biological cells (mitochondria function as electrochemical cells). Electrolytic cell: electrical energy drives non-spontaneous chemical reaction; E°_cell < 0; ΔG > 0; powered by external power source. Examples: electrolysis of water (H₂ and O₂); electroplating; aluminum production (Hall-Héroult process); rechargeable battery charging.

E°_cell = E°_cathode − E°_anode. Look up both half-reactions in the standard reduction potential table (all listed as reductions: reduced form + ne⁻ → oxidized form, but in the reverse direction for the anode). The half-reaction with higher E° is the reduction (cathode); the one with lower E° is oxidized (anode). Example: Cu²⁺/Cu: E° = +0.34 V; Zn²⁺/Zn: E° = −0.76 V. Cu²⁺ has higher E° → cathode (reduction): Cu²⁺ + 2e⁻ → Cu. Zn → anode (oxidation): Zn → Zn²⁺ + 2e⁻. E°_cell = +0.34 − (−0.76) = +1.10 V. Overall: Zn + Cu²⁺ → Zn²⁺ + Cu; E° = +1.10 V (spontaneous).

Faraday's first law: the mass of substance deposited at an electrode is proportional to the total charge passed. m = (Q × M) / (n × F). Q = charge in coulombs (= current in amperes × time in seconds). M = molar mass (g/mol). n = number of electrons per formula unit. F = Faraday constant = 96,485 C/mol. Example: how many grams of copper are deposited when 2.5 A flows for 10 minutes through a CuSO₄ solution? Q = 2.5 × 600 = 1,500 C. m = (1,500 × 63.55) / (2 × 96,485) = 95,325 / 192,970 = 0.494 g. Application: electroplating, electrorefining, industrial electrolysis.

The mitochondrial electron transport chain (ETC) is essentially a series of electrochemical reactions: NADH and FADH₂ donate electrons to complexes I and II → electrons pass through complexes III and IV → final electron acceptor is O₂ (at complex IV). Each complex has a specific reduction potential: NADH/NAD⁺ = −0.32 V; CoQ/QH₂ = +0.045 V; cytochrome c = +0.23 V; O₂/H₂O = +0.82 V. Total potential difference: ΔE° = 0.82 − (−0.32) = +1.14 V per 2 electrons (per NADH). Free energy: ΔG° = −nFΔE° = −2 × 96,485 × 1.14 = −220 kJ/mol. This energy is used to pump H⁺ across the inner mitochondrial membrane → proton motive force → ATP synthesis by ATP synthase (≈ 2.5 ATP per NADH).