Guide

Guide to Faraday's Law of Electrolysis, Nernst Equation & Cell Potential: Formulas & Worked Examples

Master electrochemistry calculations from Faraday's law of electrolysis (Q = It, m = MIt/zF, STP gas volume) to the Nernst equation (E = E° − (RT/nF)ln Q), concentration cells, standard cell EMF E°cell, Gibbs free energy ΔG° = −nFE°, and equilibrium constant K with step-by-step worked examples.

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CuSO₄ Electrolysis (5.00 A, 1930 s)Daniell Cell ([Zn²⁺]=0.01M, [Cu²⁺]=1.0M)Daniell Cell Thermo (E°=+1.100 V, n=2)

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Published: November 10, 2026Updated: November 10, 2026Tools Hub Editorial Team 4 sources

#electrochemistry#faraday law of electrolysis#nernst equation#cell potential#standard reduction potential#gibbs free energy#chemistry lab

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The essentials

Units & assumptions stated4 primary sources

Quantitative electrochemistry rests on three foundational equations: (1) Faraday's law of electrolysis (Q = It, n(e⁻) = Q/F, m = MIt/(zF)), where product moles scale as 1/z with half-reaction electron count; (2) the Nernst equation (E = E° − (0.05916/n)log₁₀Q at 25 °C) for non-standard concentrations and concentration cells; and (3) the thermodynamic bridge ΔG° = −nFE°cell = −RT ln K.

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Table of contents

“Why does passing the exact same electric current produce different molar amounts of silver ( $\text{Ag}$ ), copper ( $\text{Cu}$ ), and oxygen gas ( $\text{O}_2$ )?” “When should I use $F = 96,500\text{ C/mol}$ versus the exact SI value $F = 96,485.33\text{ C/mol}$ ?” “Which ion concentration goes in the numerator of $\log_{10} Q$ in the Nernst equation?”

From introductory electrolysis and lead-acid battery problems to university physical and analytical chemistry lab reports on Daniell cells, concentration cells, and Gibbs free energy ( $\Delta G^\circ$ ), every electrochemistry calculation follows three core principles:

Faraday’s Law of Electrolysis ( $Q = It,\ n(e^-) = Q/F$ ): First find the moles of electrons transferred, $n(e^-)$ , then divide by the half-reaction electron stoichiometry $z$ ( $n_{\text{product}} = n(e^-) / z$ ) to determine deposited mass or evolved gas volume.
The Nernst Equation ( $E = E^\circ - \frac{0.05916}{n}\log_{10} Q$ at $25^\circ\text{C}$ ): Every tenfold increase in the reaction quotient $Q = \frac{[\text{Anode oxidation products}]}{[\text{Cathode reduction reactants}]}$ lowers cell potential by $\frac{59.16\text{ mV}}{n}$ .
The Thermodynamic Bridge ( $\Delta G^\circ = -nFE^\circ_{\text{cell}} = -RT\ln K$ ): Electrode potential $E^\circ\text{ [V = J/C]}$ is an intensive property (unchanged when scaling reaction coefficients), whereas Gibbs energy $\Delta G^\circ\text{ [J/mol]}$ is extensive (proportional to transferred electrons $n$ ).

This guide provides a complete formula and unit alignment reference, compares the two Faraday constant conventions, visualizes $1/z$ stoichiometric scaling and Nernst potential slopes, and walks through four worked examples verified with hand arithmetic and our free browser calculator.

The Essentials: Core Formulas, Units & Faraday Constant Conventions

Keeping units consistent across Coulombs ( $\text{C}$ ), Amperes ( $\text{A}$ ), Volts ( $\text{V = J/C}$ ), and Joules ( $\text{J}$ ) eliminates arithmetic errors.

1. Summary of Fundamental Equations

Quantity / Law	Formula	Variables & Units	Key Rules & Scope
Electric Charge $Q$	$Q = I \times t$	$Q$ : Charge $\text{[C]}$ $I$ : Current $\text{[A]}$ $t$ : Time $\text{[s]}$	Always convert minutes ( $\times 60$ ) and hours ( $\times 3600$ ) to seconds $\text{[s]}$ ( $1\text{ mAh} = 3.6\text{ C}$ )
Moles of Electrons $n(e^-)$	$n(e^-) = \frac{Q}{F} = \frac{I \cdot t}{F}$	$n(e^-)$ : Electron moles $\text{[mol]}$ $F$ : Faraday constant $\text{[C/mol]}$	Identical across all electrolytic cells connected in series
Deposited Mass $m$	$m = M \cdot \frac{n(e^-)}{z} \cdot \frac{\eta}{100} = \frac{M \cdot I \cdot t}{z \cdot F} \cdot \frac{\eta}{100}$	$m$ : Mass $\text{[g]}$ $M$ : Molar mass $\text{[g/mol]}$ $z$ : Electrons per formula unit $\eta$ : Current efficiency $\text{[\%]}$	Divide $n(e^-)$ by $z$ ( $z=1$ for $\text{Ag}^+$ , $z=2$ for $\text{Cu}^{2+}$ , $z=3$ for $\text{Al}^{3+}$ )
STP Gas Volume $V_{\text{STP}}$	$V_{\text{STP}} = 22.4\text{ [L/mol]} \times \frac{n(e^-)}{z_{\text{gas}}}$	$z_{\text{gas}}$ : Electrons per mole of gas	$z_{\text{gas}} = 2$ for $\text{H}_2,\ \text{Cl}_2$ ; $z_{\text{gas}} = 4$ for anode $\text{O}_2$ evolution
Standard Cell EMF $E^\circ_{\text{cell}}$	$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$	$E^\circ_{\text{cathode}}$ : Cathode reduction potential $\text{[V]}$ $E^\circ_{\text{anode}}$ : Anode reduction potential $\text{[V]}$	Never multiply $E^\circ$ by stoichiometric coefficients
Nernst Equation (at $T$ )	$E = E^\circ - \frac{R T}{n F} \ln Q = E^\circ - \frac{2.3026 R T}{n F} \log_{10} Q$	$R = 8.3145\text{ J/(mol}\cdot\text{K)}$ $T$ : Temperature $\text{[K]}$ $n$ : Transferred electrons $Q$ : Reaction quotient	At $25.0^\circ\text{C}$ ( $298.15\text{ K}$ ): $E = E^\circ - \frac{0.05916}{n} \log_{10} Q$
Gibbs Energy & Equilibrium $K$	$\Delta G^\circ = -n F E^\circ_{\text{cell}} = -R T \ln K$	$\Delta G^\circ$ : Standard Gibbs energy $\text{[J/mol]}$ $K$ : Equilibrium constant	$E^\circ_{\text{cell}} > 0 \iff \Delta G^\circ < 0 \iff K > 1$ (spontaneous galvanic discharge)

2. Comparing the Two Faraday Constant Conventions

The Faraday constant $F$ represents the electric charge carried by one mole of electrons ( $F = e \cdot N_A$ ). Depending on your curriculum or analytical setting, two values are used:

Convention	Value of $F$	Basis / Definition	When to Use
High-School / Exam Standard	$96,500\text{ C/mol}$ ( $9.65 \times 10^4\text{ C/mol}$ )	Rounded to 3 significant figures	High-school chemistry and entrance exams where problem times ( $193\text{ s}$ , $965\text{ s}$ , $1,930\text{ s}$ ) are engineered to divide cleanly by $965$
Exact SI / CODATA Value	$96,485.33212\text{ C/mol}$	Exact 2019 SI definition $e \times N_A$ $e = 1.602176634 \times 10^{-19}\text{ C}$ $N_A = 6.02214076 \times 10^{23}\text{ mol}^{-1}$	University physical/analytical chemistry labs, potentiometry, Nernst slopes ( $59.16\text{ mV/dec}$ ), and thermodynamic $\Delta G^\circ / K$ derivations

Practical Tip:
The two values differ by $0.015\%$ . You can switch between 96,500 C/mol and 96,485.33212 C/mol with a single click at the top of our Electrochemistry Calculator.

Visual Guide: 1/z Stoichiometry & Nernst Slopes

Figure 1 illustrates how a fixed electric charge distributes across half-reactions of different valence $z$ (left) and how the Nernst equation shifts cell voltage across $\log_{10} Q$ (right).

Diagram comparing Faraday's law 1/z molar scaling for z = 1, 2, 3, 4 at Q = 9,650 C (left) and Nernst equation potential slopes at 25°C with E°–ΔG°–K relations (right) — Figure 1: Left — Molar and mass yields per 0.100 mol e⁻ (Q = 9,650 C) as a function of electron number z. Right — Nernst potential slopes at 25.0 °C (−59.16 mV/n per decade) and the thermodynamic bridge connecting E°cell, ΔG°, and K. View full size image

1. Why Product Moles Scale as $1/z$

Passing $5.00\text{ A}$ for $1,930\text{ s}$ delivers $Q = 9,650\text{ C}$ , which corresponds to $n(e^-) = 0.1000\text{ mol}$ of electrons (at $F = 96,500\text{ C/mol}$ ).

$z = 1$ ( $\text{Ag}^+ + e^- \to \text{Ag}$ ): $1\text{ mol } e^-$ reduces $1\text{ mol Ag}^+ \implies 0.1000\text{ mol Ag}$ ( $10.79\text{ g}$ ).
$z = 2$ ( $\text{Cu}^{2+} + 2e^- \to \text{Cu}$ ): $2\text{ mol } e^-$ required per $\text{mol Cu} \implies 0.05000\text{ mol Cu}$ ( $3.178\text{ g}$ ).
$z = 3$ ( $\text{Al}^{3+} + 3e^- \to \text{Al}$ ): $3\text{ mol } e^-$ required per $\text{mol Al} \implies 0.03333\text{ mol Al}$ ( $0.899\text{ g}$ ).
$z = 4$ ( $2\text{H}_2\text{O} \to \text{O}_2\uparrow + 4\text{H}^+ + 4e^-$ ): Oxidizing water to produce $1\text{ mol O}_2$ releases $4\text{ mol } e^- \implies 0.02500\text{ mol O}_2$ ( $560.0\text{ mL}$ at STP).

2. The $59.16\text{ mV}/n$ Thermal Slope at $25.0^\circ\text{C}$

At $T = 298.15\text{ K}$ ( $25.0^\circ\text{C}$ ), converting natural logarithm $\ln Q$ to base-10 logarithm $\log_{10} Q$ yields:

$\frac{R T \ln 10}{F} = \frac{8.3144626 \times 298.15 \times 2.302585}{96,485.33212} \approx 0.059159\text{ V} = 59.16\text{ mV}$

Thus, a one-electron transfer ( $n = 1$ ) shifts by $-59.16\text{ mV}$ per decade of $Q$ , whereas a two-electron transfer ( $n = 2$ , Daniell cell) shifts by $-29.58\text{ mV}$ per decade.

Four Step-by-Step Worked Examples

Example 1: Aqueous CuSO₄ Electrolysis (Cathode Copper Mass & Anode O₂ Volume)

Problem:
An aqueous $\text{CuSO}_4$ solution is electrolyzed using inert platinum electrodes with a steady current of $5.00\text{ A}$ for $32\text{ min } 10\text{ s}$ ( $1,930\text{ s}$ ). Using $F = 96,500\text{ C/mol}$ and $M(\text{Cu}) = 63.55\text{ g/mol}$ , calculate the mass of copper deposited at the cathode and the volume of $\text{O}_2$ gas evolved at the anode at STP ( $22.4\text{ L/mol}$ ).

Step-by-Step Solution

Compute total electric charge $Q$ and moles of electrons $n(e^-)$ : $Q = I \times t = 5.00\text{ A} \times 1,930\text{ s} = 9,650\text{ C}$ $n(e^-) = \frac{9,650\text{ C}}{96,500\text{ C/mol}} = 0.1000\text{ mol } e^-$
Cathode copper deposition ( $\text{Cu}^{2+} + 2e^- \to \text{Cu},\ z = 2$ ): $n(\text{Cu}) = \frac{0.1000\text{ mol}}{2} = 0.05000\text{ mol}$ $m(\text{Cu}) = 0.05000\text{ mol} \times 63.55\text{ g/mol} = 3.1775\text{ g} \approx \mathbf{3.178\text{ g}}$
Anode oxygen gas evolution ( $2\text{H}_2\text{O} \to \text{O}_2\uparrow + 4\text{H}^+ + 4e^-,\ z_{\text{gas}} = 4$ ): $n(\text{O}_2) = \frac{0.1000\text{ mol}}{4} = 0.02500\text{ mol}$ $V(\text{O}_2) = 0.02500\text{ mol} \times 22.4\text{ L/mol} = 0.5600\text{ L} = \mathbf{560.0\text{ mL}}$

👉 Load Example 1 (CuSO₄ Electrolysis: 5.00 A, 1930 s) in the Electrochemistry Calculator

Example 2: Chlor-Alkali Brine Electrolysis Using Exact CODATA F

Problem:
In a chlor-alkali membrane cell electrolyzing saturated aqueous $\text{NaCl}$ , a current of $10.0\text{ A}$ is passed for $1.00\text{ h}$ at $100\%$ Faradaic efficiency. Using the exact CODATA Faraday constant $F = 96,485.33212\text{ C/mol}$ , find the mass of $\text{NaOH}$ ( $M = 40.00\text{ g/mol}$ ) produced and the STP volume of $\text{Cl}_2$ gas evolved.

Step-by-Step Solution

Convert time to seconds and find $Q$ and $n(e^-)$ : $t = 1.00\text{ h} \times 3,600\text{ s/h} = 3,600\text{ s}$ $Q = 10.0\text{ A} \times 3,600\text{ s} = 36,000\text{ C} \quad (10,000\text{ mAh})$ $n(e^-) = \frac{36,000\text{ C}}{96,485.33212\text{ C/mol}} \approx 0.373114\text{ mol } e^-$
Mass of $\text{NaOH}$ formed ( $z = 1$ mole of $\text{OH}^-$ per mole of $e^-$ ): $m(\text{NaOH}) = 0.373114\text{ mol} \times 40.00\text{ g/mol} \approx \mathbf{14.925\text{ g}}$
STP volume of $\text{Cl}_2$ evolved at the anode ( $2\text{Cl}^- \to \text{Cl}_2\uparrow + 2e^-,\ z_{\text{gas}} = 2$ ): $n(\text{Cl}_2) = \frac{0.373114\text{ mol}}{2} \approx 0.186557\text{ mol}$ $V(\text{Cl}_2) = 0.186557\text{ mol} \times 22.4\text{ L/mol} \approx 4.1789\text{ L} = \mathbf{4,178.9\text{ mL}}$

👉 Load Example 2 (Brine Electrolysis: 10.0 A, 1.00 h, CODATA F) in the Calculator

Example 3: Non-Standard Daniell Cell Potential via the Nernst Equation

Problem:
A Daniell cell $\text{(-)\ Zn(s)}\mid\text{Zn}^{2+}\text{(0.010 M)}\parallel\text{Cu}^{2+}\text{(1.00 M)}\mid\text{Cu(s)\ (+)}$ operates at $25.0^\circ\text{C}$ ( $298.15\text{ K}$ ), with standard potential $E^\circ_{\text{cell}} = +1.100\text{ V}$ . Calculate its cell potential $E$ and Gibbs free energy change $\Delta G$ .

Step-by-Step Solution

Determine reaction quotient $Q$ for $\text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \to \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)}$ ( $n = 2$ ): $Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.010}{1.00} = 0.010 = 10^{-2} \implies \log_{10} Q = -2.00$
Apply the Nernst equation at $25.0^\circ\text{C}$ : $E = E^\circ_{\text{cell}} - \frac{0.05916\text{ V}}{n} \log_{10} Q = 1.100 - \frac{0.05916}{2} \times (-2.00) = 1.100 + 0.05916 \approx \mathbf{+1.1592\text{ V}}$
Calculate non-standard Gibbs free energy $\Delta G$ : $\Delta G = -n F E = -2 \times 96,485.33\text{ C/mol} \times 1.15916\text{ V} \approx \mathbf{-223.68\text{ kJ/mol}}$

👉 Load Example 3 (Daniell Cell Nernst: 0.010 M Zn²⁺ / 1.00 M Cu²⁺) in the Calculator

Example 4: Ag⁺ Concentration Cell & Standard Equilibrium Constant K

Problem:
(1) Find the EMF of a silver concentration cell $\text{(-)\ Ag}\mid\text{Ag}^+(0.0010\text{ M})\parallel\text{Ag}^+(0.100\text{ M})\mid\text{Ag\ (+)}$ at $25.0^\circ\text{C}$ .
(2) For the Daniell cell ( $E^\circ_{\text{cell}} = +1.100\text{ V},\ n = 2$ ), calculate $\Delta G^\circ$ and the thermodynamic equilibrium constant $K$ at $25.0^\circ\text{C}$ .

Step-by-Step Solution

(1) Silver concentration cell ( $E^\circ_{\text{cell}} = 0\text{ V},\ n = 1$ ): $Q = \frac{[\text{Ag}^+]_{\text{dilute (anode)}}}{[\text{Ag}^+]_{\text{conc (cathode)}}} = \frac{0.0010}{0.100} = 0.010 \implies \log_{10} Q = -2.00$ $E = 0 - \frac{0.05916\text{ V}}{1} \times (-2.00) = \mathbf{+0.1183\text{ V}} \quad (+118.3\text{ mV})$
(2) Daniell cell $\Delta G^\circ$ and equilibrium constant $K$ : $\Delta G^\circ = -n F E^\circ_{\text{cell}} = -2 \times 96,485.33\text{ C/mol} \times 1.100\text{ V} \approx \mathbf{-212.27\text{ kJ/mol}}$ $\log_{10} K = \frac{n F E^\circ_{\text{cell}}}{R T \ln 10} = \frac{2 \times 1.100}{0.059159} \approx +37.188 \implies K = 10^{37.188} \approx \mathbf{1.54 \times 10^{37}}$

👉 Load Example 4a (Ag⁺ Concentration Cell) in the Calculator
👉 Load Example 4b (Daniell Cell ΔG° & K) in the Calculator

Our Electrochemistry, Nernst Equation & Faraday’s Law Calculator streamlines multi-step verification:

Choose the Faraday Constant Convention: Use the top selector (#ec-f-mode) to pick either F = 96,500 C/mol (textbook rounded) or F = 96,485.33212 C/mol (SI/CODATA exact).
Pick Your Calculation Tab:
- Faraday’s Law Tab: Solve in 4 directions for deposited mass $m$ , required current $I$ , electrolysis time $t$ , or ionic valence $z$ , while simultaneously reading charge $Q$ ( $\text{C}$ & $\text{mAh}$ ), $n(e^-)$ , and STP gas volume.
- Nernst Equation Tab: Compute non-standard potential $E$ , standard potential $E^\circ$ , or reaction quotient $Q$ with an interactive SVG plot of $E$ vs. $\log_{10} Q$ .
- Standard EMF, ΔG° & K Tab: Select cathode and anode half-cells to compute $E^\circ_{\text{cell}}$ , $\Delta G^\circ$ , equilibrium constant $K$ , and IUPAC line notation.
Connect with Related Calculators:
- For redox stoichiometric titrations ( $\text{KMnO}_4$ , iodometry): Redox Titration Calculator (Redox Titration Guide)
- For hydrogen electrode $\text{pH}$ dependence: pH Calculator and Buffer Solution Calculator
- For non-STP gas volumes using $PV = nRT$ : Ideal Gas Law Calculator
- For cell resistance and power dissipation: Ohm’s Law Calculator

Five Common Mistakes & Model Limitations

Forgetting to Convert Minutes or Hours to Seconds: Since $1\text{ A} = 1\text{ C/s}$ , multiplying amperes by minutes underestimates charge $Q$ by a factor of $60$ .
Using $z = 2$ Instead of $z = 4$ for Anode $\text{O}_2$ Evolution: Oxidizing water ( $2\text{H}_2\text{O} \to \text{O}_2 + 4\text{H}^+ + 4e^-$ ) transfers $4$ electrons per $\text{O}_2$ molecule.
Misinterpreting Lead-Acid Battery Electrode Mass Changes: During discharge, both the $\text{Pb}$ anode ( $+48.0\text{ g/mol } e^-$ ) and the $\text{PbO}_2$ cathode ( $+32.0\text{ g/mol } e^-$ ) gain mass as insoluble $\text{PbSO}_4$ precipitates onto both plates.
Multiplying $E^\circ$ by Stoichiometric Coefficients: Electrode potential $E^\circ\text{ [V = J/C]}$ is intensive and never scales when balancing half-reactions.
Scope & Real-World Deviations (Overpotential & Activity): Replacing thermodynamic activities $a_i = \gamma_i c_i / c^\circ$ with molar concentrations assumes dilute ideal solutions ( $\gamma_i \approx 1$ ), and equilibrium Nernst potentials exclude activation overpotential ( $\eta$ ) and internal ohmic drop ( $I R_{\text{int}}$ ).

References & Primary Specifications

NIST CODATA — Faraday constant F Official SI/CODATA recommended value of the Faraday constant ( $F = 96,485.33212\dots\text{ C mol}^{-1}$ ).
IUPAC Gold Book — Nernst Equation International standard nomenclature and thermodynamic definition of the Nernst equation.
OpenStax Chemistry 2e — Section 17.4: Potential, Free Energy, and Equilibrium University general chemistry derivations of $E^\circ_{\text{cell}}$ , $\Delta G^\circ$ , equilibrium constant $K$ , and quantitative electrolysis.
Atkins’ Physical Chemistry (11th Edition) — Chapter 6: Chemical Equilibrium Rigorous physical chemistry treatment of electrochemical cells, concentration cells, and activity coefficients.

FAQ

Should I use F = 96,500 C/mol or F = 96,485.33212 C/mol for the Faraday constant?

Use F = 96,500 C/mol (9.65 × 10⁴ C/mol) when solving introductory or high-school chemistry exam problems where electrolysis durations (such as 193 s or 1,930 s) are specifically chosen to divide cleanly by 965. Use the exact 2019 SI / CODATA constant F = e · NA = 96,485.33212 C/mol for university physical chemistry, analytical chemistry lab reports, and research.

Why do we divide moles of electrons by z = 4 when calculating anode oxygen (O₂) evolution?

During the electrolysis of aqueous sulfate, nitrate, or hydroxide solutions with inert electrodes (Pt or C), water is oxidized at the anode via 2H₂O → O₂ + 4H⁺ + 4e⁻ (or 4OH⁻ → O₂ + 2H₂O + 4e⁻ in base). Generating 1 mole of O₂ molecules requires transferring 4 moles of electrons (z = 4), so n(O₂) = n(e⁻) / 4.

If I double the stoichiometric coefficients of a half-reaction, do I also double E°?

No. Standard Gibbs free energy ΔG° [J/mol] is an extensive property that scales with molar quantity, whereas standard electrode potential E° = −ΔG° / (nF) [V = J/C] is an intensive property representing energy per unit electric charge. Doubling a half-reaction doubles both ΔG° and n, leaving their ratio E° unchanged.

How does a concentration cell generate voltage when its standard cell potential E°cell is 0 V?

Because both half-cells use the identical electrode/ion couple, E°cell = 0 V. However, the spontaneous thermodynamic drive to equalize concentrations (entropy of mixing, ΔG < 0) oxidizes metal in the dilute half-cell (anode) and reduces ions in the concentrated half-cell (cathode), generating E = −(0.05916 / n) log₁₀(C_dilute / C_conc) > 0 V at 25 °C.

Sources and specifications

NIST CODATA Internationally Recommended Values of the Fundamental Physical Constants — Faraday constant F
Exact SI value of the Faraday constant F = e · NA = 96,485.33212... C/mol defined by elementary charge e and Avogadro constant NA.
IUPAC Compendium of Chemical Terminology (Gold Book) — Nernst Equation
International definition of the Nernst equation relating equilibrium electrode potential E to standard potential E°, temperature T, and reaction quotient Q.
OpenStax Chemistry 2e — Section 17.4: Potential, Free Energy, and Equilibrium & Section 17.7: Electrolysis
Derivations of galvanic cell EMF E°cell, standard Gibbs energy ΔG° = −nFE°cell, equilibrium constant K, and quantitative electrolysis stoichiometry.
Atkins' Physical Chemistry (11th Edition) — Chapter 6: Chemical Equilibrium (Electrochemistry)
Thermodynamic treatment of intensive electrode potentials vs. extensive Gibbs free energies, concentration cells, and ionic activity coefficients.

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Verification Scope & Citation Formats

Formula & spec verified100% client-side

Companion tool QA verification: Checked November 10, 2026 via independent calculation and Playwright tests in both languages: CuSO₄ electrolysis (5.00 A, 1930 s, F=96,500) gives Q=9,650 C, n(e⁻)=0.1000 mol, 3.178 g Cu, and 560.0 mL STP O₂; brine electrolysis (10.0 A, 1.00 h, F=96,485.33) gives 14.92 g NaOH; Daniell cell Nernst ([Zn²⁺]=0.010 M, [Cu²⁺]=1.00 M, 25°C) gives E=+1.1592 V and ΔG=-223.68 kJ/mol; Ag⁺ concentration cell (0.0010 M / 0.100 M) gives E=+0.1183 V; standard Daniell thermodynamics (E°=+1.100 V, n=2) gives ΔG°=-212.27 kJ/mol and K=1.54×10³⁷. Applies to stated ideal models excluding overpotential and internal resistance.

All worked examples and tables in this guide are verified under their stated assumptions, units, and standard editions. You can copy the APA 7th or BibTeX citation below for lab reports or technical documentation.

APA 7th Edition

Tools Hub Editorial Team. (2026). Guide to Faraday's Law of Electrolysis, Nernst Equation & Cell Potential: Formulas & Worked Examples. Tools Hub. https://the-tools-hub.net/en/blog/electrochemistry-guide/

BibTeX (@misc)

@misc{tools_hub_electrochemistry_guide_2026,
  author = {{Tools Hub Editorial Team}},
  title = {Guide to Faraday's Law of Electrolysis, Nernst Equation & Cell Potential: Formulas & Worked Examples},
  year = {2026},
  url = {https://the-tools-hub.net/en/blog/electrochemistry-guide/}
}

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Calculate electrolysis mass, current, time, valence z, and STP gas volume via Faraday's Law (Q = It, m = MIt/(zF)), solve non-standard cell potentials and concentration cells with the Nernst equation (E = E° − (RT/nF)ln Q), and determine standard cell EMF E°cell, Gibbs free energy ΔG° = −nFE°, and equilibrium constant K with a 1-click toggle between textbook F = 96,500 C/mol and exact CODATA F = 96,485.33212 C/mol.

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Guide to Faraday's Law of Electrolysis, Nernst Equation & Cell Potential: Formulas & Worked Examples

The essentials

The Essentials: Core Formulas, Units & Faraday Constant Conventions

1. Summary of Fundamental Equations

2. Comparing the Two Faraday Constant Conventions

Visual Guide: 1/z Stoichiometry & Nernst Slopes

1. Why Product Moles Scale as $1/z$

2. The $59.16\text{ mV}/n$ Thermal Slope at $25.0^\circ\text{C}$

Four Step-by-Step Worked Examples

Example 1: Aqueous CuSO₄ Electrolysis (Cathode Copper Mass & Anode O₂ Volume)

Step-by-Step Solution

Example 2: Chlor-Alkali Brine Electrolysis Using Exact CODATA F

Step-by-Step Solution

Example 3: Non-Standard Daniell Cell Potential via the Nernst Equation

Step-by-Step Solution

Example 4: Ag⁺ Concentration Cell & Standard Equilibrium Constant K

Step-by-Step Solution

Five Common Mistakes & Model Limitations

References & Primary Specifications

FAQ

Sources and specifications

Verification Scope & Citation Formats

Electrochemistry, Nernst Equation & Faraday's Law Calculator

Molarity, Dilution, Buffer, Beer-Lambert, Solubility & pH

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Guide to Osmotic Pressure & Van ’t Hoff’s Law: Formulas, Tonicity, and Molar Mass

Arrhenius Equation & Activation Energy Guide: 2-Temp Solving, Plots & Half-Lives

Buffer Solution Preparation & Henderson-Hasselbalch Guide: Hydrates, Titration & Temperature Shifts

My Tools & Quick Launch

The essentials

The Essentials: Core Formulas, Units & Faraday Constant Conventions

1. Summary of Fundamental Equations

2. Comparing the Two Faraday Constant Conventions

Visual Guide: 1/z Stoichiometry & Nernst Slopes

1. Why Product Moles Scale as 1/z1/z1/z

2. The 59.16 mV/n59.16\text{ mV}/n59.16 mV/n Thermal Slope at 25.0∘C25.0^\circ\text{C}25.0∘C

Four Step-by-Step Worked Examples

Example 1: Aqueous CuSO₄ Electrolysis (Cathode Copper Mass & Anode O₂ Volume)

Step-by-Step Solution

Example 2: Chlor-Alkali Brine Electrolysis Using Exact CODATA F

Step-by-Step Solution

Example 3: Non-Standard Daniell Cell Potential via the Nernst Equation

Step-by-Step Solution

Example 4: Ag⁺ Concentration Cell & Standard Equilibrium Constant K

Step-by-Step Solution

How to Use the Electrochemistry Calculator & Related Tools

Five Common Mistakes & Model Limitations

References & Primary Specifications

FAQ

Sources and specifications

Verification Scope & Citation Formats

Electrochemistry, Nernst Equation & Faraday's Law Calculator

Molarity, Dilution, Buffer, Beer-Lambert, Solubility & pH

Related articles

Guide to Osmotic Pressure & Van ’t Hoff’s Law: Formulas, Tonicity, and Molar Mass

Arrhenius Equation & Activation Energy Guide: 2-Temp Solving, Plots & Half-Lives

Buffer Solution Preparation & Henderson-Hasselbalch Guide: Hydrates, Titration & Temperature Shifts

1. Why Product Moles Scale as $1/z$

2. The $59.16\text{ mV}/n$ Thermal Slope at $25.0^\circ\text{C}$