Electrochemical Cell Voltage Calculator

Electrochemical Cells Guide

What do I need to know about Cell Potential Calculation?

E°cell = E°cathode − E°anode. The cathode is the electrode where reduction occurs (gains electrons); the anode is where oxidation occurs (loses electrons). By convention, standard electrode potentials are all written as reduction potentials. The more positive the reduction potential, the stronger the oxidising agent. Example: zinc-copper cell. Cathode (Cu²⁺/Cu): +0.34 V. Anode (Zn²⁺/Zn): −0.76 V. E°cell = 0.34 − (−0.76) = +1.10 V. A positive E°cell means the reaction is spontaneous in the forward direction as written, releasing energy that can do electrical work — a negative E°cell would mean the reverse reaction is spontaneous instead, and the cell as drawn would not function as a spontaneous battery.

What should I know about Gibbs Free Energy and Spontaneity?

ΔG° = −nFE°cell. Where n = moles of electrons transferred, F = Faraday's constant (96,485 C/mol), E°cell = standard cell potential. If E°cell > 0: ΔG° < 0 → spontaneous. If E°cell < 0: ΔG° > 0 → non-spontaneous (would require external energy — electrolysis). If E°cell = 0: ΔG° = 0 → equilibrium. For the zinc-copper cell (n=2): ΔG° = −2 × 96485 × 1.10 = −212 kJ/mol. Relationship to equilibrium: ΔG° = −RT ln K, so ln K = nFE°/RT = nE°/0.02569 at 298 K.

What do I need to know about The Electrochemical Series?

The electrochemical series lists half-cells in order of standard electrode potential, from most negative (strongest reducing agents: Li, K, Na, Mg, Al) to most positive (strongest oxidising agents: F₂, MnO₄⁻, O₂, Cl₂). Rules: a more positive half-cell always oxidises a more negative one. Displacement reactions: zinc displaces copper from copper sulfate solution because Zn has a more negative E° (−0.76 V) than Cu (+0.34 V). Electroplating: the metal to be deposited is the cathode in an electrolytic cell — for example, electroplating an object with silver connects it as the cathode in a cell containing a silver salt solution, so silver ions are reduced and deposited onto its surface as a coherent metal layer.

What's the difference between Real Cells and Standard Conditions?

Standard electrode potentials apply at 298 K, 1 mol/L concentrations, and 1 atm for gases. Real cells deviate due to concentration effects (Nernst equation): E = E° − (RT/nF) × ln Q. At 298 K: E = E° − (0.0257/n) × ln Q. This is important for: batteries as they discharge (reactant concentrations decrease), pH cells (glass electrode measures H⁺ concentration), and biological systems where concentrations are far from 1 mol/L. The Daniell cell (Zn/Cu) in everyday conditions operates at approximately 1.1 V under standard conditions, but the actual voltage falls as the cell discharges and reactant concentrations drop, following the Nernst equation rather than staying fixed at the standard value — this is why a battery's voltage sags gradually over its working life rather than switching off abruptly at zero.

What do I need to know about a Worked Cell Construction Example?

Consider constructing a cell from Zn2+/Zn (E° = -0.76V) and Cu2+/Cu (E° = +0.34V). The more positive value (Cu2+/Cu) is the cathode (reduction: Cu2+ + 2e- to Cu); the more negative value (Zn2+/Zn) is the anode (oxidation, reversed: Zn to Zn2+ + 2e-). E°cell = E°cathode - E°anode = 0.34 - (-0.76) = 1.10V. The overall reaction is found by adding the cathode reduction and anode oxidation half-equations (electrons must cancel — here both already involve 2 electrons): Zn + Cu2+ to Zn2+ + Cu, E°cell = 1.10V. Conventional notation writes this as Zn | Zn2+ || Cu2+ | Cu, anode on the left, cathode on the right. Since n = 2 and E°cell is positive, delta-G° = -nFE° = -2 x 96485 x 1.10 = -212,267 J/mol, confirming a strongly spontaneous reaction — this is exactly the chemistry of the classic Daniell cell.

What should I know about Real-World Batteries?

Commercial batteries are electrochemical cells engineered for practical use, and their cell potentials follow the same E°cell = E°cathode - E°anode logic, though real cell chemistries are usually more complex than simple metal-ion half-cells. The alkaline battery uses a Zn/MnO2 system producing about 1.5V per cell. Lithium-ion batteries exploit lithium's extremely negative reduction potential and low atomic mass for high energy density, typically around 3.6-3.7V per cell. Lead-acid car batteries use Pb/PbO2 electrodes in sulfuric acid, giving about 2.0V per cell — six cells in series produce the familiar 12V battery. Fuel cells (H2/O2) are electrochemical cells consuming reactants supplied continuously from outside, giving a theoretical cell potential of about 1.23V, though practical devices achieve somewhat less due to internal resistance. Connecting multiple cells in series adds their voltages, while connecting cells in parallel increases available current without changing voltage — a distinction following from circuit principles rather than electrochemistry itself.

What's the key thing to understand about Concentration Cells?

A concentration cell is built from identical electrodes and identical ions, differing only in concentration between the two half-cells — yet it still generates a measurable voltage, driven purely by the system's tendency to equalise concentration. The Nernst equation predicts this directly: E = (RT/nF) ln(C_cathode/C_anode), which gives E = 0 only when the two concentrations are equal, and a nonzero voltage otherwise, with the more concentrated side always acting as the cathode. Concentration cells are a clean demonstration that cell voltage ultimately comes from a system seeking equilibrium, not from any difference in the chemical identity of the electrodes themselves.

What do I need to know about Standard Reduction Potentials for Common Electrodes?

Every half-reaction has a standard reduction potential, E°, measured against the standard hydrogen electrode (SHE) at 298 K with all species at 1 M (or 1 atm for gases). The more positive the value, the more readily that species is reduced — meaning it's a stronger oxidising agent — while very negative values mark strong reducing agents.

To build any cell, subtract the anode's (oxidation) E° from the cathode's (reduction) E°: E°cell = E°cathode − E°anode, using whichever half-reaction is being reduced as the cathode. For a copper-zinc Daniell cell, copper is reduced (cathode, +0.34 V) and zinc is oxidised (anode, −0.76 V), giving E°cell = 0.34 − (−0.76) = 1.10 V. Real cells almost never match these standard values exactly, since concentrations in actual batteries, corrosion cells, or lab setups are rarely exactly 1 M — which is the entire motivation for the Nernst equation to correct E° for whatever concentrations are actually present.

What do I need to know about a Worked Example — Gibbs Free Energy from Cell Potential?

Standard cell potential connects directly to thermodynamics through ΔG° = −nFE°, where F = 96,485 C/mol. A positive E°cell always corresponds to a negative ΔG° — confirming the reaction is spontaneous as written. Worked example: for the Daniell cell above, E°cell = 1.10 V and n = 2 electrons are transferred per formula unit. ΔG° = −n × F × E° = −2 × 96,485 × 1.10 = −212,267 J/mol ≈ −212.3 kJ/mol That large negative value confirms the reaction is strongly spontaneous under standard conditions. The same relationship lets you work backwards: if a reaction's ΔG° is known from thermochemical data but its E° isn't, rearranging gives E° = −ΔG°/(nF). It also connects to the equilibrium constant through ΔG° = −RT ln K, so combining the two gives E° = (RT/nF) ln K — meaning a cell with a large standard potential corresponds to a reaction that goes almost to completion at equilibrium. For the Daniell cell, K works out to an enormous number (around 1.6 × 10³⁷), which is exactly what you'd expect from a cell potential as large and positive as 1.10 V: by the time the system reaches equilibrium, essentially all the copper(II) ions have been consumed. The sign convention is worth memorising on its own: a positive ΔG° (which pairs with a negative E°cell) means the reaction as written is non-spontaneous, and the cell would actually run in reverse if connected — which is exactly what happens when you try to charge a battery, forcing a thermodynamically unfavourable reaction to proceed by supplying external electrical energy rather than letting the cell generate it.