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Standard Cell Potential

EMF from reduction potentials.

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E_{ce l l}^{θ} = E_{r e d}^{θ} - E_{o x}^{θ}

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Core idea

Overview

The standard cell potential measures the electrical potential difference between two half-cells under standard conditions of 25°C, 1 M concentration, and 1 atm pressure. It determines the maximum voltage a galvanic cell can deliver and indicates whether a redox reaction will occur spontaneously.

When to use: Use this equation when calculating the electromotive force (EMF) of a voltaic or electrolytic cell under standard state conditions. It assumes that both the reduction and oxidation half-cell values are provided as standard reduction potentials.

Why it matters: This calculation is fundamental for designing batteries and fuel cells, as it predicts the energy output of chemical reactions. It also allows chemists to determine the spontaneity of reactions; a positive standard cell potential signifies a spontaneous process.

Symbols

Variables

E_{cell}^\theta = Cell Potential, E_{red}^\theta = Cathode Potential, E_{ox}^\theta = Anode Potential

E_{ce l l}^{θ}

Cell Potential

V

E_{r e d}^{θ}

Cathode Potential

V

E_{o x}^{θ}

Anode Potential

V

Walkthrough

Derivation

Understanding Standard Cell Potential

Finds the EMF of a cell under standard conditions from standard electrode potentials.

Standard conditions apply (298 K, 100 kPa, 1.0 mol $d m^{- 3}$ ).
Electrode potentials are standard reduction potentials.

Use Right Minus Left:

Choose the more positive E° as the reduction (right) half-cell and subtract the left (oxidation) half-cell.

E_{cell}^{⊖} = E_{right}^{⊖} - E_{left}^{⊖}

Result

E_{cell}^{⊖} = E_{right}^{⊖} - E_{left}^{⊖}

Source: OCR A-Level Chemistry A — Redox and Electrode Potentials

Free formulas

Rearrangements

Solve for $E_{ce l l}^{θ}$

Standard Cell Potential

E = C - A

This process demonstrates how to simplify the Standard Cell Potential equation using shorthand notation (E=C-A) for ease of memory.

Difficulty: 2/5

Solve for $E_{r e d}^{θ}$

Make $E r e d^{t}$ heta the subject

C = E + A

Rearrange the Standard Cell Potential equation to make $E_{r e d}^{θ}$ (cathode potential) the subject.

Difficulty: 2/5

Solve for $E_{o x}^{θ}$

Make $E_{o x}$ ^ $θ$ (Anode Potential) the subject

A = C - E

Rearrange the Standard Cell Potential equation, $E_{ce l l}^{θ} = E_{r e d}^{θ} - E_{o x}^{θ}$ , to isolate $E_{o x}^{θ}$ , which represents the Anode Potential.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line with a positive slope of 1, where the cell potential increases directly as the cathode potential increases. For a chemistry student, this means that higher cathode potential values represent a stronger tendency for reduction to occur, leading to a larger overall cell potential. The most important feature is the constant slope, which indicates that any incremental change in the cathode potential results in an identical change in the cell potential regardless of the starting point.

Graph type: linear

Why it behaves this way

Intuition

The cell potential represents the difference in the inherent 'electron pulling power' or 'electron energy level' between the two half-cells, driving electrons from the higher energy (more negative reduction potential)

E_{ce l l}^{θ}

The maximum electrical potential difference (voltage) that a galvanic cell can produce, or the minimum voltage required for an electrolytic cell, under standard conditions (25°C, 1

This is the net 'push' or 'pull' driving electrons through the external circuit, indicating the overall energy change available from the redox reaction and its spontaneity.

E_{r e d}^{θ}

The standard reduction potential of the half-cell where reduction occurs, representing its inherent tendency to gain electrons under standard conditions.

This value indicates how 'eager' the species in this half-cell is to accept electrons; a more positive value means it's a stronger oxidizing agent.

E_{o x}^{θ}

The standard reduction potential of the half-cell where oxidation occurs, representing its inherent tendency to gain electrons under standard conditions.

Although it's a reduction potential, this term refers to the species that *loses* electrons. A more negative (or less positive) value indicates a stronger tendency for the species to be oxidized (lose electrons).

Signs and relationships

- E_{ox}^θ: The negative sign is applied to the standard reduction potential of the species undergoing oxidation. This effectively converts its reduction potential into an oxidation potential (since E°_oxidation = -E°_reduction)

Free study cues

Insight

Canonical usage

All terms in this equation represent electrical potential and must be expressed in the same unit, typically the Volt (V), to ensure the resulting cell potential is consistent with thermodynamic tables.

Common confusion

Students often incorrectly multiply the standard potential by stoichiometric coefficients from the balanced chemical equation. Standard potential is an intensive property and does not change with the amount of substance.

Unit systems

$E_{c} e l l^{θ}$ V · The standard electromotive force of the cell; must be positive for a spontaneous reaction in a galvanic cell.

$E_{r} e d^{θ}$ V · The standard reduction potential of the cathode (the half-cell where reduction occurs).

$E_{o} x^{θ}$ V · The standard reduction potential of the anode (the half-cell where oxidation occurs). Note that both values in this specific subtraction convention are reduction potentials.

Ballpark figures

Quantity:
Quantity:

One free problem

Practice Problem

A student constructs a silver-zinc cell. If the standard reduction potential of the silver cathode is 0.80 V and the standard reduction potential of the zinc anode is -0.76 V, calculate the standard cell potential.

Cathode Potential0.8 V

Anode Potential-0.76 V

Solve for: $E$

Hint: Subtract the anode's reduction potential from the cathode's reduction potential.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Calculating EMF of a zinc-copper cell.

Study smarter

Tips

Ensure both C and A are expressed as standard reduction potentials from a reference table.
The cathode (C) is the electrode where reduction occurs and typically has the more positive potential in a galvanic cell.
Standard cell potential is an intensive property and does not change with the size or stoichiometry of the reaction.

Avoid these traps

Common Mistakes

Subtracting in wrong order.
Changing sign of tabulated values.

Common questions

Frequently Asked Questions

Finds the EMF of a cell under standard conditions from standard electrode potentials.

Use this equation when calculating the electromotive force (EMF) of a voltaic or electrolytic cell under standard state conditions. It assumes that both the reduction and oxidation half-cell values are provided as standard reduction potentials.

This calculation is fundamental for designing batteries and fuel cells, as it predicts the energy output of chemical reactions. It also allows chemists to determine the spontaneity of reactions; a positive standard cell potential signifies a spontaneous process.

Subtracting in wrong order. Changing sign of tabulated values.

Calculating EMF of a zinc-copper cell.

Ensure both C and A are expressed as standard reduction potentials from a reference table. The cathode (C) is the electrode where reduction occurs and typically has the more positive potential in a galvanic cell. Standard cell potential is an intensive property and does not change with the size or stoichiometry of the reaction.

References

Sources

Atkins' Physical Chemistry
Brown, LeMay, Bursten, Murphy, Woodward, Stoltzfus. Chemistry: The Central Science
Wikipedia: Standard electrode potential
IUPAC Gold Book
NIST CODATA
NIST Chemistry WebBook
CRC Handbook of Chemistry and Physics
Bard and Faulkner Electrochemical Methods: Fundamentals and Applications

Standard Cell Potential

Overview

Variables

Derivation

Use Right Minus Left:

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Nernst Equation

Frequently Asked Questions

Sources