Redox Equation Balancing by Half-Reactions

Balance net ionic equations for inorganic redox reactions by the half-reaction method in acidic or basic medium, starting from a global equation or two half-reactions

Input form

Net ionic equation3 elements detected

Enter the net ionic equation without H+, OH-, or e-. For charges greater than 1 use Fe+2 or SO4-2.

Reaction medium

The medium only determines how H2O, H+, and OH- are added during balancing. The calculator preserves the species you enter; it does not predict precipitates or predominant species at a given pH.

Examples to get started

Net ionic equation preview

\text{Mn}\text{O}_{4}^{-} + \text{Fe}^{2+} \rightarrow \text{Mn}^{2+} + \text{Fe}^{3+}

Balanced global equation

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Oxidation

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Reduction

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Electron LCM

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Independent verification

Every atom is conserved

Electric charge is conserved

Electrons cancel completely

Coefficients are minimal

Matches an independent algebraic check

The method will appear here

Choose the medium and solve a global equation or two half-reactions to walk through the complete method.

Fundamentals & Explanation

What changes in a redox reaction?

An oxidation-reduction reaction transfers electrons. A species whose oxidation state increases is oxidized and releases electrons; one whose state decreases is reduced and accepts them. Oxidation and reduction therefore occur together.

\text{oxidation: } Fe^{2+} \rightarrow Fe^{3+} + e^-

The reducing agent is the species being oxidized; the oxidizing agent is the species being reduced. Each agent is named for what it causes in the other species.

In simple disproportionation, one species has both roles: one atom of the element is oxidized while another is reduced. Comproportionation follows the inverse path: two different oxidation states converge on an intermediate one. The calculator handles both simple cases when the species can be paired unambiguously.

3Cl_2 + 6OH^- \rightarrow 5Cl^- + ClO_3^- + 3H_2O

Fe + 2Fe^{3+} \rightarrow 3Fe^{2+}

Assigning oxidation states

At introductory level, conventional rules are combined with the requirement that the weighted sum of oxidation states reproduce the total charge. A free element is 0; F is usually −1; O, −2; H, +1; and a monatomic ion equals its charge. Peroxides, hydrides, and compounds with F require exceptions.

x + 4(-2) = -1 \quad \Rightarrow \quad x_{Mn}=+7 \;\text{in } MnO_4^-

These rules are an electron-bookkeeping model, not measured partial charges. The modern definition and its limits are discussed in the IUPAC Gold Book and recommendations listed below.

Ion-electron method in acidic medium

Separate oxidation and reduction.
Balance the changing element, then all elements other than O and H.
Balance O with H₂O and then H with H⁺.
Equalize charge by adding e⁻ to the more positive side.
Scale by the electron LCM, add both halves, and cancel common species.

Example: permanganate and iron(II)

MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O

Fe^{2+} \rightarrow Fe^{3+} + e^- \quad (\times 5)

MnO_4^- + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}

Converting to basic medium

First complete the half-reaction as if the medium were acidic. Then add the same amount of OH⁻ to both sides as the H⁺ present. Each H⁺ + OH⁻ pair becomes H₂O, and common water is cancelled. Adding OH⁻ to only one side would break charge conservation.

H^+ + OH^- \rightarrow H_2O

Reading the guided solution

Values above each symbol identify the two redox centers. Amber cards follow oxidation and blue cards follow reduction. Each step shows how the equation changes and which species are added or canceled. The five final checks verify atom and charge conservation, electron cancellation, minimal coefficients, and agreement with an independent algebraic balance. You can start from the global equation or supply two half-reaction skeletons; the calculator determines which one represents oxidation and which represents reduction before applying the same balancing steps.

Balancing is not speciation

Selecting acidic or basic medium determines how the method introduces H₂O, H⁺, and OH⁻; it does not predict solubility, precipitation, complexation, or the dominant species at a given pH. The calculator preserves the species in the supplied net ionic equation. For example, Cr³⁺ and Cr(OH)₃ are different products and both can be balanced, but choosing which one represents the real system depends on the chemical conditions.

Why some inputs are rejected

A chemical formula does not always determine a unique oxidation state. Fe₃O₄ has mixed valence, while thiosulfate contains non-equivalent sulfur atoms. The calculator handles simple disproportionation and comproportionation, but not cases with multiple redox centers, organic formulas, superoxides, or molecular equations with spectator ions. Rejecting these inputs avoids presenting a misleading chemical interpretation.

Quick verification

Each element has the same atom count on both sides.
Total charge is equal on the left and right.
No electrons remain in the global equation.
The integer coefficients share no divisor greater than 1.

References

IUPAC Gold Book — oxidation state.
P. Karen et al., Toward a Comprehensive Definition of Oxidation State, Pure and Applied Chemistry 86 (2014).
Chemistry LibreTexts — Half-Reaction Method.

Redox Equation Balancing by Half-Reactions

The method will appear here

Fundamentals & Explanation

What changes in a redox reaction?

Assigning oxidation states

Ion-electron method in acidic medium

Converting to basic medium

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What changes in a redox reaction?

Assigning oxidation states

Ion-electron method in acidic medium

Converting to basic medium