using Gauss elimination method

This calculator uses the Gaussian elimination method to determine the stoichiometric coefficients of a chemical equation. Gaussian elimination (also known as row reduction) is a numerical method for solving a system of linear equations. The method is named after the German mathematician Carl Friedrich Gauss (1777-1855).

Every chemical equations must be balanced. What does it mean to be balanced? It means that the law of conservation of mass is obeyed. The law of conservation of mass states that in an ordinary chemical reaction, matter is neither created nor destroyed, that is, a chemical equation must have the same number of atoms of each element on both sides of the equation.

Write an unbalanced chemical equation in the input field using following rules and click 'Balance' (for example: ca3(po4)2(s) + h2so4(aq) = h3po4(aq) + caso4(s) ).

- A valid equation must have the same elements on both sides of the equation
- Spaces are irrelevant, for example ag no3 is equal agno3
- All types of parentheses are correct, for example Na2Zn3[Fe(CN)6]2*9H2O
- To enter charge species, just type them as they are (Al3+, NH4+, SO42-) or explicit declare (Hg2^2+)
- To enter the equation sign, you can use either "=" or "-->" or "→" symbols.
- The equation can be written in lowercase letters. If the elements in a chemical formula are properly capitalized, the smart case converter leaves them as you have typed.
- To indicate the physical states you can use (s) for solid, (l) for liquids, (g) for gases, and (aq) for substances dissolved in water.

*Non-redox reactions*

*"Redox Challenges: Good Times for Puzzle Fanatics"* (R. Stout, *J. Chem. Educ.* 1995, **72**, p.1125)

Two problems can occur when balancing redox reactions with mathematical methods:

1. Balancing equations of redox reactions by inspection or with a mathematical method (such as Gauss's elimination method) can create results that are mathematically accurate, but not chemically. This is because equations of redox reactions must also satisfy the electron balance, i.e. the number of electrons released in the oxidation reaction must be equal to the number of electrons recieved in the reduction reaction.

*Oxidation number change method*

*Gauss elimination method*

2. Redox equations are often written in such a way that water and its ions are left out. H_{2}O, H^{+} or OH^{-} (depending on the medium) can be added as necessary since its assumed the reaction occurs in water. Contrary to that, the mathematical method requires that all species participating in the reaction are explicitly stated.

*Oxidation number change method*

*Gauss elimination method*

Citing this page:

Generalic, Eni. "Balancing chemical equations." *EniG. Periodic Table of the Elements*. KTF-Split, 25 Jan. 2022. Web. {Date of access}. <https://www.periodni.com/balancing_chemical_equations.php>.

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