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The law of conservation of mass dictates the quantity of each element does not change in a chemical reaction. Thus, each side of the chemical equation must represent the same quantity of any particular element. Similarly, the charge is conserved in a chemical reaction. Therefore, the same charge must be present on both sides of the balanced equation.

One balances a chemical equation by changing the scalar number for each chemical formula. Simple chemical equations can be balanced by inspection, that is, by trial and error. Another technique involves solving a system of linear equations.

Ordinarily, balanced equations are written with smallest whole-number coefficients. If there is no coefficient before a chemical formula, the coefficient 1 is understood.

The method of inspection can be outlined as putting a coefficient of 1 in front of the most complex chemical formula and putting the other coefficients before everything else such that both sides of the arrows have the same number of each atom. If any fractional coefficient exist, multiply every coefficient with the smallest number required to make them whole, typically the denominator of the fractional coefficient for a reaction with a single fractional coefficient.

As an example, the burning of methane would be balanced by putting a coefficient of 1 before the CH4:

1 CH4 + O2 CO2 + H2O

Since there is one carbon on each side of the arrow, the first atom (carbon) is balanced.

Looking at the next atom (hydrogen), the right hand side has two atoms, while the left hand side has four. To balance the hydrogens, 2 goes in front of the H2O, which yields:

1 CH4 + O2 CO2 + 2 H2O

Inspection of the last atom to be balanced (oxygen) shows that the right hand side has four atoms, while the left hand side has two. It can be balanced by putting a 2 before O2, giving the balanced equation:

CH4 + 2 O2 CO2 + 2 H2O

This equation does not have any coefficients in front of CH4 and CO2, since a coefficient of 1 is dropped....