c2h2 c6h6

To balance the equation C2H2 = C6H6 using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable to tướng represent the unknown coefficients.

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a C2H2 = b C6H6

Step 2: Create a System of Equations

Create an equation for each element (C, H) where each term represents the number of atoms of the element in each reactant or product.

C:	2a	=	6b
H:	2a	=	6b

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator to tướng solve for each variable.

Use your graphing calculator's rref() function (or an online rref calculator) to tướng convert the following matrix into reduced row-echelon-form:

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[ 2	-6	0]
[ 2	-6	0]

The resulting matrix can be used to tướng determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result to tướng get the lowest, whole integer values.

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  • a = 3 (C2H2)
  • b = 1 (C6H6)

Step 4: Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

3 C2H2 = C6H6

Reactants Products

Since there is an equal number of each element in the reactants and products of 3C2H2 = C6H6, the equation is balanced.