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