c6h5 ch ch2 br2

To balance the equation C6H5CHCH2 + Br2 = C6H5CHBrCH2Br 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 đồ sộ represent the unknown coefficients.

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a C6H5CHCH2 + b Br2 = c C6H5CHBrCH2Br

Step 2: Create a System of Equations

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

C:	8a	+	0b	=	8c
H:	8a	+	0b	=	8c
Br:	0a	+	2b	=	2c

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.

  • 8a - 8c = 0
  • 8a - 8c = 0
  • 2b - 2c = 0

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

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[ 8	 0	-8	0]
[ 8	 0	-8	0]
[ 0	 2	-2	0]

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

Simplify the result đồ sộ get the lowest, whole integer values.

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  • a = 1 (C6H5CHCH2)
  • b = 1 (Br2)
  • c = 1 (C6H5CHBrCH2Br)

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.

C6H5CHCH2 + Br2 = C6H5CHBrCH2Br

Reactants Products

Since there is an equal number of each element in the reactants and products of C6H5CHCH2 + Br2 = C6H5CHBrCH2Br, the equation is balanced.