# c 6 h 6 + br2

To balance the equation C6H6 + Br2 = C6H5Br + HBr 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 lớn represent the unknown coefficients.

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a C6H6 + b Br2 = c C6H5Br + d HBr

### 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:	6a	+	0b	=	6c	+	0d
H:	6a	+	0b	=	5c	+	1d
Br:	0a	+	2b	=	1c	+	1d

```

### Step 3: Solve For All Variables

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

• 6a - 6c = 0
• 6a - 5c - 1d = 0
• 2b - 1c - 1d = 0

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

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```[ 6	 0	-6	 0	0]
[ 6	 0	-5	-1	0]
[ 0	 2	-1	-1	0]
```

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

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

• a = 1 (C6H6)
• b = 1 (Br2)
• c = 1 (C6H5Br)
• d = 1 (HBr)

### 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.

C6H6 + Br2 = C6H5Br + HBr

Reactants Products C 6 6 ✔️ 6 6 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of C6H6 + Br2 = C6H5Br + HBr, the equation is balanced.