# c6h5br ra c6h5ona

To balance the equation C6H5Br + NaOH = C6H5ONa + NaBr + H2O 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 C6H5Br + b NaOH = c C6H5ONa + d NaBr + f H2O

### Step 2: Create a System of Equations

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

```C:	6a	+	0b	=	6c	+	0d	+	0f
H:	5a	+	1b	=	5c	+	0d	+	2f
Br:	1a	+	0b	=	0c	+	1d	+	0f
Na:	0a	+	1b	=	1c	+	1d	+	0f
O:	0a	+	1b	=	1c	+	0d	+	1f

```

### Step 3: Solve For All Variables

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

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

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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```[ 6	 0	-6	 0	 0	0]
[ 5	 1	-5	 0	-2	0]
[ 1	 0	 0	-1	 0	0]
[ 0	 1	-1	-1	 0	0]
[ 0	 1	-1	 0	-1	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 = 1 (C6H5Br)
• b = 2 (NaOH)
• c = 1 (C6H5ONa)
• d = 1 (NaBr)
• f = 1 (H2O)

### 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.

C6H5Br + 2 NaOH = C6H5ONa + NaBr + H2O

Reactants Products C 6 6 ✔️ 7 7 ✔️ 1 1 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of C6H5Br + 2NaOH = C6H5ONa + NaBr + H2O, the equation is balanced.