# fe oh 2 ra fe oh 3

To balance the equation Fe(OH)2 + O2 + H2O = Fe(OH)3 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 tát represent the unknown coefficients.

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a Fe(OH)2 + b O2 + c H2O = d Fe(OH)3

### Step 2: Create a System of Equations

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

```Fe:	1a	+	0b	+	0c	=	1d
O:	2a	+	2b	+	1c	=	3d
H:	2a	+	0b	+	2c	=	3d

```

### Step 3: Solve For All Variables

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

• 1a - 1d = 0
• 2a + 2b + 1c - 3d = 0
• 2a + 2c - 3d = 0

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

```[ 1	 0	 0	-1	0]
[ 2	 2	 1	-3	0]
[ 2	 0	 2	-3	0]
```

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

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

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• a = 4 (Fe(OH)2)
• b = 1 (O2)
• c = 2 (H2O)
• d = 4 (Fe(OH)3)

### 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.

4 Fe(OH)2 + O2 + 2 H2O = 4 Fe(OH)3

Reactants Products Fe 4 4 ✔️ 12 12 ✔️ 12 12 ✔️

Since there is an equal number of each element in the reactants and products of 4Fe(OH)2 + O2 + 2H2O = 4Fe(OH)3, the equation is balanced.