# fe3o4 + naoh

To balance the equation Fe3O4 + NaOH = Fe(OH)2 + Fe(OH)3 + Na2O 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 Fe3O4 + b NaOH = c Fe(OH)2 + d Fe(OH)3 + f Na2O

### Step 2: Create a System of Equations

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

```Fe:	3a	+	0b	=	1c	+	1d	+	0f
O:	4a	+	1b	=	2c	+	3d	+	1f
Na:	0a	+	1b	=	0c	+	0d	+	2f
H:	0a	+	1b	=	2c	+	3d	+	0f

```

### Step 3: Solve For All Variables

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

• 3a - 1c - 1d = 0
• 4a + 1b - 2c - 3d - 1f = 0
• 1b - 2f = 0
• 1b - 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:

```[ 3	 0	-1	-1	 0	0]
[ 4	 1	-2	-3	-1	0]
[ 0	 1	 0	 0	-2	0]
[ 0	 1	-2	-3	 0	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.

Xem thêm: tiếng anh 8 tập 1

• a = 1 (Fe3O4)
• b = 8 (NaOH)
• c = 1 (Fe(OH)2)
• d = 2 (Fe(OH)3)
• f = 4 (Na2O)

### 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.

Fe3O4 + 8 NaOH = Fe(OH)2 + 2 Fe(OH)3 + 4 Na2O

Reactants Products Fe 3 3 ✔️ 12 12 ✔️ 8 8 ✔️ 8 8 ✔️

Since there is an equal number of each element in the reactants and products of Fe3O4 + 8NaOH = Fe(OH)2 + 2Fe(OH)3 + 4Na2O, the equation is balanced.