# feso4 ra fe oh 2

To balance the equation FeSO4 + NaOH = Fe(OH)2 + Na2SO4 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 FeSO4 + b NaOH = c Fe(OH)2 + d Na2SO4

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

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

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

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

• a = 1 (FeSO4)
• b = 2 (NaOH)
• c = 1 (Fe(OH)2)
• d = 1 (Na2SO4)

### 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.

FeSO4 + 2 NaOH = Fe(OH)2 + Na2SO4

Reactants Products Fe 1 1 ✔️ 1 1 ✔️ 6 6 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of FeSO4 + 2NaOH = Fe(OH)2 + Na2SO4, the equation is balanced.