# fecl3+naoh

To balance the equation NaOH + FeCl3 = NaCl + 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 vĩ đại represent the unknown coefficients.

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a NaOH + b FeCl3 = c NaCl + d Fe(OH)3

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.

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

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

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

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

Simplify the result vĩ đại get the lowest, whole integer values.

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• a = 3 (NaOH)
• b = 1 (FeCl3)
• c = 3 (NaCl)
• d = 1 (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.

3 NaOH + FeCl3 = 3 NaCl + Fe(OH)3

Reactants Products Na 3 3 ✔️ 3 3 ✔️ 3 3 ✔️ 1 1 ✔️ 3 3 ✔️

Since there is an equal number of each element in the reactants and products of 3NaOH + FeCl3 = 3NaCl + Fe(OH)3, the equation is balanced.