# alcl3 ra naalo2

To balance the equation AlCl3 + NaOH = NaAlO2 + NaCl + 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 đồ sộ represent the unknown coefficients.

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a AlCl3 + b NaOH = c NaAlO2 + d NaCl + f H2O

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

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

• 1a - 1c = 0
• 3a - 1d = 0
• 1b - 1c - 1d = 0
• 1b - 2c - 1f = 0
• 1b - 2f = 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	0]
[ 3	 0	 0	-1	 0	0]
[ 0	 1	-1	-1	 0	0]
[ 0	 1	-2	 0	-1	0]
[ 0	 1	 0	 0	-2	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.

Xem thêm: nh3 + nacl

• a = 1 (AlCl3)
• b = 4 (NaOH)
• c = 1 (NaAlO2)
• d = 3 (NaCl)
• f = 2 (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.

AlCl3 + 4 NaOH = NaAlO2 + 3 NaCl + 2 H2O

Reactants Products Al 1 1 ✔️ 3 3 ✔️ 4 4 ✔️ 4 4 ✔️ 4 4 ✔️

Since there is an equal number of each element in the reactants and products of AlCl3 + 4NaOH = NaAlO2 + 3NaCl + 2H2O, the equation is balanced.