# alcl3 + naalo2

To balance the equation NaAlO2 + AlCl3 + H2O = Al(OH)3 + NaCl 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 lớn represent the unknown coefficients.

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a NaAlO2 + b AlCl3 + c H2O = d Al(OH)3 + f NaCl

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

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

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

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

Xem thêm: fes + h2 so4

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

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

Simplify the result lớn get the lowest, whole integer values.

Xem thêm: soạn bài ca huế lớp 7

• a = 3 (NaAlO2)
• b = 1 (AlCl3)
• c = 6 (H2O)
• d = 4 (Al(OH)3)
• f = 3 (NaCl)

### 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 NaAlO2 + AlCl3 + 6 H2O = 4 Al(OH)3 + 3 NaCl

Reactants Products Na 3 3 ✔️ 4 4 ✔️ 12 12 ✔️ 3 3 ✔️ 12 12 ✔️

Since there is an equal number of each element in the reactants and products of 3NaAlO2 + AlCl3 + 6H2O = 4Al(OH)3 + 3NaCl, the equation is balanced.