# al baoh2 h2o

To balance the equation Al + Ba(OH)2 + H2O = Ba(AlO2)2 + H2 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 Al + b Ba(OH)2 + c H2O = d Ba(AlO2)2 + f H2

### Step 2: Create a System of Equations

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

```Al:	1a	+	0b	+	0c	=	2d	+	0f
Ba:	0a	+	1b	+	0c	=	1d	+	0f
O:	0a	+	2b	+	1c	=	4d	+	0f
H:	0a	+	2b	+	2c	=	0d	+	2f

```

### Step 3: Solve For All Variables

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

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

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

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

• a = 2 (Al)
• b = 1 (Ba(OH)2)
• c = 2 (H2O)
• d = 1 (Ba(AlO2)2)
• f = 3 (H2)

### 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.

2 Al + Ba(OH)2 + 2 H2O = Ba(AlO2)2 + 3 H2

Reactants Products Al 2 2 ✔️ 1 1 ✔️ 4 4 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of 2Al + Ba(OH)2 + 2H2O = Ba(AlO2)2 + 3H2, the equation is balanced.