# baco3 + h2o

To balance the equation BaCO3 + H2O = Ba(OH)2 + H2CO3 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 lớn represent the unknown coefficients.

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a BaCO3 + b H2O = c Ba(OH)2 + d H2CO3

### Step 2: Create a System of Equations

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

```Ba:	1a	+	0b	=	1c	+	0d
C:	1a	+	0b	=	0c	+	1d
O:	3a	+	1b	=	2c	+	3d
H:	0a	+	2b	=	2c	+	2d

```

### Step 3: Solve For All Variables

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

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

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

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

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

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

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• a = 1 (BaCO3)
• b = 2 (H2O)
• c = 1 (Ba(OH)2)
• d = 1 (H2CO3)

### 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.

BaCO3 + 2 H2O = Ba(OH)2 + H2CO3

Reactants Products Ba 1 1 ✔️ 1 1 ✔️ 5 5 ✔️ 4 4 ✔️

Since there is an equal number of each element in the reactants and products of BaCO3 + 2H2O = Ba(OH)2 + H2CO3, the equation is balanced.