# hcl k2co3

To balance the equation K2CO3 + HCl = H2O + CO2 + KCl 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 tướng represent the unknown coefficients.

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a K2CO3 + b HCl = c H2O + d CO2 + f KCl

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

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

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

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

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

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

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

• a = 1 (K2CO3)
• b = 2 (HCl)
• c = 1 (H2O)
• d = 1 (CO2)
• f = 2 (KCl)

### 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.

K2CO3 + 2 HCl = H2O + CO2 + 2 KCl

Reactants Products K 2 2 ✔️ 1 1 ✔️ 3 3 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of K2CO3 + 2HCl = H2O + CO2 + 2KCl, the equation is balanced.