# ch3cooh + caco3

To balance the equation CH3COOH + CaCO3 = (CH3COO)2Ca + H2O + CO2 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 CH3COOH + b CaCO3 = c (CH3COO)2Ca + d H2O + f CO2

### Step 2: Create a System of Equations

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

```C:	2a	+	1b	=	4c	+	0d	+	1f
H:	4a	+	0b	=	6c	+	2d	+	0f
O:	2a	+	3b	=	4c	+	1d	+	2f
Ca:	0a	+	1b	=	1c	+	0d	+	0f

```

### Step 3: Solve For All Variables

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

• 2a + 1b - 4c - 1f = 0
• 4a - 6c - 2d = 0
• 2a + 3b - 4c - 1d - 2f = 0
• 1b - 1c = 0

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

Xem thêm: có yolksac bào lâu thì có phôi thai

```[ 2	 1	-4	 0	-1	0]
[ 4	 0	-6	-2	 0	0]
[ 2	 3	-4	-1	-2	0]
[ 0	 1	-1	 0	 0	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.

Xem thêm: các bài luận mẫu

• a = 2 (CH3COOH)
• b = 1 (CaCO3)
• c = 1 ((CH3COO)2Ca)
• d = 1 (H2O)
• f = 1 (CO2)

### 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 CH3COOH + CaCO3 = (CH3COO)2Ca + H2O + CO2

Reactants Products C 5 5 ✔️ 8 8 ✔️ 7 7 ✔️ 1 1 ✔️

Since there is an equal number of each element in the reactants and products of 2CH3COOH + CaCO3 = (CH3COO)2Ca + H2O + CO2, the equation is balanced.