# ch3cho + br2 + h2o

To balance the equation CH3CHO + Br2 + H2O = CH3COOH + HBr 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 vĩ đại represent the unknown coefficients.

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a CH3CHO + b Br2 + c H2O = d CH3COOH + f HBr

### Step 2: Create a System of Equations

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

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

```

### Step 3: Solve For All Variables

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

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

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

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

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

Simplify the result vĩ đại get the lowest, whole integer values.

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• a = 1 (CH3CHO)
• b = 1 (Br2)
• c = 1 (H2O)
• d = 1 (CH3COOH)
• f = 2 (HBr)

### 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.

CH3CHO + Br2 + H2O = CH3COOH + 2 HBr

Reactants Products C 2 2 ✔️ 6 6 ✔️ 2 2 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of CH3CHO + Br2 + H2O = CH3COOH + 2HBr, the equation is balanced.