CH3CHO + Br2 + H2O = CH3COOH + HBr - Chemical Equation Balancer

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:

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[ 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