CH3COOC6H5 + KOH = C6H5OK + CH3COOK + H2O - Chemical Equation Balancer

To balance the equation CH3COOC6H5 + KOH = C6H5OK + CH3COOK + H2O 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 đồ sộ represent the unknown coefficients.

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a CH₃COOC₆H₅ + b KOH = c C₆H₅OK + d CH₃COOK + f H₂O

Step 2: Create a System of Equations

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

C:	8a	+	0b	=	6c	+	2d	+	0f
H:	8a	+	1b	=	5c	+	3d	+	2f
O:	2a	+	1b	=	1c	+	2d	+	1f
K:	0a	+	1b	=	1c	+	1d	+	0f

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator đồ sộ solve for each variable.

8a - 6c - 2d = 0
8a + 1b - 5c - 3d - 2f = 0
2a + 1b - 1c - 2d - 1f = 0
1b - 1c - 1d = 0

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

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[ 8	 0	-6	-2	 0	0]
[ 8	 1	-5	-3	-2	0]
[ 2	 1	-1	-2	-1	0]
[ 0	 1	-1	-1	 0	0]

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

Simplify the result đồ sộ get the lowest, whole integer values.

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a = 1 (CH3COOC6H5)
b = 2 (KOH)
c = 1 (C6H5OK)
d = 1 (CH3COOK)
f = 1 (H2O)

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.

CH₃COOC₆H₅ + 2 KOH = C₆H₅OK + CH₃COOK + H₂O