# ch3cooc6h5 + koh

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.

• 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

Reactants Products C 8 8 ✔️ 10 10 ✔️ 4 4 ✔️ 2 2 ✔️

Since there is an equal number of each element in the reactants and products of CH3COOC6H5 + 2KOH = C6H5OK + CH3COOK + H2O, the equation is balanced.